Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D9×D19 |
| unambiguous semidirect product | (D9×C19)⋊(C2×C11) |
| unambiguous semidirect product | (C9×D19)⋊(C2×C11) |
| unambiguous semidirect product | D171⋊(C2×C11) |
| Fitting, Hall | C9×C11×C19 ⋊ C22 |
| derived, Hall | C9×C19 ⋊ C22×C11 |
| Hall | C11×C19 ⋊ C2×D9 |
| Hall | C9×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C11×D9 |
| Sylow | C9 ⋊ C2×C11×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D9×D19 |
| commutator, hypocenter | C9×C19 | C22×C11 |
| Frattini | C3 | D3×C11×D19 |
| Fitting | C9×C11×C19 | C22 |
| socle | C3×C11×C19 | C2×D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C11 | |
60 conjugacy classes of subgroups.
726 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D19×C11⋊C5, C5×C11×D9×D19, C11×D19×D45, … |
| maximal normal subgroup of | D9×D19×C11⋊C5, C5×C11×D9×D19 |
| maximal quotient of | C5×C11×D9×D19, C11×D19×D45, C11×D9×D95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 19);