Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C19 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×C19×D11 |
| unambiguous semidirect product | (D3×C11)⋊(C2×C3×C19) |
| unambiguous semidirect product | (C3×D11)⋊(C2×C3×C19) |
| unambiguous semidirect product | D33⋊(C2×C3×C19) |
| Fitting, socle, Hall | C32×C11×C19 ⋊ C22 |
| derived | C3×C11 ⋊ C22×C3×C19 |
| Hall | C11×C19 ⋊ C2×C3×D3 |
| Hall | C32×C19 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C22×C19 |
| Sylow | C11 ⋊ C2×C3×D3×C19 |
| Sylow | C32 ⋊ C2×C19×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | D3×D11 |
| commutator, hypocenter | C3×C11 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C19 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C3×C19 | |
88 conjugacy classes of subgroups.
1197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 84);