Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D33⋊D19 |
| unambiguous semidirect product | D33⋊(C3×D19) |
| Fitting, socle, Hall | C32×C11×C19 ⋊ C22 |
| derived | C3×C11×C19 ⋊ C22×C3 |
| Hall | C11×C19 ⋊ C2×C3×D3 |
| Hall | C32×C19 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ C3×D3×D11 |
| Sylow | C11 ⋊ C3×D3×D19 |
| Sylow | C32 ⋊ D11×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D33⋊D19 |
| commutator, hypocenter | C3×C11×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C19 | C22 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
549 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D57⋊AGL(1,𝔽11), C3×C5×D33⋊D19, C3×D209⋊D15, … |
| maximal normal subgroup of | C3×D57⋊AGL(1,𝔽11), C3×C5×D33⋊D19 |
| maximal quotient of | C3×C5×D33⋊D19, C3×D209⋊D15, C3×D57⋊D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 87);