S4×C2

Also called  full octahedral group.

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

Statistics

Order of group48
GAP identifier48,48
Presentation
Orders of elements
CentreC2
Derived subgroupA4
Automorphism groupS4×C2
Inner automorphism groupS4
"Out" (quotient of above)C2
Schur multiplierC2×C2
Sylow-2-subgroupD8×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


the cube, type III

Regular maps with S4×C2 symmetry

S4×C2 is the rotational symmetry group of the regular maps N4:{4,6}6,   N4:{4,6}3,   N4:{6,4}3,   rectification of C4:{6,4}3.