Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊(C3⋊#1181) |
| unambiguous semidirect product | C3⋊(C23×C3⋊#1181) |
| Fitting, socle, Hall | C32×C23×C29 ⋊ C4 |
| derived, Hall | C32×C29 ⋊ C4×C23 |
| Hall | C23×C29 ⋊ C3⋊Dic3 |
| Hall | C32×C23 ⋊ #1181 |
| Sylow | C29 ⋊ C23×C3⋊Dic3 |
| Sylow | C32 ⋊ C23×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C3⋊#1181) |
| commutator, hypocenter | C32×C29 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C29 | C4 |
| prime radical | C32×C23×D29 | C2 |
| cosocle | C32×D29 | C2×C23 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C23 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6003 |
1725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 69);