Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D171 |
| unambiguous semidirect product | (C2×C9)⋊(C11×D19) |
| unambiguous semidirect product | (C2×C19)⋊(C11×D9) |
| Fitting | C2×C9×C11×C19 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C22×C11 |
| Hall | C9×C11×C19 ⋊ C22 |
| Hall | C11×C19 ⋊ C2×D9 |
| Hall | C9×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C11×D9 |
| Sylow | C9 ⋊ C2×C11×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D171 |
| commutator, hypocenter | C9×C19 | C22×C11 |
| Frattini | C3 | C2×C11×D57 |
| Fitting | C2×C9×C11×C19 | C2 |
| socle | C2×C3×C11×C19 | D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C2×C11 | |
60 conjugacy classes of subgroups.
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊C5×D171, D5×C11×D171, C2×C11×D855, … |
| maximal normal subgroup of | C2×C11⋊C5×D171, C2×C5×C11×D171 |
| maximal quotient of | D5×C11×D171, C2×C11×D855, C2×C5×C11×D171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 32);