Automorphism Classes of Quadilateral Actions on Sufaces of Genus 3 

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

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

 
bdata:  3, 16, [ 2, 2, 2, 4 ] 
G = small group 13 of 14 group(s) of order 16 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.4 
1  generating vector(s)
<<G.2, G.1 * G.2 * G.3 * G.4, G.1 * G.4, G.3>, <true, true, true>> 

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

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

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

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

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

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

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