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

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.

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.

Groups of order 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 27 28 30 48 60 120 168 336 360 720

Index to regular maps