Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic171 |
| unambiguous semidirect product | C9⋊(C11×Dic19) |
| unambiguous semidirect product | C19⋊(C11×Dic9) |
| derived, Hall | C9×C19 ⋊ C4×C11 |
| Hall | C9×C11×C19 ⋊ C4 |
| Hall | C11×C19 ⋊ Dic9 |
| Hall | C9×C11 ⋊ Dic19 |
| Sylow | C19 ⋊ C11×Dic9 |
| Sylow | C9 ⋊ C11×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D171 |
| commutator, hypocenter | C9×C19 | C4×C11 |
| Frattini | C2×C3 | C11×D57 |
| Fitting | C2×C9×C11×C19 | C2 |
| socle | C2×C3×C11×C19 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C2×C11 | |
36 conjugacy classes of subgroups.
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×Dic171, C11×Dic855, C11⋊C5×Dic171, … |
| maximal normal subgroup of | C5×C11×Dic171, C11⋊C5×Dic171 |
| maximal quotient of | C5×C11×Dic171, C11×Dic855, C11×C9⋊(C19⋊AGL(1,𝔽5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 10);