Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic627 |
| unambiguous semidirect product | C3⋊(C3×Dic209) |
| unambiguous semidirect product | C11⋊(C3×Dic57) |
| derived | C3×C11×C19 ⋊ C3×C4 |
| Hall | C32×C11×C19 ⋊ C4 |
| Hall | C11×C19 ⋊ C3×Dic3 |
| Hall | C32×C19 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic19 |
| Sylow | C19 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ C3×Dic57 |
| Sylow | C32 ⋊ Dic209 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D627 |
| commutator, hypocenter | C3×C11×C19 | C3×C4 |
| Frattini | C2 | C3×D627 |
| Fitting, socle | C2×C32×C11×C19 | C2 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
1890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 54);