Automorphism Classes of Quadilateral Actions on Sufaces of Genus 11 

 
bdata: 11,120, [ 2, 2, 2, 3 ] 
G = small group 35 of 47 group(s) of order 120 
Permutation group G acting on a set of cardinality 7
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 5, 4)
(1, 3)(2, 4)(6, 7) 
27 generating vector(s)
<<(1, 5)(3, 4), (1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (2, 5, 4)>, <false, true, true>> 
<<(1, 5)(3, 4), (1, 3)(2, 4)(6, 7), (2, 4)(3, 5)(6, 7), (1, 4, 3)>, <false, true, false>> 
<<(1, 5)(3, 4), (1, 3)(2, 4)(6, 7), (1, 4)(2, 3)(6, 7), (1, 2, 5)>, <true, true, false>> 
<<(1, 5)(3, 4), (1, 3)(2, 4)(6, 7), (1, 4)(3, 5)(6, 7), (1, 2, 3)>, <false, false, false>> 
<<(1, 5)(3, 4), (1, 3)(2, 4)(6, 7), (1, 5)(2, 4)(6, 7), (3, 5, 4)>, <false, false, false>> 
<<(1, 5)(3, 4), (1, 5)(2, 3)(6, 7), (2, 4)(3, 5)(6, 7), (2, 3, 5)>, <false, false, true>> 
<<(1, 5)(3, 4), (1, 5)(2, 3)(6, 7), (1, 4)(2, 3)(6, 7), (1, 3, 4)>, <true, false, false>> 
<<(1, 5)(3, 4), (1, 5)(2, 3)(6, 7), (1, 2)(3, 4)(6, 7), (1, 4, 2)>, <false, false, false>> 
<<(1, 5)(3, 4), (1, 3)(4, 5)(6, 7), (2, 4)(3, 5)(6, 7), (1, 4, 2)>, <true, false, true>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 5), (1, 2)(3, 4)(6, 7), (1, 5, 4)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 5), (1, 2)(4, 5)(6, 7), (1, 5, 3)>, <true, true, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 5), (2, 5)(3, 4)(6, 7), (1, 2, 4)>, <false, true, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 5), (1, 3)(4, 5)(6, 7), (2, 5, 3)>, <false, true, true>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 5), (1, 3)(2, 5)(6, 7), (2, 4, 3)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (2, 4)(3, 5), (1, 5, 4)>, <false, true, true>> 
<<(1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (1, 2)(3, 4), (2, 5, 3)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (1, 5)(2, 4), (1, 3, 4)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (1, 5)(3, 4), (1, 3, 2)>, <false, true, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 5)(2, 3)(6, 7), (1, 2)(3, 5), (2, 5, 4)>, <true, true, false>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5)(6, 7), (1, 5)(2, 3), (2, 5, 3)>, <false, false, true>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5)(6, 7), (1, 4)(3, 5), (1, 4, 3)>, <true, false, false>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5)(6, 7), (1, 3)(4, 5), (1, 5, 4)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5), (1, 5)(2, 3)(6, 7), (2, 5, 3)>, <false, false, true>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5), (1, 4)(3, 5)(6, 7), (1, 4, 3)>, <true, false, false>> 
<<(1, 3)(2, 4)(6, 7), (2, 4)(3, 5), (1, 3)(4, 5)(6, 7), (1, 5, 4)>, <false, false, false>> 
<<(1, 3)(2, 4)(6, 7), (1, 4)(2, 3)(6, 7), (2, 5)(3, 4), (1, 2, 5)>, <true, false, true>> 
<<(1, 3)(2, 4)(6, 7), (1, 2)(3, 4), (1, 5)(2, 3)(6, 7), (1, 5, 4)>, <true, false, true>> 

 
bdata: 11, 80, [ 2, 2, 2, 4 ] 
G = small group 39 of 52 group(s) of order 80 
GrpPC : G of order 80 = 2^4 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^2 = Id(G), 
G.5^5 = Id(G), 
G.3^G.2 = G.3 * G.4, 
G.5^G.1 = G.5^4 
18 generating vector(s)
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.4, G.1 * G.2 * G.3 * G.5^2>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.4 * G.5^3, G.1 * G.2 * G.3>, <true, true, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.2 * G.3 * G.5^4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.5^4, G.1 * G.2 * G.3 * G.4 * G.5>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.5, G.1 * G.2 * G.3 * G.4 * G.5^3>, <false, true, true>> 
<<G.1, G.1 * G.3, G.1 * G.2 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.4 * G.5^3>, <true, false, true>> 
<<G.1 * G.3, G.1 * G.5^3, G.1 * G.2 * G.4, G.1 * G.2 * G.3 * G.4 * G.5^2>, <false, false, false>> 
<<G.1 * G.3, G.1 * G.5^3, G.1 * G.2 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.4>, <true, true, false>> 
<<G.1 * G.3, G.1 * G.5^3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.2 * G.3 * G.4 * G.5^4>, <false, false, false>> 
<<G.1 * G.3, G.1 * G.5^3, G.1 * G.2 * G.5^4, G.1 * G.2 * G.3 * G.5>, <false, false, false>> 
<<G.1 * G.3, G.1 * G.5^3, G.1 * G.2 * G.5, G.1 * G.2 * G.3 * G.5^3>, <false, true, true>> 
<<G.1 * G.3, G.1 * G.4, G.1 * G.2 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.5^3>, <true, false, true>> 
<<G.1 * G.3, G.1 * G.2 * G.4, G.1 * G.5^4, G.1 * G.2 * G.3 * G.4 * G.5^4>, <true, false, true>> 
<<G.1 * G.3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.5^4, G.1 * G.2 * G.3 * G.4 * G.5^2>, <false, true, true>> 
<<G.1 * G.3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.5, G.1 * G.2 * G.3 * G.4 * G.5^4>, <false, false, false>> 
<<G.1 * G.3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.5^3, G.1 * G.2 * G.3 * G.4 * G.5>, <false, false, false>> 
<<G.1 * G.3, G.1 * G.2 * G.4 * G.5^2, G.1 * G.5^2, G.1 * G.2 * G.3 * G.4>, <true, true, false>> 
<<G.1 * G.3, G.1 * G.2 * G.4 * G.5^2, G.1, G.1 * G.2 * G.3 * G.4 * G.5^3>, <false, false, false>> 

 
bdata: 11, 80, [ 2, 2, 2, 4 ] 
G = small group 42 of 52 group(s) of order 80 
GrpPC : G of order 80 = 2^4 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.5^5 = Id(G), 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.5^G.1 = G.5^4 
6  generating vector(s)
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.3, G.1 * G.2 * G.4 * G.5^2>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.5, G.1 * G.2 * G.4 * G.5^3>, <false, true, true>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.5^2, G.1 * G.2 * G.4 * G.5^4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.5^4, G.1 * G.2 * G.4 * G.5>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4 * G.5^3, G.1 * G.2 * G.3 * G.4 * G.5^3, G.1 * G.2>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3 * G.4 * G.5^2, G.1 * G.2 * G.5^2>, <true, false, true>> 

 
bdata: 11, 60, [ 2, 2, 2, 6 ] 
G = small group 8 of 13 group(s) of order 60 
GrpPC : G of order 60 = 2^2 * 3 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^3 = Id(G), 
G.4^5 = Id(G), 
G.3^G.2 = G.3^2, 
G.4^G.1 = G.4^4 
18 generating vector(s)
<<G.1, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3^2, G.1 * G.3 * G.4^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3 * G.4, G.1 * G.3^2 * G.4^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3^2 * G.4^3, G.1 * G.3 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3 * G.4^4, G.1 * G.3^2 * G.4^2>, <false, true, true>> 
<<G.1, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3^2 * G.4^2, G.1 * G.3>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.4^2, G.1 * G.3 * G.4^2>, <true, false, true>> 
<<G.1 * G.2, G.1 * G.4^3, G.1 * G.2 * G.3^2, G.1 * G.3 * G.4^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.4^3, G.1 * G.2 * G.3 * G.4, G.1 * G.3^2 * G.4^3>, <false, true, true>> 
<<G.1 * G.2, G.1 * G.4^3, G.1 * G.2 * G.3^2 * G.4^3, G.1 * G.3>, <true, true, false>> 
<<G.1 * G.2, G.1 * G.4^3, G.1 * G.2 * G.3 * G.4^4, G.1 * G.3^2 * G.4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.4^3, G.1 * G.2 * G.3^2 * G.4^2, G.1 * G.3 * G.4^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3^2, G.1 * G.4^2, G.1 * G.3 * G.4^2>, <true, false, true>> 
<<G.1 * G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.4^2, G.1 * G.3^2 * G.4>, <false, true, true>> 
<<G.1 * G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.4, G.1 * G.3^2>, <true, true, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3 * G.4, G.1, G.1 * G.3^2 * G.4^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.4^3, G.1 * G.3^2 * G.4^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.4^4, G.1 * G.3^2 * G.4^3>, <false, false, false>> 
<<G.1 * G.2, G.1, G.1 * G.2 * G.3 * G.4, G.1 * G.3^2 * G.4>, <true, false, true>> 

 
bdata: 11, 48, [ 2, 2, 2, 12 ] 
G = small group 36 of 52 group(s) of order 48 
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.5^3 = Id(G), 
G.3^G.1 = G.3 * G.4, 
G.5^G.1 = G.5^2 
3  generating vector(s)
<<G.2, G.1 * G.3 * G.5^2, G.1 * G.5, G.2 * G.3 * G.5>, <true, true, true>> 
<<G.1, G.1 * G.3 * G.5^2, G.2, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.1, G.2 * G.4, G.1 * G.3 * G.4 * G.5^2, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 

 
bdata: 11, 48, [ 2, 2, 2, 12 ] 
G = small group 37 of 52 group(s) of order 48 
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.4, 
G.3^2 = Id(G), 
G.4^2 = Id(G), 
G.5^3 = Id(G), 
G.3^G.1 = G.3 * G.4, 
G.5^G.1 = G.5^2 
3  generating vector(s)
<<G.3, G.1 * G.4, G.1 * G.2 * G.3 * G.5^2, G.2 * G.5>, <true, true, true>> 
<<G.1, G.1 * G.2 * G.3 * G.5^2, G.3 * G.4, G.2 * G.5>, <true, true, true>> 
<<G.1, G.3 * G.4, G.1 * G.2 * G.3 * G.5^2, G.2 * G.4 * G.5>, <true, true, true>> 

 
bdata: 11, 48, [ 2, 2, 2, 12 ] 
G = small group 38 of 52 group(s) of order 48 
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^2 = Id(G), 
G.5^3 = Id(G), 
G.3^G.2 = G.3 * G.4, 
G.5^G.1 = G.5^2 
6  generating vector(s)
<<G.3, G.1 * G.5^2, G.1 * G.2 * G.4 * G.5, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.3, G.1 * G.2 * G.4, G.1 * G.5, G.2 * G.3 * G.4 * G.5^2>, <true, true, true>> 
<<G.1, G.1 * G.3 * G.5^2, G.2 * G.4, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.1, G.2 * G.4, G.1 * G.3 * G.4 * G.5^2, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.1 * G.3, G.1 * G.5^2, G.2 * G.4, G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.1 * G.3, G.2 * G.4, G.1 * G.5, G.2 * G.3 * G.4 * G.5^2>, <true, true, true>> 

 
bdata: 11, 44, [ 2, 2, 2, 22 ] 
G = small group 3 of 4 group(s) of order 44 
GrpPC : G of order 44 = 2^2 * 11
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^11 = Id(G), 
G.3^G.1 = G.3^10 
3  generating vector(s)
<<G.2, G.1 * G.2 * G.3^5, G.1 * G.2 * G.3^3, G.2 * G.3^2>, <true, true, true>> 
<<G.1, G.2, G.1 * G.3^2, G.2 * G.3^9>, <true, true, true>> 
<<G.1, G.1 * G.3^6, G.2, G.2 * G.3^5>, <true, true, true>> 

 
bdata: 11, 60, [ 2, 2, 3, 3 ] 
G = small group 5 of 13 group(s) of order 60 
Permutation group G acting on a set of cardinality 5
Order = 60 = 2^2 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2, 3) 
9  generating vector(s)
<<(1, 2)(3, 4), (2, 4)(3, 5), (1, 2, 4), (3, 5, 4)>, <true, true, false>> 
<<(1, 2)(3, 4), (2, 4)(3, 5), (1, 2, 3), (1, 5, 4)>, <false, false, false>> 
<<(1, 2)(3, 4), (2, 4)(3, 5), (3, 5, 4), (1, 2, 3)>, <false, false, false>> 
<<(1, 2)(3, 4), (2, 4)(3, 5), (2, 3, 5), (1, 2, 4)>, <false, true, true>> 
<<(1, 2)(3, 4), (2, 4)(3, 5), (1, 5, 4), (2, 3, 5)>, <false, false, false>> 
<<(1, 2)(3, 4), (1, 2)(3, 4), (2, 5, 3), (2, 3, 5)>, <true, false, true>> 
<<(1, 2)(3, 4), (1, 5)(3, 4), (1, 3, 2), (2, 3, 5)>, <false, true, false>> 
<<(1, 2)(3, 4), (1, 5)(3, 4), (1, 5, 3), (1, 3, 2)>, <true, false, false>> 
<<(1, 2)(3, 4), (1, 5)(3, 4), (2, 3, 5), (1, 5, 3)>, <false, false, true>> 

 
bdata: 11, 48, [ 2, 2, 3, 4 ] 
G = small group 29 of 52 group(s) of order 48 
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = Id(G), 
G.3^2 = G.5, 
G.4^2 = G.5, 
G.5^2 = Id(G), 
G.2^G.1 = G.2^2, 
G.3^G.1 = G.4, 
G.3^G.2 = G.4 * G.5, 
G.4^G.1 = G.3, 
G.4^G.2 = G.3 * G.4, 
G.4^G.3 = G.4 * G.5 
6  generating vector(s)
<<G.1, G.1 * G.2 * G.4, G.2^2 * G.3 * G.4, G.4 * G.5>, <false, false, true>> 
<<G.1, G.1 * G.2 * G.4, G.2^2, G.3>, <false, true, false>> 
<<G.1, G.1 * G.2 * G.4, G.2^2 * G.4, G.3 * G.4>, <true, false, false>> 
<<G.1, G.1 * G.2^2, G.2 * G.3, G.3 * G.5>, <false, false, true>> 
<<G.1, G.1 * G.2^2, G.2 * G.3 * G.4 * G.5, G.3 * G.4>, <true, false, false>> 
<<G.1, G.1 * G.2^2, G.2 * G.4 * G.5, G.4>, <false, true, false>> 

 
bdata: 11, 48, [ 2, 2, 3, 4 ] 
G = small group 48 of 52 group(s) of order 48 
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^3 = Id(G), 
G.4^2 = Id(G), 
G.5^2 = Id(G), 
G.3^G.1 = G.3^2, 
G.4^G.1 = G.5, 
G.4^G.3 = G.5, 
G.5^G.1 = G.4, 
G.5^G.3 = G.4 * G.5 
8  generating vector(s)
<<G.2, G.1 * G.4 * G.5, G.3 * G.5, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.2 * G.4, G.1 * G.4 * G.5, G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.4 * G.5>, <true, false, false>> 
<<G.2 * G.4, G.1 * G.4 * G.5, G.3^2, G.1 * G.2 * G.3^2 * G.5>, <true, true, false>> 
<<G.2 * G.4, G.1 * G.3^2 * G.4, G.3^2 * G.4 * G.5, G.1 * G.2 * G.3 * G.4>, <true, false, true>> 
<<G.1, G.2, G.3^2 * G.4 * G.5, G.1 * G.2 * G.3^2 * G.5>, <true, true, true>> 
<<G.1, G.2 * G.4, G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.4 * G.5>, <false, false, true>> 
<<G.1, G.2 * G.4, G.3^2, G.1 * G.2 * G.3^2 * G.5>, <false, true, true>> 
<<G.1, G.2 * G.4 * G.5, G.3 * G.5, G.1 * G.2 * G.3 * G.4>, <true, false, true>> 

 
bdata: 11, 40, [ 2, 2, 4, 4 ] 
G = small group 5 of 14 group(s) of order 40 
GrpPC : G of order 40 = 2^3 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.3, 
G.3^2 = Id(G), 
G.4^5 = Id(G), 
G.4^G.1 = G.4^4 
12 generating vector(s)
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4, G.1 * G.2 * G.4^4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^3, G.1 * G.2 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^2, G.1 * G.2>, <true, true, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^4, G.1 * G.2 * G.4^2>, <false, true, true>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2, G.1 * G.2 * G.4^3>, <false, false, false>> 
<<G.1, G.1, G.1 * G.2 * G.4, G.1 * G.2 * G.3 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4^3, G.1 * G.2 * G.3 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3>, <true, true, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4^4, G.1 * G.2 * G.3 * G.4^2>, <false, true, true>> 
<<G.1, G.1 * G.4^2, G.1 * G.2, G.1 * G.2 * G.3 * G.4^3>, <false, false, false>> 
<<G.1, G.1 * G.3, G.1 * G.2 * G.4, G.1 * G.2 * G.4>, <true, false, true>> 

 
bdata: 11, 40, [ 2, 2, 4, 4 ] 
G = small group 8 of 14 group(s) of order 40 
GrpPC : G of order 40 = 2^3 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^5 = Id(G), 
G.2^G.1 = G.2 * G.3, 
G.4^G.1 = G.4^4 
12 generating vector(s)
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.3, G.1 * G.2 * G.3 * G.4^3>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.3 * G.4^3, G.1 * G.2 * G.3 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^2, G.1 * G.2>, <true, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4, G.1 * G.2 * G.4^4>, <false, false, false>> 
<<G.1, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^4, G.1 * G.2 * G.4^2>, <false, false, true>> 
<<G.1, G.1, G.1 * G.2 * G.3 * G.4^3, G.1 * G.2 * G.4^3>, <true, false, true>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.3, G.1 * G.2 * G.4^3>, <false, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.3 * G.4^3, G.1 * G.2 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4^2, G.1 * G.2 * G.3>, <true, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.1, G.1 * G.4^2, G.1 * G.2 * G.4^4, G.1 * G.2 * G.3 * G.4^2>, <false, false, true>> 
<<G.1, G.1 * G.3, G.1 * G.2 * G.3 * G.4^3, G.1 * G.2 * G.3 * G.4^3>, <true, false, true>> 

 
bdata: 11, 40, [ 2, 2, 4, 4 ] 
G = small group 12 of 14 group(s) of order 40 
GrpPC : G of order 40 = 2^3 * 5
PC-Relations:
G.1^2 = G.3, 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^5 = Id(G), 
G.4^G.1 = G.4^2, 
G.4^G.3 = G.4^4 
44 generating vector(s)
<<G.2, G.3 * G.4^3, G.1 * G.4^2, G.1 * G.2 * G.4^4>, <false, false, false>> 
<<G.2, G.3 * G.4^3, G.1 * G.3 * G.4, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.2, G.2 * G.3 * G.4^3, G.1 * G.4^2, G.1 * G.4^4>, <false, false, false>> 
<<G.2, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4, G.1 * G.3>, <false, false, false>> 
<<G.3, G.2, G.1 * G.4^2, G.1 * G.2 * G.4>, <false, false, false>> 
<<G.3, G.2, G.1 * G.3 * G.4, G.1 * G.2 * G.3 * G.4^2>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.4^2, G.1 * G.2 * G.3 * G.4>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.4, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1, G.1 * G.2 * G.3 * G.4^2>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.4^3, G.1 * G.2 * G.3 * G.4^3>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.4^4, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4, G.1 * G.2>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^4, G.1 * G.2 * G.4^4>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^3>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.3, G.1 * G.2 * G.4^2>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^3, G.1 * G.2 * G.4>, <false, false, false>> 
<<G.3, G.2 * G.3, G.1 * G.4^2, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.3, G.2 * G.3, G.1 * G.3 * G.4, G.1 * G.2 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.2, G.1 * G.4^2, G.1 * G.4>, <false, false, false>> 
<<G.2 * G.3, G.2, G.1 * G.3 * G.4, G.1 * G.3 * G.4^2>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.4^2, G.1 * G.2 * G.3 * G.4>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.4, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1, G.1 * G.2 * G.3 * G.4^2>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.4^3, G.1 * G.2 * G.3 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.4^4, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.3 * G.4, G.1 * G.2>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.3 * G.4^4, G.1 * G.2 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.3 * G.4^2, G.1 * G.2 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.3, G.1 * G.2 * G.4^2>, <false, false, false>> 
<<G.2 * G.3, G.3 * G.4^3, G.1 * G.3 * G.4^3, G.1 * G.2 * G.4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.4^2, G.1 * G.3 * G.4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.4, G.1 * G.3 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1, G.1 * G.3 * G.4^2>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.4^3, G.1 * G.3 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.4^4, G.1 * G.3>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4, G.1>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^4, G.1 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^2, G.1 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.3, G.1 * G.4^2>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3 * G.4^3, G.1 * G.3 * G.4^3, G.1 * G.4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3, G.1 * G.4^2, G.1 * G.3 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.2 * G.3, G.1 * G.3 * G.4, G.1 * G.4^3>, <false, false, false>> 
<<G.2 * G.3, G.3, G.1 * G.4^2, G.1 * G.2 * G.3 * G.4^4>, <false, false, false>> 
<<G.2 * G.3, G.3, G.1 * G.3 * G.4, G.1 * G.2 * G.4^3>, <false, false, false>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 9 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
6  generating vector(s)
<<G.4, G.2 * G.4, G.1 * G.5, G.1 * G.2 * G.4 * G.5>, <true, true, true>> 
<<G.5, G.2 * G.4, G.1 * G.5, G.1 * G.2>, <true, true, true>> 
<<G.4 * G.5, G.2 * G.4, G.1 * G.5, G.1 * G.2 * G.4>, <true, true, true>> 
<<G.2, G.4, G.1 * G.5, G.1 * G.2 * G.5>, <true, true, true>> 
<<G.2, G.4 * G.5, G.1 * G.5, G.1 * G.2>, <true, true, true>> 
<<G.2, G.5, G.1 * G.5, G.1 * G.2 * G.4>, <true, true, true>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 11 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
6  generating vector(s)
<<G.5, G.2 * G.3, G.1 * G.2 * G.3, G.1 * G.3 * G.4>, <true, true, true>> 
<<G.3 * G.4, G.2 * G.3, G.1 * G.2 * G.3, G.1 * G.5>, <false, true, true>> 
<<G.3 * G.4, G.2 * G.3, G.1 * G.2, G.1 * G.3>, <false, true, true>> 
<<G.2, G.5, G.1 * G.2 * G.3, G.1 * G.4>, <true, true, true>> 
<<G.2, G.3 * G.4 * G.5, G.1 * G.2 * G.3, G.1 * G.3>, <true, true, false>> 
<<G.2, G.3 * G.4 * G.5, G.1 * G.2, G.1>, <true, true, false>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 39 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
<<G.2, G.1 * G.4, G.3 * G.4 * G.5, G.1 * G.2 * G.3>, <true, true, true>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 40 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
2  generating vector(s)
<<G.3, G.2 * G.4, G.1 * G.5, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.2, G.3, G.1 * G.5, G.1 * G.2 * G.3>, <true, true, true>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 42 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.3^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
3  generating vector(s)
<<G.3 * G.4, G.1 * G.4 * G.5, G.2 * G.3 * G.4, G.1 * G.2>, <true, true, true>> 
<<G.2, G.1 * G.4 * G.5, G.3, G.1 * G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.2, G.3 * G.4 * G.5, G.1 * G.3 * G.5, G.1 * G.2 * G.4 * G.5>, <true, true, true>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 43 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.4, 
G.3^G.1 = G.3 * G.5, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
4  generating vector(s)
<<G.3, G.2 * G.4, G.1 * G.3 * G.5, G.1 * G.2 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.4, G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.5>, <true, true, true>> 
<<G.2, G.3 * G.5, G.1 * G.3 * G.5, G.1 * G.2 * G.5>, <true, true, true>> 
<<G.1, G.2 * G.4, G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.4 * G.5>, <true, true, true>> 

 
bdata: 11, 32, [ 2, 2, 4, 8 ] 
G = small group 44 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.2^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.4, 
G.3^G.1 = G.3 * G.5, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
2  generating vector(s)
<<G.3, G.1 * G.5, G.2 * G.4 * G.5, G.1 * G.2 * G.3 * G.5>, <true, true, true>> 
<<G.1, G.3 * G.5, G.2 * G.4 * G.5, G.1 * G.2 * G.3>, <true, true, true>> 

 
bdata: 11, 30, [ 2, 2, 6, 6 ] 
G = small group 2 of 4 group(s) of order 30 
GrpPC : G of order 30 = 2 * 3 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = Id(G), 
G.3^5 = Id(G), 
G.3^G.1 = G.3^4 
6  generating vector(s)
<<G.1, G.1, G.1 * G.2 * G.3, G.1 * G.2^2 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.3^3, G.1 * G.2, G.1 * G.2^2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3, G.1 * G.2^2 * G.3^3>, <false, true, true>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^2, G.1 * G.2^2 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^3, G.1 * G.2^2>, <true, true, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^4, G.1 * G.2^2 * G.3>, <false, false, false>> 

 
bdata: 11, 24, [ 2, 2, 12, 12 ] 
G = small group 5 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.3, 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.4^G.1 = G.4^2 
4  generating vector(s)
<<G.1, G.1 * G.3 * G.4, G.2 * G.4, G.2 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.4^2, G.2 * G.4^2, G.2 * G.3 * G.4^2>, <true, false, true>> 
<<G.1, G.1, G.2 * G.4, G.2 * G.3 * G.4^2>, <true, false, true>> 
<<G.1, G.1 * G.3, G.2 * G.4, G.2 * G.4^2>, <true, false, true>> 

 
bdata: 11, 24, [ 2, 2, 12, 12 ] 
G = small group 6 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.3, 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.2^G.1 = G.2 * G.3, 
G.4^G.1 = G.4^2 
4  generating vector(s)
<<G.1, G.1 * G.3 * G.4^2, G.2 * G.3 * G.4^2, G.2 * G.3 * G.4^2>, <true, false, true>> 
<<G.1, G.1, G.2 * G.3 * G.4^2, G.2 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.4^2, G.2 * G.3 * G.4^2, G.2 * G.4^2>, <true, false, true>> 
<<G.1, G.1 * G.3, G.2 * G.3 * G.4^2, G.2 * G.3 * G.4>, <true, false, true>> 

 
bdata: 11, 24, [ 2, 2, 12, 12 ] 
G = small group 9 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = G.4, 
G.2^2 = Id(G), 
G.3^3 = Id(G), 
G.4^2 = Id(G) 
4  generating vector(s)
<<G.4, G.2 * G.4, G.1 * G.3, G.1 * G.2 * G.3^2 * G.4>, <true, true, true>> 
<<G.2, G.4, G.1 * G.3, G.1 * G.2 * G.3^2>, <true, true, true>> 
<<G.2, G.2 * G.4, G.1 * G.3, G.1 * G.3^2>, <true, true, true>> 
<<G.2, G.2, G.1 * G.3, G.1 * G.3^2 * G.4>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 2, 12, 12 ] 
G = small group 10 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^3 = Id(G), 
G.4^2 = Id(G), 
G.2^G.1 = G.2 * G.4 
2  generating vector(s)
<<G.2, G.2 * G.4, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.3^2 * G.4>, <true, false, true>> 
<<G.2, G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.3^2>, <true, false, true>> 

 
bdata: 11, 22, [ 2, 2, 22, 22 ] 
G = small group 2 of 2 group(s) of order 22 
GrpPC : G of order 22 = 2 * 11
PC-Relations:
G.1^2 = Id(G), 
G.2^11 = Id(G) 
1  generating vector(s)
<<G.1, G.1, G.1 * G.2, G.1 * G.2^10>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 3, 4, 12 ] 
G = small group 5 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.3, 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.4^G.1 = G.4^2 
2  generating vector(s)
<<G.1, G.4^2, G.1 * G.2 * G.4, G.2 * G.3 * G.4>, <false, true, true>> 
<<G.1, G.4^2, G.1 * G.2, G.2 * G.3 * G.4^2>, <false, true, true>> 

 
bdata: 11, 24, [ 2, 3, 4, 12 ] 
G = small group 9 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = G.4, 
G.2^2 = Id(G), 
G.3^3 = Id(G), 
G.4^2 = Id(G) 
1  generating vector(s)
<<G.2, G.3, G.1, G.1 * G.2 * G.3^2 * G.4>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 3, 6, 6 ] 
G = small group 3 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^3 = Id(G), 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.2^G.1 = G.3, 
G.3^G.1 = G.2 * G.3, 
G.3^G.2 = G.3 * G.4 
1  generating vector(s)
<<G.4, G.1, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.4>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 3, 6, 6 ] 
G = small group 13 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = Id(G), 
G.3^2 = Id(G), 
G.4^2 = Id(G), 
G.3^G.2 = G.4, 
G.4^G.2 = G.3 * G.4 
4  generating vector(s)
<<G.3, G.2 * G.3 * G.4, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.4>, <true, true, false>> 
<<G.3, G.2 * G.3 * G.4, G.1 * G.2 * G.4, G.1 * G.2>, <false, false, false>> 
<<G.3, G.2 * G.3 * G.4, G.1 * G.2 * G.3, G.1 * G.2 * G.3>, <true, false, true>> 
<<G.3, G.2 * G.3 * G.4, G.1 * G.2, G.1 * G.2 * G.3 * G.4>, <false, true, true>> 

 
bdata: 11, 24, [ 2, 4, 4, 6 ] 
G = small group 5 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = G.3, 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.4^G.1 = G.4^2 
2  generating vector(s)
<<G.1, G.2, G.1 * G.2 * G.4, G.3 * G.4^2>, <true, true, true>> 
<<G.1, G.1 * G.2 * G.3 * G.4, G.2 * G.3, G.3 * G.4^2>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 4, 4, 6 ] 
G = small group 7 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = G.3, 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.4^G.1 = G.4^2 
4  generating vector(s)
<<G.3, G.1 * G.4^2, G.1 * G.2 * G.4, G.2 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.4^2, G.1 * G.4, G.2 * G.3 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.4^2, G.1 * G.3 * G.4, G.2 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.4^2, G.1 * G.2 * G.4, G.3 * G.4>, <true, true, true>> 

 
bdata: 11, 24, [ 2, 4, 4, 6 ] 
G = small group 8 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^2 = Id(G), 
G.4^3 = Id(G), 
G.2^G.1 = G.2 * G.3, 
G.4^G.1 = G.4^2 
2  generating vector(s)
<<G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.3, G.2 * G.3 * G.4>, <true, true, false>> 
<<G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.4^2, G.2 * G.4^2>, <true, true, false>> 

 
bdata: 11, 20, [ 2, 4, 5, 20 ] 
G = small group 2 of 5 group(s) of order 20 
GrpPC : G of order 20 = 2^2 * 5
PC-Relations:
G.1^2 = G.3, 
G.2^5 = Id(G), 
G.3^2 = Id(G) 
1  generating vector(s)
<<G.3, G.1, G.2, G.1 * G.2^4>, <true, true, true>> 

 
bdata: 11, 18, [ 2, 6, 9, 9 ] 
G = small group 2 of 5 group(s) of order 18 
GrpPC : G of order 18 = 2 * 3^2
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = G.3, 
G.3^3 = Id(G) 
2  generating vector(s)
<<G.1, G.1 * G.3, G.2, G.2^2 * G.3>, <true, true, true>> 
<<G.1, G.1 * G.3, G.2^2, G.2 * G.3>, <true, true, true>> 

 
bdata: 11, 16, [ 2, 8, 16, 16 ] 
G = small group 1 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.2, 
G.2^2 = G.3, 
G.3^2 = G.4 
4  generating vector(s)
<<G.4, G.2, G.1, G.1 * G.3>, <true, true, true>> 
<<G.4, G.2, G.1 * G.2, G.1 * G.2>, <true, true, true>> 
<<G.4, G.2, G.1 * G.3, G.1>, <true, true, true>> 
<<G.4, G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 

 
bdata: 11, 24, [ 3, 3, 3, 6 ] 
G = small group 3 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^3 = Id(G), 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.2^G.1 = G.3, 
G.3^G.1 = G.2 * G.3, 
G.3^G.2 = G.3 * G.4 
6  generating vector(s)
<<G.1, G.1, G.1^2 * G.3 * G.4, G.1^2 * G.2>, <true, false, true>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.1, G.1^2 * G.2 * G.3>, <false, true, true>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.1 * G.3, G.1^2 * G.3>, <false, true, true>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.1^2 * G.3 * G.4, G.1 * G.4>, <true, true, false>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.1^2 * G.2 * G.3 * G.4, G.1 * G.3 * G.4>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.1^2 * G.2 * G.3 * G.4, G.1^2 * G.2 * G.3>, <true, false, true>> 

 
bdata: 11, 24, [ 3, 3, 4, 4 ] 
G = small group 3 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^3 = Id(G), 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.2^G.1 = G.3, 
G.3^G.1 = G.2 * G.3, 
G.3^G.2 = G.3 * G.4 
6  generating vector(s)
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.3 * G.4, G.2>, <false, true, false>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.2 * G.4, G.3 * G.4>, <false, false, false>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.2, G.3>, <false, false, false>> 
<<G.1, G.1^2 * G.2 * G.3 * G.4, G.3, G.2 * G.4>, <false, true, false>> 
<<G.1, G.1^2, G.3 * G.4, G.3>, <true, false, true>> 
<<G.1, G.1^2, G.2 * G.3, G.2 * G.3 * G.4>, <true, false, true>> 

 
bdata: 11, 24, [ 3, 3, 4, 4 ] 
G = small group 12 of 15 group(s) of order 24 
GrpPC : G of order 24 = 2^3 * 3
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = Id(G), 
G.3^2 = Id(G), 
G.4^2 = Id(G), 
G.2^G.1 = G.2^2, 
G.3^G.1 = G.4, 
G.3^G.2 = G.4, 
G.4^G.1 = G.3, 
G.4^G.2 = G.3 * G.4 
8  generating vector(s)
<<G.2, G.2^2 * G.3, G.1 * G.2^2 * G.3 * G.4, G.1 * G.2^2 * G.3 * G.4>, <true, false, true>> 
<<G.2, G.2^2 * G.3, G.1 * G.2^2 * G.4, G.1 * G.2^2 * G.4>, <true, false, true>> 
<<G.2, G.2 * G.3 * G.4, G.1 * G.2 * G.3 * G.4, G.1 * G.2^2 * G.3 * G.4>, <false, false, false>> 
<<G.2, G.2 * G.3 * G.4, G.1 * G.4, G.1 * G.2 * G.3 * G.4>, <true, false, false>> 
<<G.2, G.2 * G.3 * G.4, G.1 * G.2^2 * G.3 * G.4, G.1 * G.4>, <false, false, true>> 
<<G.2, G.2^2, G.1 * G.2 * G.3 * G.4, G.1 * G.2 * G.3>, <true, false, true>> 
<<G.2, G.2^2, G.1 * G.4, G.1 * G.3>, <true, false, true>> 
<<G.2, G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.2^2 * G.4>, <true, false, true>> 

 
bdata: 11, 15, [ 3, 5, 15, 15 ] 
G = small group 1 of 1 group(s) of order 15 
GrpPC : G of order 15 = 3 * 5
PC-Relations:
G.1^3 = Id(G), 
G.2^5 = Id(G) 
3  generating vector(s)
<<G.1, G.2, G.1 * G.2, G.1 * G.2^3>, <true, true, true>> 
<<G.1, G.2, G.1 * G.2^2, G.1 * G.2^2>, <true, true, true>> 
<<G.1, G.2, G.1 * G.2^3, G.1 * G.2>, <true, true, true>> 

 
bdata: 11, 20, [ 4, 4, 4, 4 ] 
G = small group 1 of 5 group(s) of order 20 
GrpPC : G of order 20 = 2^2 * 5
PC-Relations:
G.1^2 = G.2, 
G.2^2 = Id(G), 
G.3^5 = Id(G), 
G.3^G.1 = G.3^4 
24 generating vector(s)
<<G.1, G.1, G.1 * G.3^3, G.1 * G.3^3>, <true, false, true>> 
<<G.1, G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.2, G.1 * G.3^3, G.1 * G.2 * G.3^3>, <true, false, true>> 
<<G.1, G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.1, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^3, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^4, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^2, G.1 * G.2 * G.3>, <false, true, true>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3, G.1 * G.2>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2, G.1 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3, G.1>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^2, G.1 * G.3>, <false, true, true>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^3, G.1 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^4, G.1 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1, G.1 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^3, G.1>, <true, true, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^4, G.1 * G.3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^2, G.1 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3, G.1 * G.3^3>, <false, true, true>> 
<<G.1, G.1 * G.3^3, G.1 * G.2, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3, G.1 * G.2 * G.3^3>, <false, true, true>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^2, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^3, G.1 * G.2>, <true, true, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^4, G.1 * G.2 * G.3>, <false, false, false>> 

 
bdata: 11, 20, [ 4, 4, 4, 4 ] 
G = small group 3 of 5 group(s) of order 20 
GrpPC : G of order 20 = 2^2 * 5
PC-Relations:
G.1^2 = G.2, 
G.2^2 = Id(G), 
G.3^5 = Id(G), 
G.3^G.1 = G.3^2, 
G.3^G.2 = G.3^4 
48 generating vector(s)
<<G.1, G.1, G.1 * G.3^4, G.1 * G.3^2>, <false, false, false>> 
<<G.1, G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.2, G.1 * G.3^4, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^4, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^3, G.1 * G.2>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3^2, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.3, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2, G.1 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3, G.1 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^3, G.1 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^2, G.1>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.1 * G.2 * G.3^4, G.1 * G.3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1, G.1 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^4, G.1>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^3, G.1 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3^2, G.1 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.3, G.1 * G.3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3, G.1 * G.2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^3, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^2, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1, G.1 * G.3^3, G.1 * G.2 * G.3^4, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.1 * G.2, G.1, G.1 * G.3^4, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1, G.1 * G.2 * G.3, G.1 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2, G.1 * G.3^4, G.1 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1, G.1 * G.3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3^4, G.1 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3^3, G.1>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3^2, G.1 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.3, G.1 * G.3^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3^3, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3^2, G.1 * G.2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.3^4, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1, G.1 * G.2 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.3^4, G.1 * G.2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.3^3, G.1 * G.2 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.3^2, G.1 * G.2 * G.3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.3, G.1 * G.2 * G.3^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.2, G.1 * G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.2 * G.3, G.1>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.2 * G.3^3, G.1 * G.3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.2 * G.3^2, G.1 * G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.1 * G.2 * G.3^4, G.1 * G.3^4>, <false, false, false>> 

 
bdata: 11, 16, [ 4, 4, 8, 8 ] 
G = small group 5 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4 
6  generating vector(s)
<<G.3, G.2 * G.3 * G.4, G.1, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.3, G.2 * G.3 * G.4, G.1 * G.3, G.1 * G.2 * G.4>, <true, true, true>> 
<<G.2 * G.3, G.3, G.1, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.2 * G.3, G.3, G.1 * G.3, G.1 * G.2>, <true, true, true>> 
<<G.2 * G.3, G.2 * G.3 * G.4, G.1, G.1 * G.3 * G.4>, <true, true, true>> 
<<G.2 * G.3, G.2 * G.3, G.1, G.1 * G.3>, <true, true, true>> 

 
bdata: 11, 16, [ 4, 4, 8, 8 ] 
G = small group 6 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.4 
6  generating vector(s)
<<G.3, G.2 * G.3 * G.4, G.1 * G.4, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.3, G.2 * G.3 * G.4, G.1 * G.2 * G.4, G.1 * G.3 * G.4>, <true, true, true>> 
<<G.2 * G.3, G.3, G.1 * G.4, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.2 * G.3, G.3, G.1 * G.2 * G.4, G.1 * G.3>, <true, true, true>> 
<<G.2 * G.3, G.2 * G.3 * G.4, G.1 * G.4, G.1 * G.3>, <true, false, true>> 
<<G.2 * G.3, G.2 * G.3, G.1 * G.4, G.1 * G.3 * G.4>, <true, false, true>> 

 
bdata: 11, 16, [ 4, 4, 8, 8 ] 
G = small group 8 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4 
4  generating vector(s)
<<G.1, G.1 * G.3 * G.4, G.1 * G.2 * G.3, G.1 * G.2 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.3 * G.4, G.1 * G.2, G.1 * G.2 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.4, G.1 * G.2 * G.3, G.1 * G.2 * G.4>, <true, false, true>> 
<<G.1, G.1, G.1 * G.2 * G.3, G.1 * G.2>, <true, false, true>> 

 
bdata: 11, 16, [ 4, 4, 8, 8 ] 
G = small group 9 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4 
4  generating vector(s)
<<G.2, G.2 * G.3 * G.4, G.1 * G.2 * G.3, G.1 * G.2 * G.3 * G.4>, <true, false, true>> 
<<G.2, G.2 * G.3 * G.4, G.1 * G.2, G.1 * G.2>, <true, false, true>> 
<<G.2, G.2 * G.4, G.1 * G.2 * G.3, G.1 * G.2>, <true, false, true>> 
<<G.2, G.2, G.1 * G.2 * G.3, G.1 * G.2 * G.4>, <true, false, true>> 

 
bdata: 11, 12, [ 12, 12, 12, 12 ] 
G = small group 2 of 5 group(s) of order 12 
GrpPC : G of order 12 = 2^2 * 3
PC-Relations:
G.1^2 = G.3, 
G.2^3 = Id(G), 
G.3^2 = Id(G) 
12 generating vector(s)
<<G.1 * G.2, G.1 * G.2, G.1 * G.2^2, G.1 * G.2^2>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2, G.1 * G.2^2 * G.3, G.1 * G.2^2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2^2, G.1 * G.2^2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2 * G.3, G.1 * G.2^2 * G.3, G.1 * G.2^2>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2, G.1 * G.2, G.1 * G.2^2>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2, G.1 * G.2 * G.3, G.1 * G.2^2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2, G.1 * G.2^2, G.1 * G.2>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2, G.1 * G.2^2 * G.3, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2 * G.3, G.1 * G.2, G.1 * G.2^2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2 * G.3, G.1 * G.2 * G.3, G.1 * G.2^2>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2 * G.3, G.1 * G.2^2, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.1 * G.2, G.1 * G.2^2 * G.3, G.1 * G.2^2 * G.3, G.1 * G.2>, <true, true, true>>