Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×Dic33 |
| unambiguous semidirect product | C3⋊(Dic11×C19⋊C3) |
| unambiguous semidirect product | C11⋊(Dic3×C19⋊C3) |
| unambiguous semidirect product | (C19×Dic33)⋊C3 |
| derived | C3×C11×C19 ⋊ C3×C4 |
| Hall | C3×C11×C19⋊C3 ⋊ C4 |
| Hall | C11×C19 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ Dic11 |
| Sylow | C19 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ Dic3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×D33 |
| commutator, hypocenter | C3×C11×C19 | C3×C4 |
| Fitting, socle | C2×C3×C11×C19 | C2×C3 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 46);