Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D209 |
| Fitting, socle, derived, Hall | C32×C11×C19 ⋊ C22 |
| Hall | C11×C19 ⋊ D32 |
| Hall | C32×C19 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ (C3⋊D3)⋊D11 |
| Sylow | C11 ⋊ (C3⋊D3)⋊D19 |
| Sylow | C32 ⋊ C2×D209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C19 | C22 |
| LCS | G ▷ C32×C11×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,11,19|d^a=d^2,e^a=e^10,f^a=f^18,c^b=c^2,d^b=d^2633 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 103);