Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C961⋊C3)⋊C4 |
| unambiguous semidirect product | Dic961⋊C3 |
| derived, Sylow | C961 ⋊ C3×C4 |
| Hall | Dic961 ⋊ C3 |
| Hall | C961⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D961⋊C3 |
| commutator, hypocenter | C961 | C3×C4 |
| Frattini, socle | C2×C31 | D31⋊C3 |
| Fitting, cosocle | C2×C961 | C2×C3 |
| prime radical | C2×C961⋊C3 | C2 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31,2,31|a^2=d,c^31=e^30,c^a=c^30e,e^a=e^30,c^b=c^25e^15,e^b=e^25332 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C961⋊C3)⋊C4, C3⋊((C961⋊C3)⋊C4) |
| maximal normal subgroup of | C3×(C961⋊C3)⋊C4 |
| maximal quotient of | Dic961⋊C9, C3×(C961⋊C3)⋊C4, C3⋊((C961⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 2);