C3 ⋊ D8

Also called  (C2×C2, C3) ⋊ C2.

Statistics

Order of group24
GAP identifier24,8
Presentation< k,r,g | k3, g4, r2, gkg3k, (rg)2, [r,k] >
Orders of elements1 of 1, 1+2+6 of 1, 2 of 3, 6 of 4, 2+2*2 of 6
CentreC2
Derived subgroupC6
Automorphism groupC3×C2×C2×C2
Inner automorphism groupD12
"Out" (quotient of above)D6×C2×C2
Schur multiplierC2
Sylow-2-subgroupD8
 

Permutation Diagrams


Not transitive.

Not transitive.

Not transitive.

Cayley Graphs





Regular maps with C3 ⋊ D8 symmetry

C3 ⋊ D8 is the rotational symmetry group of the regular maps S2:{6,4},   S2:{4,6},   S4:{6,12},   S4:{12,6},   cubohemioctahedron.


Index to regular maps

Orientable sphere | torus | 2 | 3 | 4 | 5 | 6
Non-orientable projective plane | 4 | 5 | 6 | 7