C2×C2×C2

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

Statistics
Order of group	8
GAP identifier	8,5
Presentation	< r,g,b \| r², g², b², [r,g], [g,b], [b,r] >
Orders of elements	1 of 1, 7*1 of 2
Centre	.5
Derived subgroup	1
Automorphism group	PSL(2,7)
Inner automorphism group	1
"Out" (quotient of above)	PSL(2,7)
Schur multiplier	C2×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