Automorphism Classes of Quadilateral Actions on Sufaces of Genus 12 

 
bdata: 12, 52, [ 2, 2, 2, 13 ] 
G = small group 4 of 5 group(s) of order 52 
GrpPC : G of order 52 = 2^2 * 13
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^13 = Id(G), 
G.3^G.1 = G.3^12 
3  generating vector(s)
<<G.2, G.1 * G.2 * G.3^3, G.1 * G.3^6, G.3^10>, <true, true, true>> 
<<G.1, G.2, G.1 * G.2 * G.3^5, G.3^8>, <true, true, true>> 
<<G.1, G.1 * G.2 * G.3^3, G.2, G.3^10>, <true, true, true>> 

 
bdata: 12, 48, [ 2, 2, 2, 24 ] 
G = small group 7 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.3 * G.4, 
G.3^2 = G.4, 
G.4^2 = Id(G), 
G.5^3 = Id(G), 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.5^G.1 = G.5^2 
3  generating vector(s)
<<G.4, G.1 * G.3 * G.5^2, G.1 * G.2 * G.4, G.2 * G.4 * G.5^2>, <true, true, true>> 
<<G.1, G.4, G.1 * G.2 * G.4 * G.5^2, G.2 * G.3 * G.5>, <true, true, true>> 
<<G.1, G.1 * G.2 * G.4 * G.5^2, G.4, G.2 * G.3 * G.5>, <true, true, true>> 

 
bdata: 12, 42, [ 2, 2, 3, 7 ] 
G = small group 5 of 6 group(s) of order 42 
GrpPC : G of order 42 = 2 * 3 * 7
PC-Relations:
G.1^2 = Id(G), 
G.2^3 = Id(G), 
G.3^7 = Id(G), 
G.2^G.1 = G.2^2, 
G.3^G.1 = G.3^6 
1  generating vector(s)
<<G.1, G.1 * G.2^2 * G.3, G.2, G.3^6>, <true, true, true>> 

 
bdata: 12, 36, [ 2, 2, 3, 18 ] 
G = small group 4 of 14 group(s) of order 36 
GrpPC : G of order 36 = 2^2 * 3^2
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^3 = G.4^2, 
G.4^3 = Id(G), 
G.3^G.1 = G.3^2 * G.4, 
G.4^G.1 = G.4^2 
2  generating vector(s)
<<G.1, G.1 * G.2 * G.3^2, G.4^2, G.2 * G.3 * G.4^2>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3^2, G.4, G.2 * G.3>, <true, false, true>> 

 
bdata: 12, 40, [ 2, 2, 4, 5 ] 
G = small group 6 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.2^G.1 = G.2 * G.3, 
G.4^G.1 = G.4^4 
1  generating vector(s)
<<G.1, G.1 * G.2 * G.4^4, G.2 * G.3, G.4>, <true, true, true>> 

 
bdata: 12, 40, [ 2, 2, 4, 5 ] 
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 
2  generating vector(s)
<<G.2, G.1 * G.3 * G.4^2, G.1 * G.2 * G.3, G.4^2>, <true, true, true>> 
<<G.1, G.2 * G.3, G.1 * G.2 * G.4^2, G.4^3>, <true, true, true>> 

 
bdata: 12, 32, [ 2, 2, 4, 16 ] 
G = small group 18 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.3^2 = G.4 * G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
2  generating vector(s)
<<G.2, G.1 * G.4 * G.5, G.4 * G.5, G.1 * G.2 * G.5>, <true, false, true>> 
<<G.2, G.1 * G.4 * G.5, G.4, G.1 * G.2>, <true, false, true>> 

 
bdata: 12, 32, [ 2, 2, 4, 16 ] 
G = small group 19 of 51 group(s) of order 32 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.5, 
G.3^2 = G.4 * G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
2  generating vector(s)
<<G.5, G.2 * G.3 * G.4, G.1 * G.5, G.1 * G.2 * G.3 * G.4 * G.5>, <true, true, true>> 
<<G.2, G.5, G.1 * G.5, G.1 * G.2 * G.5>, <true, true, true>> 

 
bdata: 12, 30, [ 2, 2, 5, 15 ] 
G = small group 1 of 4 group(s) of order 30 
GrpPC : G of order 30 = 2 * 3 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^5 = Id(G), 
G.3^3 = Id(G), 
G.3^G.1 = G.3^2 
1  generating vector(s)
<<G.1, G.1 * G.3^2, G.2, G.2^4 * G.3>, <true, true, true>> 

 
bdata: 12, 30, [ 2, 2, 5, 15 ] 
G = small group 3 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.2^G.1 = G.2^2, 
G.3^G.1 = G.3^4 
4  generating vector(s)
<<G.1, G.1 * G.2^2 * G.3^2, G.3, G.2 * G.3^2>, <true, false, true>> 
<<G.1, G.1 * G.2^2 * G.3^2, G.3^4, G.2 * G.3^4>, <true, false, true>> 
<<G.1, G.1 * G.2^2 * G.3^2, G.3^2, G.2 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.2, G.3, G.2^2 * G.3^4>, <true, false, true>> 

 
bdata: 12, 28, [ 2, 2, 7, 14 ] 
G = small group 3 of 4 group(s) of order 28 
GrpPC : G of order 28 = 2^2 * 7
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^7 = Id(G), 
G.3^G.1 = G.3^6 
6  generating vector(s)
<<G.1, G.1 * G.2 * G.3^5, G.3, G.2 * G.3>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3^5, G.3^6, G.2 * G.3^3>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3^5, G.3^5, G.2 * G.3^4>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3^5, G.3^3, G.2 * G.3^6>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3^5, G.3^4, G.2 * G.3^5>, <true, false, true>> 
<<G.1, G.1 * G.2, G.3, G.2 * G.3^6>, <true, false, true>> 

 
bdata: 12, 28, [ 2, 2, 7, 14 ] 
G = small group 4 of 4 group(s) of order 28 
GrpPC : G of order 28 = 2^2 * 7
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^7 = Id(G) 
1  generating vector(s)
<<G.2, G.1 * G.2, G.3, G.1 * G.3^6>, <true, true, true>> 

 
bdata: 12, 26, [ 2, 2, 13, 13 ] 
G = small group 1 of 2 group(s) of order 26 
GrpPC : G of order 26 = 2 * 13
PC-Relations:
G.1^2 = Id(G), 
G.2^13 = Id(G), 
G.2^G.1 = G.2^12 
12 generating vector(s)
<<G.1, G.1 * G.2^5, G.2, G.2^7>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^12, G.2^9>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^2, G.2^6>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^11, G.2^10>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^3, G.2^5>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^10, G.2^11>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^9, G.2^12>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^4, G.2^4>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^5, G.2^3>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^6, G.2^2>, <true, false, true>> 
<<G.1, G.1 * G.2^5, G.2^7, G.2>, <true, false, true>> 
<<G.1, G.1, G.2, G.2^12>, <true, false, true>> 

 
bdata: 12, 26, [ 2, 2, 13, 13 ] 
G = small group 2 of 2 group(s) of order 26 
GrpPC : G of order 26 = 2 * 13
PC-Relations:
G.1^2 = Id(G), 
G.2^13 = Id(G) 
1  generating vector(s)
<<G.1, G.1, G.2, G.2^12>, <true, true, true>> 

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

 
bdata: 12, 24, [ 2, 3, 6, 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 
1  generating vector(s)
<<G.2, G.3, G.1 * G.3 * G.4, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 

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

 
bdata: 12, 24, [ 2, 4, 4, 12 ] 
G = small group 4 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 = 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 
1  generating vector(s)
<<G.3, G.1 * G.3 * G.4^2, G.1 * G.2 * G.3 * G.4, G.2 * G.3 * G.4>, <true, true, true>> 

 
bdata: 12, 24, [ 2, 4, 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.3 * G.4, G.1 * G.2 * G.4, G.1^2 * G.2>, <true, true, true>> 

 
bdata: 12, 24, [ 2, 4, 6, 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 
4  generating vector(s)
<<G.1, G.1 * G.2 * G.3 * G.4, G.3 * G.4, G.2 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3 * G.4, G.2 * G.4, G.3 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.3 * G.4, G.2 * G.4^2>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.2 * G.4, G.3 * G.4^2>, <true, false, true>> 

 
bdata: 12, 24, [ 2, 4, 6, 6 ] 
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 
3  generating vector(s)
<<G.4, G.1 * G.2 * G.4, G.2 * G.3 * G.4, G.1 * G.3^2 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.2 * G.4, G.3 * G.4, G.1 * G.3^2 * G.4>, <true, true, true>> 
<<G.2, G.1 * G.2 * G.4, G.1 * G.3 * G.4, G.3^2 * G.4>, <true, true, true>> 

 
bdata: 12, 20, [ 2, 4, 10, 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.3, G.1 * G.2^4 * G.3>, <true, true, true>> 

 
bdata: 12, 20, [ 2, 5, 10, 10 ] 
G = small group 5 of 5 group(s) of order 20 
GrpPC : G of order 20 = 2^2 * 5
PC-Relations:
G.1^2 = Id(G), 
G.2^2 = Id(G), 
G.3^5 = Id(G) 
3  generating vector(s)
<<G.2, G.3, G.1 * G.3, G.1 * G.2 * G.3^3>, <true, true, true>> 
<<G.2, G.3, G.1 * G.3^2, G.1 * G.2 * G.3^2>, <true, true, true>> 
<<G.2, G.3, G.1 * G.3^3, G.1 * G.2 * G.3>, <true, true, true>> 

 
bdata: 12, 18, [ 2, 6, 18, 18 ] 
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.1 * G.2, G.1 * G.2^2 * G.3>, <true, true, true>> 
<<G.1, G.1 * G.3, G.1 * G.2^2, G.1 * G.2 * G.3>, <true, true, true>> 

 
bdata: 12, 18, [ 2, 9, 9, 18 ] 
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) 
3  generating vector(s)
<<G.1, G.2, G.2, G.1 * G.2 * G.3^2>, <true, true, true>> 
<<G.1, G.2, G.2 * G.3, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.1, G.2, G.2 * G.3^2, G.1 * G.2>, <true, true, true>> 

 
bdata: 12, 24, [ 3, 3, 4, 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 
4  generating vector(s)
<<G.1, G.1, G.2 * G.3, G.1 * G.2 * G.4>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.3 * G.4, G.1 * G.3 * G.4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.2 * G.3, G.1 * G.4>, <true, true, false>> 
<<G.1, G.1 * G.2 * G.3, G.2, G.1 * G.2 * G.3 * G.4>, <false, true, true>> 

 
bdata: 12, 21, [ 3, 3, 7, 7 ] 
G = small group 1 of 2 group(s) of order 21 
GrpPC : G of order 21 = 3 * 7
PC-Relations:
G.1^3 = Id(G), 
G.2^7 = Id(G), 
G.2^G.1 = G.2^2 
12 generating vector(s)
<<G.1, G.1^2 * G.2^5, G.2, G.2>, <false, false, false>> 
<<G.1, G.1^2 * G.2^5, G.2^4, G.2^5>, <false, false, false>> 
<<G.1, G.1^2 * G.2^5, G.2^3, G.2^6>, <false, false, false>> 
<<G.1, G.1^2 * G.2^5, G.2^6, G.2^3>, <false, false, false>> 
<<G.1, G.1^2 * G.2^5, G.2^5, G.2^4>, <false, false, false>> 
<<G.1, G.1^2, G.2, G.2^6>, <false, false, false>> 
<<G.1^2, G.1 * G.2, G.2, G.2^5>, <false, false, false>> 
<<G.1^2, G.1 * G.2, G.2^2, G.2^4>, <false, false, false>> 
<<G.1^2, G.1 * G.2, G.2^4, G.2^2>, <false, false, false>> 
<<G.1^2, G.1 * G.2, G.2^3, G.2^3>, <false, false, false>> 
<<G.1^2, G.1 * G.2, G.2^5, G.2>, <false, false, false>> 
<<G.1^2, G.1, G.2, G.2^6>, <false, false, false>> 

 
bdata: 12, 21, [ 3, 3, 7, 7 ] 
G = small group 2 of 2 group(s) of order 21 
GrpPC : G of order 21 = 3 * 7
PC-Relations:
G.1^3 = Id(G), 
G.2^7 = Id(G) 
1  generating vector(s)
<<G.1, G.1^2, G.2, G.2^6>, <true, true, true>> 

 
bdata: 12, 18, [ 3, 3, 18, 18 ] 
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) 
4  generating vector(s)
<<G.3, G.3, G.1 * G.2, G.1 * G.2^2>, <true, true, true>> 
<<G.3, G.3, G.1 * G.2^2, G.1 * G.2>, <true, true, true>> 
<<G.3, G.3^2, G.1 * G.2, G.1 * G.2^2 * G.3^2>, <true, true, true>> 
<<G.3, G.3^2, G.1 * G.2^2, G.1 * G.2 * G.3^2>, <true, true, true>> 

 
bdata: 12, 24, [ 3, 4, 4, 4 ] 
G = small group 4 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 = 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 
3  generating vector(s)
<<G.4, G.2 * G.3, G.1 * G.3 * G.4, G.1 * G.2>, <true, true, true>> 
<<G.4, G.1 * G.3 * G.4^2, G.2 * G.3, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.4, G.1 * G.3 * G.4^2, G.1 * G.2 * G.3 * G.4, G.2>, <true, true, true>> 

 
bdata: 12, 15, [ 3, 15, 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) 
9  generating vector(s)
<<G.1, G.1 * G.2, G.1^2 * G.2, G.1^2 * G.2^3>, <true, true, true>> 
<<G.1, G.1 * G.2, G.1^2 * G.2^2, G.1^2 * G.2^2>, <true, true, true>> 
<<G.1, G.1 * G.2, G.1^2 * G.2^3, G.1^2 * G.2>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1 * G.2, G.1^2 * G.2^3>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1 * G.2^2, G.1^2 * G.2^2>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1 * G.2^3, G.1^2 * G.2>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1^2 * G.2, G.1 * G.2^3>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1^2 * G.2^2, G.1 * G.2^2>, <true, true, true>> 
<<G.1, G.1^2 * G.2, G.1^2 * G.2^3, G.1 * G.2>, <true, true, true>> 

 
bdata: 12, 20, [ 4, 4, 5, 5 ] 
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 
4  generating vector(s)
<<G.1, G.1 * G.2, G.3, G.3^4>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.3, G.3^3>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.3^3, G.3>, <true, false, true>> 
<<G.1, G.1 * G.2 * G.3, G.3^2, G.3^2>, <true, false, true>> 

 
bdata: 12, 20, [ 4, 4, 5, 5 ] 
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.1, G.1 * G.3, G.2, G.2^4>, <true, true, true>> 

 
bdata: 12, 20, [ 4, 4, 5, 5 ] 
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 
8  generating vector(s)
<<G.1, G.1 * G.2, G.3, G.3^4>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.3, G.3^3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.3^3, G.3>, <false, false, false>> 
<<G.1, G.1 * G.2 * G.3, G.3^2, G.3^2>, <false, false, false>> 
<<G.1 * G.2, G.1, G.3, G.3^4>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.3, G.3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.3^4, G.3^3>, <false, false, false>> 
<<G.1 * G.2, G.1 * G.3^3, G.3^3, G.3^4>, <false, false, false>> 

 
bdata: 12, 16, [ 4, 4, 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.3, G.3, G.1, G.1 * G.2 * G.3>, <true, true, true>> 
<<G.3, G.3, G.1 * G.2, G.1 * G.3>, <true, true, true>> 
<<G.3, G.3 * G.4, G.1, G.1 * G.2 * G.3 * G.4>, <true, true, true>> 
<<G.3, G.3 * G.4, G.1 * G.2, G.1 * G.3 * G.4>, <true, true, true>> 

 
bdata: 12, 15, [ 5, 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) 
13 generating vector(s)
<<G.2, G.2, G.1 * G.2, G.1^2 * G.2^2>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^2, G.1^2 * G.2>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^4, G.1^2 * G.2^4>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^2, G.1^2 * G.2^4>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^3, G.1^2 * G.2^3>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^4, G.1^2 * G.2^2>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2, G.1^2 * G.2>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^3, G.1^2 * G.2^4>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^4, G.1^2 * G.2^3>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2, G.1^2 * G.2^4>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^2, G.1^2 * G.2^3>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^3, G.1^2 * G.2^2>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^4, G.1^2 * G.2>, <true, true, true>> 

 
bdata: 12, 14, [ 7, 7, 14, 14 ] 
G = small group 2 of 2 group(s) of order 14 
GrpPC : G of order 14 = 2 * 7
PC-Relations:
G.1^2 = Id(G), 
G.2^7 = Id(G) 
31 generating vector(s)
<<G.2, G.2, G.1 * G.2, G.1 * G.2^4>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^2, G.1 * G.2^3>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^3, G.1 * G.2^2>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^4, G.1 * G.2>, <true, true, true>> 
<<G.2, G.2, G.1 * G.2^6, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2, G.1 * G.2^2>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^2, G.1 * G.2>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^4, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^5, G.1 * G.2^5>, <true, true, true>> 
<<G.2, G.2^3, G.1 * G.2^6, G.1 * G.2^4>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2, G.1 * G.2^3>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^2, G.1 * G.2^2>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^3, G.1 * G.2>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^5, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^2, G.1 * G.2^6, G.1 * G.2^5>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2^2, G.1 * G.2^5>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2^3, G.1 * G.2^4>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2^4, G.1 * G.2^3>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2^5, G.1 * G.2^2>, <true, true, true>> 
<<G.2, G.2^6, G.1 * G.2^6, G.1 * G.2>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2, G.1 * G.2>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^3, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^4, G.1 * G.2^5>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^5, G.1 * G.2^4>, <true, true, true>> 
<<G.2, G.2^4, G.1 * G.2^6, G.1 * G.2^3>, <true, true, true>> 
<<G.2, G.2^5, G.1 * G.2^2, G.1 * G.2^6>, <true, true, true>> 
<<G.2, G.2^5, G.1 * G.2^3, G.1 * G.2^5>, <true, true, true>> 
<<G.2, G.2^5, G.1 * G.2^4, G.1 * G.2^4>, <true, true, true>> 
<<G.2, G.2^5, G.1 * G.2^5, G.1 * G.2^3>, <true, true, true>> 
<<G.2, G.2^5, G.1 * G.2^6, G.1 * G.2^2>, <true, true, true>> 

 
bdata: 12, 13, [ 13, 13, 13, 13 ] 
G = small group 1 of 1 group(s) of order 13 
GrpPC : G of order 13
PC-Relations:
G.1^13 = Id(G) 
133 generating vector(s)
<<G.1, G.1, G.1, G.1^10>, <true, true, true>> 
<<G.1, G.1, G.1^2, G.1^9>, <true, true, true>> 
<<G.1, G.1, G.1^3, G.1^8>, <true, true, true>> 
<<G.1, G.1, G.1^4, G.1^7>, <true, true, true>> 
<<G.1, G.1, G.1^5, G.1^6>, <true, true, true>> 
<<G.1, G.1, G.1^6, G.1^5>, <true, true, true>> 
<<G.1, G.1, G.1^7, G.1^4>, <true, true, true>> 
<<G.1, G.1, G.1^8, G.1^3>, <true, true, true>> 
<<G.1, G.1, G.1^9, G.1^2>, <true, true, true>> 
<<G.1, G.1, G.1^10, G.1>, <true, true, true>> 
<<G.1, G.1, G.1^12, G.1^12>, <true, true, true>> 
<<G.1, G.1^3, G.1, G.1^8>, <true, true, true>> 
<<G.1, G.1^3, G.1^2, G.1^7>, <true, true, true>> 
<<G.1, G.1^3, G.1^3, G.1^6>, <true, true, true>> 
<<G.1, G.1^3, G.1^4, G.1^5>, <true, true, true>> 
<<G.1, G.1^3, G.1^5, G.1^4>, <true, true, true>> 
<<G.1, G.1^3, G.1^6, G.1^3>, <true, true, true>> 
<<G.1, G.1^3, G.1^7, G.1^2>, <true, true, true>> 
<<G.1, G.1^3, G.1^8, G.1>, <true, true, true>> 
<<G.1, G.1^3, G.1^10, G.1^12>, <true, true, true>> 
<<G.1, G.1^3, G.1^11, G.1^11>, <true, true, true>> 
<<G.1, G.1^3, G.1^12, G.1^10>, <true, true, true>> 
<<G.1, G.1^2, G.1, G.1^9>, <true, true, true>> 
<<G.1, G.1^2, G.1^2, G.1^8>, <true, true, true>> 
<<G.1, G.1^2, G.1^3, G.1^7>, <true, true, true>> 
<<G.1, G.1^2, G.1^4, G.1^6>, <true, true, true>> 
<<G.1, G.1^2, G.1^5, G.1^5>, <true, true, true>> 
<<G.1, G.1^2, G.1^6, G.1^4>, <true, true, true>> 
<<G.1, G.1^2, G.1^7, G.1^3>, <true, true, true>> 
<<G.1, G.1^2, G.1^8, G.1^2>, <true, true, true>> 
<<G.1, G.1^2, G.1^9, G.1>, <true, true, true>> 
<<G.1, G.1^2, G.1^11, G.1^12>, <true, true, true>> 
<<G.1, G.1^2, G.1^12, G.1^11>, <true, true, true>> 
<<G.1, G.1^9, G.1, G.1^2>, <true, true, true>> 
<<G.1, G.1^9, G.1^2, G.1>, <true, true, true>> 
<<G.1, G.1^9, G.1^4, G.1^12>, <true, true, true>> 
<<G.1, G.1^9, G.1^5, G.1^11>, <true, true, true>> 
<<G.1, G.1^9, G.1^6, G.1^10>, <true, true, true>> 
<<G.1, G.1^9, G.1^7, G.1^9>, <true, true, true>> 
<<G.1, G.1^9, G.1^8, G.1^8>, <true, true, true>> 
<<G.1, G.1^9, G.1^9, G.1^7>, <true, true, true>> 
<<G.1, G.1^9, G.1^10, G.1^6>, <true, true, true>> 
<<G.1, G.1^9, G.1^11, G.1^5>, <true, true, true>> 
<<G.1, G.1^9, G.1^12, G.1^4>, <true, true, true>> 
<<G.1, G.1^8, G.1, G.1^3>, <true, true, true>> 
<<G.1, G.1^8, G.1^2, G.1^2>, <true, true, true>> 
<<G.1, G.1^8, G.1^3, G.1>, <true, true, true>> 
<<G.1, G.1^8, G.1^5, G.1^12>, <true, true, true>> 
<<G.1, G.1^8, G.1^6, G.1^11>, <true, true, true>> 
<<G.1, G.1^8, G.1^7, G.1^10>, <true, true, true>> 
<<G.1, G.1^8, G.1^8, G.1^9>, <true, true, true>> 
<<G.1, G.1^8, G.1^9, G.1^8>, <true, true, true>> 
<<G.1, G.1^8, G.1^10, G.1^7>, <true, true, true>> 
<<G.1, G.1^8, G.1^11, G.1^6>, <true, true, true>> 
<<G.1, G.1^8, G.1^12, G.1^5>, <true, true, true>> 
<<G.1, G.1^11, G.1^2, G.1^12>, <true, true, true>> 
<<G.1, G.1^11, G.1^3, G.1^11>, <true, true, true>> 
<<G.1, G.1^11, G.1^4, G.1^10>, <true, true, true>> 
<<G.1, G.1^11, G.1^5, G.1^9>, <true, true, true>> 
<<G.1, G.1^11, G.1^6, G.1^8>, <true, true, true>> 
<<G.1, G.1^11, G.1^7, G.1^7>, <true, true, true>> 
<<G.1, G.1^11, G.1^8, G.1^6>, <true, true, true>> 
<<G.1, G.1^11, G.1^9, G.1^5>, <true, true, true>> 
<<G.1, G.1^11, G.1^10, G.1^4>, <true, true, true>> 
<<G.1, G.1^11, G.1^11, G.1^3>, <true, true, true>> 
<<G.1, G.1^11, G.1^12, G.1^2>, <true, true, true>> 
<<G.1, G.1^10, G.1, G.1>, <true, true, true>> 
<<G.1, G.1^10, G.1^3, G.1^12>, <true, true, true>> 
<<G.1, G.1^10, G.1^4, G.1^11>, <true, true, true>> 
<<G.1, G.1^10, G.1^5, G.1^10>, <true, true, true>> 
<<G.1, G.1^10, G.1^6, G.1^9>, <true, true, true>> 
<<G.1, G.1^10, G.1^7, G.1^8>, <true, true, true>> 
<<G.1, G.1^10, G.1^8, G.1^7>, <true, true, true>> 
<<G.1, G.1^10, G.1^9, G.1^6>, <true, true, true>> 
<<G.1, G.1^10, G.1^10, G.1^5>, <true, true, true>> 
<<G.1, G.1^10, G.1^11, G.1^4>, <true, true, true>> 
<<G.1, G.1^10, G.1^12, G.1^3>, <true, true, true>> 
<<G.1, G.1^5, G.1, G.1^6>, <true, true, true>> 
<<G.1, G.1^5, G.1^2, G.1^5>, <true, true, true>> 
<<G.1, G.1^5, G.1^3, G.1^4>, <true, true, true>> 
<<G.1, G.1^5, G.1^4, G.1^3>, <true, true, true>> 
<<G.1, G.1^5, G.1^5, G.1^2>, <true, true, true>> 
<<G.1, G.1^5, G.1^6, G.1>, <true, true, true>> 
<<G.1, G.1^5, G.1^8, G.1^12>, <true, true, true>> 
<<G.1, G.1^5, G.1^9, G.1^11>, <true, true, true>> 
<<G.1, G.1^5, G.1^10, G.1^10>, <true, true, true>> 
<<G.1, G.1^5, G.1^11, G.1^9>, <true, true, true>> 
<<G.1, G.1^5, G.1^12, G.1^8>, <true, true, true>> 
<<G.1, G.1^4, G.1, G.1^7>, <true, true, true>> 
<<G.1, G.1^4, G.1^2, G.1^6>, <true, true, true>> 
<<G.1, G.1^4, G.1^3, G.1^5>, <true, true, true>> 
<<G.1, G.1^4, G.1^4, G.1^4>, <true, true, true>> 
<<G.1, G.1^4, G.1^5, G.1^3>, <true, true, true>> 
<<G.1, G.1^4, G.1^6, G.1^2>, <true, true, true>> 
<<G.1, G.1^4, G.1^7, G.1>, <true, true, true>> 
<<G.1, G.1^4, G.1^9, G.1^12>, <true, true, true>> 
<<G.1, G.1^4, G.1^10, G.1^11>, <true, true, true>> 
<<G.1, G.1^4, G.1^11, G.1^10>, <true, true, true>> 
<<G.1, G.1^4, G.1^12, G.1^9>, <true, true, true>> 
<<G.1, G.1^7, G.1, G.1^4>, <true, true, true>> 
<<G.1, G.1^7, G.1^2, G.1^3>, <true, true, true>> 
<<G.1, G.1^7, G.1^3, G.1^2>, <true, true, true>> 
<<G.1, G.1^7, G.1^4, G.1>, <true, true, true>> 
<<G.1, G.1^7, G.1^6, G.1^12>, <true, true, true>> 
<<G.1, G.1^7, G.1^7, G.1^11>, <true, true, true>> 
<<G.1, G.1^7, G.1^8, G.1^10>, <true, true, true>> 
<<G.1, G.1^7, G.1^9, G.1^9>, <true, true, true>> 
<<G.1, G.1^7, G.1^10, G.1^8>, <true, true, true>> 
<<G.1, G.1^7, G.1^11, G.1^7>, <true, true, true>> 
<<G.1, G.1^7, G.1^12, G.1^6>, <true, true, true>> 
<<G.1, G.1^6, G.1, G.1^5>, <true, true, true>> 
<<G.1, G.1^6, G.1^2, G.1^4>, <true, true, true>> 
<<G.1, G.1^6, G.1^3, G.1^3>, <true, true, true>> 
<<G.1, G.1^6, G.1^4, G.1^2>, <true, true, true>> 
<<G.1, G.1^6, G.1^5, G.1>, <true, true, true>> 
<<G.1, G.1^6, G.1^7, G.1^12>, <true, true, true>> 
<<G.1, G.1^6, G.1^8, G.1^11>, <true, true, true>> 
<<G.1, G.1^6, G.1^9, G.1^10>, <true, true, true>> 
<<G.1, G.1^6, G.1^10, G.1^9>, <true, true, true>> 
<<G.1, G.1^6, G.1^11, G.1^8>, <true, true, true>> 
<<G.1, G.1^6, G.1^12, G.1^7>, <true, true, true>> 
<<G.1, G.1^12, G.1, G.1^12>, <true, true, true>> 
<<G.1, G.1^12, G.1^2, G.1^11>, <true, true, true>> 
<<G.1, G.1^12, G.1^3, G.1^10>, <true, true, true>> 
<<G.1, G.1^12, G.1^4, G.1^9>, <true, true, true>> 
<<G.1, G.1^12, G.1^5, G.1^8>, <true, true, true>> 
<<G.1, G.1^12, G.1^6, G.1^7>, <true, true, true>> 
<<G.1, G.1^12, G.1^7, G.1^6>, <true, true, true>> 
<<G.1, G.1^12, G.1^8, G.1^5>, <true, true, true>> 
<<G.1, G.1^12, G.1^9, G.1^4>, <true, true, true>> 
<<G.1, G.1^12, G.1^10, G.1^3>, <true, true, true>> 
<<G.1, G.1^12, G.1^11, G.1^2>, <true, true, true>> 
<<G.1, G.1^12, G.1^12, G.1>, <true, true, true>>