Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D171 |
| unambiguous semidirect product | (C9×D11)⋊D19 |
| unambiguous semidirect product | (C19×D11)⋊D9 |
| Fitting, derived, Hall | C9×C11×C19 ⋊ C22 |
| Hall | C11×C19 ⋊ C2×D9 |
| Hall | C9×C19 ⋊ C2×D11 |
| Hall | C9×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ D9×D11 |
| Sylow | C11 ⋊ C2×D171 |
| Sylow | C9 ⋊ D11×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C11×C19 | C22 |
| Frattini | C3 | D11×D57 |
| socle | C3×C11×C19 | C2×D3 |
| LCS | G ▷ C9×C11×C19 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
609 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×D171, C5×D11×D171, D11×D855, … |
| maximal normal subgroup of | AGL(1,𝔽11)×D171, C5×D11×D171 |
| maximal quotient of | C5×D11×D171, D11×D855, D55×D171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 22);