Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic961 |
| derived, Sylow | C961 ⋊ C3×C4 |
| Hall | C3×C961 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D961 |
| commutator, hypocenter | C961 | C3×C4 |
| Frattini | C2×C31 | C3×D31 |
| Fitting | C2×C3×C961 | C2 |
| socle, prime radical | C2×C3×C31 | D31 |
| cosocle | C2×C961 | C2×C3 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
2892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic961⋊C9, C9×Dic961, C3×(C961⋊C3)⋊C4, … |
| maximal normal subgroup of | Dic961⋊C9, C9×Dic961, C3×(C961⋊C3)⋊C4, … |
| maximal quotient of | C9×Dic961, C32×Dic961, C3×Dic2883 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 5);