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
Centre(2.1)
Derived subgroup(4.2)
Automorphism group(24.12)
Inner automorphism group(12.3)
"Out" (quotient of above)(2.1)
Schur multiplier(2.1)
Sylow-2-subgroup(8.5)
 

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 regular map with C&D number R0.2p, type IIa



the regular map with C&D number R1.t2-2p, type IIa

the regular map with C&D number R1.t0-4p, type I

Regular maps with A4×C2 symmetry

A4×C2 is the rotational symmetry group of the regular maps the regular map with C&D number R1.t2-2,   the regular map with C&D number R1.t2-2p,   the regular map with C&D number R3.8,   the regular map with C&D number Q1.t2-2.


Index to regular maps