D6×C2×C2

D6×C2×C2 is the direct product of two smaller groups.

Statistics Order of group 24 GAP identifier 24,14 Presentation < k,r,g | k6, r2, g2, (kr)2, [k,g], [r,g] > Orders of elements 1 of 1, 3*1+4*3 of 2, 2 of 3, 3*2 of 6 Centre C2×C2 Derived subgroup C3 Automorphism group D6 ⋊ S4 Inner automorphism group D6 "Out" (quotient of above) S4 Schur multiplier C2×C2×C2 Sylow-2-subgroup C2×C2×C2

Permutation Diagrams Not transitive. Not transitive. 1-transitive on 12 points, even.

Cayley Graphs

the 6-hosohedron, type III

Regular maps with D6×C2×C2 symmetry

D6×C2×C2 is the full symmetry group of the regular maps S2:{6,6},   the 6-hosohedron,   the di-hexagon,   the 6-lucanicohedron.

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