Finite Group DatabasebetaFinite Group Databasebeta| order | 11132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C4×C23⋊C121 |
| unambiguous semidirect product | (C4×C23)⋊C121 |
| derived, Sylow | C23 ⋊ C4×C121 |
| Hall | C4×C23 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C11 | C23⋊C11 |
| commutator, hypocenter | C23 | C4×C121 |
| Frattini | C2×C11 | C2×C23⋊C11 |
| Fitting | C4×C11×C23 | C11 |
| socle, prime radical, cosocle | C2×C11×C23 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C4×C11 | |
18 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×C23⋊C121, C3×C4×C23⋊C121 |
| maximal normal subgroup of | C3×C4×C23⋊C121 |
| maximal quotient of | Dic3×C23⋊C121, C3×C4×C23⋊C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11132, 3);