Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D207⋊D29 |
| unambiguous semidirect product | D261⋊D23 |
| unambiguous semidirect product | D667⋊D9 |
| Fitting, derived, Hall | C9×C23×C29 ⋊ C22 |
| Hall | C23×C29 ⋊ C2×D9 |
| Hall | C9×C29 ⋊ C2×D23 |
| Hall | C9×C23 ⋊ C2×D29 |
| Sylow | C29 ⋊ D9×D23 |
| Sylow | C23 ⋊ D9×D29 |
| Sylow | C9 ⋊ D23×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C23×C29 | C22 |
| Frattini | C3 | D69⋊D29 |
| socle | C3×C23×C29 | C2×D3 |
| LCS | G ▷ C9×C23×C29 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6003 |
Polycyclic presentation:
2^2,3,23,29,3|c^3=f^2,d^a=d^22,e^a=e^28,c^b=c^2f,d^b=d^22,f^b=f^21548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 20);