Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic209 |
| unambiguous semidirect product | C11⋊(C32×Dic19) |
| derived, Hall | C11×C19 ⋊ C32×C4 |
| Hall | C32×C11×C19 ⋊ C4 |
| Hall | C32×C19 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic19 |
| Sylow | C19 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C32×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D209 |
| commutator, hypocenter | C11×C19 | C32×C4 |
| Frattini | C2 | C32×D209 |
| Fitting, socle | C2×C32×C11×C19 | C2 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
1908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C19⋊(Dic11⋊C5), C32×Dic1045, C32×C5×Dic209, … |
| maximal normal subgroup of | C32×C19⋊(Dic11⋊C5), C32×C5×Dic209 |
| maximal quotient of | C32×Dic1045, C32×C5×Dic209, C32×C11⋊(C19⋊AGL(1,𝔽5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 50);