S4×C2

Also called full octahedral group.

S4×C2 is the direct product of two smaller groups.

Statistics
Order of group	48
GAP identifier	48,48
Presentation
Orders of elements
Centre	C2
Derived subgroup	A4
Automorphism group	S4×C2
Inner automorphism group	S4
"Out" (quotient of above)	C2
Schur multiplier	C2×C2
Sylow-2-subgroup	D8×C2

Permutation Diagrams

1-transitive on 6
points, odd.

1-transitive on 6
points, odd.

1-transitive on 6
points, odd.

1-transitive on 6
points, odd.

Cayley Graphs

sphere/trunco

the cube, type III

Regular maps with S4×C2 symmetry

S4×C2 is the rotational symmetry group of the regular maps C4:{4,6}₆, C4:{4,6}₃, C4:{6,4}₃, rectification of C4:{6,4}₃.

S4×C2 is the full symmetry group of the regular maps {3,6}_(2,2), {6,3}_(2,2), the octahedron, the cube, the cuboctahedron, octahemioctahedron, small cubicuboctahedron.

Index to regular maps