C24

Also called  C8×C3.

C24 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group24
GAP identifier24,2
Presentation< k | k24 >
Orders of elements1 of 1, 1 of 2, 2*1 of 3, 2*1 of 4, 4*1 of 8, 6*1 of 12, 6*1 of 24
CentreC24
Derived subgroup1
Automorphism groupC2×C2×C2
Inner automorphism group1
"Out" (quotient of above)C2×C2×C2
Schur multiplier1
Sylow-2-subgroupC8
 

Permutation Diagrams


Not transitive.

Not transitive.

Sharply 1-transitive
on 24 points, odd.

Cayley Graphs






Regular maps with C24 symmetry

C24 is the rotational symmetry group of the regular map S6:{24,24}.


Index to regular maps

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