D8×C2 is the direct product of two smaller groups.


Order of group16
GAP identifier16,11
Presentation< k,r,g | k4, r2, g2, (kr)2, [k,g], [r,g] >
Orders of elements1 of 1, 1+2*1+4*2 of 2, 2*2 of 4
Derived subgroupC2
Automorphism groupa group of order 64
Inner automorphism groupC2×C2
"Out" (quotient of above)a group of order 16
Schur multiplierC2×C2×C2

Permutation Diagrams

Not transitive.

Cayley Graphs

the 4-hosohedron, type III

{4,4}(4,0), type I

Regular maps with D8×C2 symmetry

D8×C2 is the full symmetry group of the regular maps {4,4}(1,1),   the 4-hosohedron,   the di-square,   the 4-lucanicohedron.

Index to regular maps