Finite Group DatabasebetaFinite Group Databasebeta| order | 11132 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D121 |
| unambiguous semidirect product | C121⋊(C22×C23) |
| unambiguous semidirect product | (C2×C121)⋊(C2×C23) |
| Fitting | C2×C23×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C22×C23 |
| Hall | C23×C121 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D121 |
| commutator, cosocle, hypocenter | C121 | C22×C23 |
| Frattini | C11 | C2×D11×C23 |
| Fitting | C2×C23×C121 | C2 |
| socle | C2×C11×C23 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C2×C23 | |
30 conjugacy classes of subgroups.
2852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C23×D121, C2×C23×D363, C2×C3×C23×D121 |
| maximal normal subgroup of | C2×C3×C23×D121 |
| maximal quotient of | D3×C23×D121, C2×C23×D363, C2×C3×C23×D121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11132, 12);