Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C23⋊#11760330 |
| Fitting, socle, derived, Hall | C32×C23×C29 ⋊ C4 |
| Hall | C23×C29 ⋊ #157 |
| Hall | C32×C29 ⋊ Dic23 |
| Hall | C32×C23 ⋊ Dic29 |
| Sylow | C29 ⋊ C23⋊#157 |
| Sylow | C23 ⋊ #11760330 |
| Sylow | C32 ⋊ Dic667 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C23×C29 | C4 |
| prime radical, cosocle | C3⋊D3×C23×C29 | C2 |
| LCS | G ▷ C32×C23×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4002 |
Polycyclic presentation:
2^2,3^2,23,29|a^2=b,c^a=cd,d^a=cd^2,e^a=e^22,f^a=f^28,c^b=c^2,d^b=d^22004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 47);