Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×#4296 |
| unambiguous semidirect product | C11⋊(C22×#4296) |
| unambiguous semidirect product | (C2×C11)⋊(C2×#4296) |
| Fitting, socle | C2×C11×C19 ⋊ C2×C9 |
| derived, Hall | C11×C19 ⋊ C22×C9 |
| Hall | C11×#4296 ⋊ C22 |
| Hall | C2×C19×D11 ⋊ C9 |
| Sylow | C19 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C22×#4296 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D11×#4296 |
| commutator, hypocenter | C11×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C19 | C2×C9 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽11)×#4296, D5×D11×#4296, C2×C5×D11×#4296, … |
| maximal normal subgroup of | C2×AGL(1,𝔽11)×#4296, C2×C5×D11×#4296 |
| maximal quotient of | D5×D11×#4296, C2×C5×D11×#4296, C2×D55×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 63);