C2×C2×C2 is Abelian, and is a direct product of two smaller groups.


Order of group8
GAP identifier8,5
Presentation< r,g,b | r2, g2, b2, [r,g], [g,b], [b,r] >
Orders of elements1 of 1, 7*1 of 2
Derived subgroup1
Automorphism groupPSL(2,7)
Inner automorphism group1
"Out" (quotient of above)PSL(2,7)
Schur multiplierC2×C2×C2

Permutation Diagrams

Not transitive.

Cayley Graphs

the cube, type I

Regular maps with C2×C2×C2 symmetry

C2×C2×C2 is the full symmetry group of the regular map the 2-hosohedron.

Index to regular maps