Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic11×#4294 |
| unambiguous semidirect product | C11⋊(C4×#4294) |
| derived, Hall | C11×C19 ⋊ C4×C9 |
| Hall | C11×#4294 ⋊ C4 |
| Hall | C19×Dic11 ⋊ C9 |
| Sylow | C19 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ C4×#4294 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D11×C19⋊C3 |
| commutator, hypocenter | C11×C19 | C4×C9 |
| Fitting, socle | C2×C3×C11×C19 | C2×C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
378 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic11×#4294, #4294×Dic55, #4294×Dic11⋊C5, … |
| maximal normal subgroup of | C5×Dic11×#4294, #4294×Dic11⋊C5 |
| maximal quotient of | C5×Dic11×#4294, #4294×Dic55, #4294×C11⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 3);