Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D99⋊D19 |
| unambiguous semidirect product | D171⋊D11 |
| unambiguous semidirect product | D209⋊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 ⋊ D9×D19 |
| Sylow | C9 ⋊ D11×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C11×C19 | C22 |
| Frattini | C3 | D33⋊D19 |
| socle | C3×C11×C19 | C2×D3 |
| LCS | G ▷ C9×C11×C19 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,11,19,3|c^3=f^2,d^a=d^10,e^a=e^18,c^b=c^2f,d^b=d^10,f^b=f^2501 conjugacy classes — view the full character table.
| maximal subgroup of | D171⋊AGL(1,𝔽11), C5×D99⋊D19, D209⋊D45, … |
| maximal normal subgroup of | D171⋊AGL(1,𝔽11), C5×D99⋊D19 |
| maximal quotient of | C5×D99⋊D19, D209⋊D45, D171⋊D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 24);