D6×C4

D6×C4 is the direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,5
Presentation< k,r,g | k3, r2, g4, (kr)2, [k,g], [r,g] >
Orders of elements1 of 1, 1+2*3 of 2, 2 of 3, 2*1+2*3 of 4, 2 of 6, 2*2 of 12
CentreC4
Derived subgroupC3
Automorphism groupD6×C2×C2
Inner automorphism groupD6
"Out" (quotient of above)C2×C2
Schur multiplierC2
Sylow-2-subgroupC4×C2
 

Permutation Diagrams


Not transitive.

Not transitive.

Cayley Graphs




Regular maps with D6×C4 symmetry

D6×C4 is the rotational symmetry group of the regular maps S3:{12,4},   S3:{4,12},   rectification of S3:{12,4}.


Index to regular maps

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