Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1 |
| direct product | C11×C19×Dic9 |
| unambiguous semidirect product | C9⋊(C4×C11×C19) |
| derived, Sylow | C9 ⋊ C4×C11×C19 |
| Hall | C9×C11×C19 ⋊ C4 |
| Hall | C9×C19 ⋊ C4×C11 |
| Hall | C9×C11 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C19 | D9 |
| commutator, hypocenter | C9 | C4×C11×C19 |
| Frattini | C2×C3 | D3×C11×C19 |
| Fitting | C2×C9×C11×C19 | C2 |
| socle | C2×C3×C11×C19 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C11×C19 | |
36 conjugacy classes of subgroups.
2508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×C19×Dic9, C11×C19×Dic45, C19×Dic9×C11⋊C5, … |
| maximal normal subgroup of | C5×C11×C19×Dic9, C19×Dic9×C11⋊C5 |
| maximal quotient of | C5×C11×C19×Dic9, C11×C19×Dic45, C11×C19×C9⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 9);