A4×C2

A4×C2 is the direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,13
Presentation< r,g,b,e | r2, g2, b2, e3, (rg)2, (gb)2, (br)2, gere2, bege2, rebe2 >
Orders of elements1 of 1, 1+3+3 of 2, 2*4 of 3, 2*4 of 6
CentreC2
Derived subgroupC2×C2
Automorphism groupS4
Inner automorphism groupA4
"Out" (quotient of above)C2
Schur multiplierC2
Sylow-2-subgroupC2×C2×C2
 

Permutation Diagrams


1-transitive on 6
points, odd.

2-transitive on 6
points, odd.

2-transitive on 6
points, odd.

1-transitive on 6
points, odd.

1-transitive on 8
points, even.

Cayley Graphs


the cube, type IIa



{6,3}(2,2), type IIa

{6,3}(0,4), type I

Regular maps with A4×C2 symmetry

A4×C2 is the rotational symmetry group of the regular maps {3,6}(2,2),   {6,3}(2,2),   S3:{6,6},   octahemioctahedron.


Index to regular maps

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