Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D99 |
| unambiguous semidirect product | C9⋊(C5×C11×D11) |
| Fitting, Hall | C5×C9×C112 ⋊ C2 |
| derived | C9×C11 ⋊ C2×C5×C11 |
| Hall | C9×C112 ⋊ C2×C5 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ C11×D11 |
| Sylow | C9 ⋊ C5×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D99 |
| commutator, cosocle, hypocenter | C9×C11 | C2×C5×C11 |
| Frattini | C3 | C5×C11×D33 |
| Fitting | C5×C9×C112 | C2 |
| socle | C3×C5×C112 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C5×C11 | |
78 conjugacy classes of subgroups.
2805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×D9×D11, C5×D11×D99, C5×D99⋊D11, … |
| maximal normal subgroup of | C5×C11×D9×D11, C5×D11×D99, C5×D99⋊D11, … |
| maximal quotient of | C5×C11×Dic99, C2×C5×C11×D99 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 77);