Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D165 |
| unambiguous semidirect product | C3⋊(C11×D165) |
| unambiguous semidirect product | C5⋊(C11×C3⋊D33) |
| unambiguous semidirect product | C11⋊(C11×C3⋊D15) |
| Fitting, socle, Hall | C32×C5×C112 ⋊ C2 |
| derived | C32×C5×C11 ⋊ C2×C11 |
| Hall | C32×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ C11×D11 |
| Sylow | C32 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11×C3⋊D33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D165 |
| commutator, cosocle, hypocenter | C32×C5×C11 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C2 |
| LCS | G ▷ C32×C5×C11 | |
| UCS | C1 ◁ C11 | |
156 conjugacy classes of subgroups.
2739 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D165, C11×D15×D33, D33⋊D165, … |
| maximal normal subgroup of | D3×C11×D165, C11×D15×D33, D33⋊D165, … |
| maximal quotient of | C11×C3⋊Dic165, C2×C11×C3⋊D165 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 147);