C3×C2×C2×C2

C3×C2×C2×C2 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,15
Presentation< r,g,e | r2, g2, e6, [r,g], [g,e], [e,r] >
Orders of elements1 of 1, 7*1 of 2, 6*1 of 3, 14*1 of 6
CentreC3×C2×C2×C2
Derived subgroup1
Automorphism groupPSL(3,2)×C2
Inner automorphism group1
"Out" (quotient of above)PSL(3,2)×C2
Schur multiplierC2×C2×C2
Sylow-2-subgroupC2×C2×C2
 

Permutation Diagrams


Not transitive.

Cayley Graphs





Index to regular maps

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