Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2001 |
| unambiguous semidirect product | (C3×D3)⋊D667 |
| unambiguous semidirect product | (D3×C23)⋊D87 |
| unambiguous semidirect product | (D3×C29)⋊D69 |
| Fitting, socle, derived, Hall | C32×C23×C29 ⋊ C22 |
| Hall | C23×C29 ⋊ D32 |
| Hall | C32×C29 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D69 |
| Sylow | C23 ⋊ D3×D87 |
| Sylow | C32 ⋊ C2×D667 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C23×C29 | C22 |
| LCS | G ▷ C32×C23×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4002 |
3006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 63);