Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D961 |
| unambiguous semidirect product | (D3×C961)⋊C2 |
| unambiguous semidirect product | (C3×D961)⋊C2 |
| unambiguous semidirect product | D2883⋊C2 |
| Fitting, derived, Hall | C3×C961 ⋊ C22 |
| Sylow | C961 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C961 | C22 |
| Frattini | C31 | D3×D31 |
| socle | C3×C31 | C2×D31 |
| LCS | G ▷ C3×C961 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
1446 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D961, D3×D961⋊C3, C3×D3×D961, … |
| maximal normal subgroup of | D3×D961⋊C3, C3×D3×D961 |
| maximal quotient of | D9×D961, C3×D3×D961, C3⋊D3×D961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 9);