Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D33×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×D33) |
| unambiguous semidirect product | (C3×D19⋊C3)⋊D11 |
| unambiguous semidirect product | (C11×D19⋊C3)⋊D3 |
| unambiguous semidirect product | (D19×D33)⋊C3 |
| Fitting, socle, derived | C3×C11×C19 ⋊ C22×C3 |
| Hall | C3×C11×C19⋊C3 ⋊ C22 |
| Hall | C11×C19 ⋊ C2×C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×D11 |
| Sylow | C19 ⋊ C2×C3×D33 |
| Sylow | C11 ⋊ D3×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C19 | C22×C3 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
162 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×C3⋊AGL(1,𝔽11), C5×D33×D19⋊C3, D19⋊C3×D165, … |
| maximal normal subgroup of | D19⋊C3×C3⋊AGL(1,𝔽11), C5×D33×D19⋊C3 |
| maximal quotient of | C5×D33×D19⋊C3, D19⋊C3×D165, D33×C5⋊(D19⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 66);