Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D99 |
| unambiguous semidirect product | C9⋊(D11×C11⋊C5) |
| Fitting, derived, Hall | C9×C112 ⋊ C2×C5 |
| Hall | C9×C11×C11⋊C5 ⋊ C2 |
| Hall | C11×D99 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| Sylow | C9 ⋊ D11×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C2×C5 |
| Frattini | C3 | C11⋊C5×D33 |
| socle | C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
51 conjugacy classes of subgroups.
357 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×D99, (C9⋊AGL(1,𝔽11))⋊D11, D9×D11×C11⋊C5, … |
| maximal normal subgroup of | AGL(1,𝔽11)×D99, (C9⋊AGL(1,𝔽11))⋊D11, D9×D11×C11⋊C5, … |
| maximal quotient of | C11⋊C5×Dic99, C2×C11⋊C5×D99 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 59);