GL(2,3)

Also called  C2 ↑ S4.

Statistics

Order of group48
GAP identifier48,29
Presentation
Orders of elements1 of 1, 1+12 of 2, 8 of 3, 6 of 4, 8 of 6, 2*6 of 8
CentreC2
Derived subgroupSL(2,3)
Automorphism groupS4×C2
Inner automorphism groupS4
"Out" (quotient of above)C2
Schur multiplier1
Sylow-2-subgroupquasidihedral(16)
 

Permutation Diagrams


1-transitive on 6
points, odd.

1-transitive on 8
points, odd.

1-transitive on 8
points, odd.

1-transitive on 8
points, odd.

1-transitive on 8
points, odd.

1-transitive on 16
points, even.

Cayley Graphs


S2:{8,3}, type II

Regular maps with GL(2,3) symmetry

GL(2,3) is the rotational symmetry group of the regular maps S2:{8,3},   S2:{3,8}.


Index to regular maps