GL(2,3)

Also called C2 ↑ S4.

Statistics
Order of group	48
GAP identifier	48,29
Presentation
Orders of elements	1 of 1, 1+12 of 2, 8 of 3, 6 of 4, 8 of 6, 2*6 of 8
Centre	C2
Derived subgroup	SL(2,3)
Automorphism group	S4×C2
Inner automorphism group	S4
"Out" (quotient of above)	C2
Schur multiplier	1
Sylow-2-subgroup	quasidihedral(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