Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D495 |
| unambiguous semidirect product | C5⋊(C11×D99) |
| unambiguous semidirect product | C9⋊(C11×D55) |
| unambiguous semidirect product | C11⋊(C11×D45) |
| Fitting, Hall | C5×C9×C112 ⋊ C2 |
| derived | C5×C9×C11 ⋊ C2×C11 |
| Hall | C9×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C112 ⋊ D45 |
| Hall | C5×C9 ⋊ C11×D11 |
| Sylow | C9 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11×D99 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D495 |
| commutator, cosocle, hypocenter | C5×C9×C11 | C2×C11 |
| Frattini | C3 | C11×D165 |
| Fitting | C5×C9×C112 | C2 |
| socle | C3×C5×C112 | D3 |
| LCS | G ▷ C5×C9×C11 | |
| UCS | C1 ◁ C11 | |
78 conjugacy classes of subgroups.
2739 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D45, D11×D495, #36344937, … |
| maximal normal subgroup of | C11×D11×D45, D11×D495, #36344937, … |
| maximal quotient of | C11×Dic495, C2×C11×D495 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 80);