Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D9×#10597243 |
| unambiguous semidirect product | C9⋊(C2×#10597243) |
| Fitting, derived, Hall | C9×C112 ⋊ C2×C5 |
| Hall | C9×#10597243 ⋊ C2 |
| Hall | C112×D9 ⋊ C5 |
| Sylow | C112 ⋊ C5×D9 |
| Sylow | C9 ⋊ C2×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C2×C5 |
| Frattini | C3 | D3×#10597243 |
| socle | C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#11925892, D9×#11925895, C2×D9×#10597243 |
| maximal normal subgroup of | D9×#11925892, D9×#11925895, C2×D9×#10597243 |
| maximal quotient of | Dic9×#10597243, C2×D9×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 56);