Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×C3⋊#1181 |
| unambiguous semidirect product | C3⋊(C3×C23×#1181) |
| Fitting, socle, Hall | C32×C23×C29 ⋊ C4 |
| derived | C3×C29 ⋊ C3×C4×C23 |
| Hall | C23×C29 ⋊ C3×Dic3 |
| Hall | C32×C29 ⋊ C4×C23 |
| Hall | C32×C23 ⋊ #1181 |
| Sylow | C29 ⋊ C3×Dic3×C23 |
| Sylow | C32 ⋊ C23×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C3⋊#1181 |
| commutator, hypocenter | C3×C29 | C3×C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C29 | C4 |
| prime radical | C32×C23×D29 | C2 |
| cosocle | C3×D29 | C2×C3×C23 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C3×C23 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4002 |
1863 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 51);