Finite Group DatabasebetaFinite Group Databasebeta| order | 8811 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C9×C89⋊C11 |
| unambiguous semidirect product | C89⋊(C9×C11) |
| unambiguous semidirect product | (C9×C89)⋊C11 |
| Fitting, Hall | C9×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C89⋊C11 |
| commutator, hypocenter | C89 | C9×C11 |
| Frattini | C3 | C3×C89⋊C11 |
| Fitting | C9×C89 | C11 |
| socle | C3×C89 | C3×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
171 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×C89⋊C11, C9×D89⋊C11, D9×C89⋊C11, … |
| maximal normal subgroup of | C2×C9×C89⋊C11, C9×D89⋊C11, D9×C89⋊C11, … |
| maximal quotient of | C2×C9×C89⋊C11, C22⋊C9×C89⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8811, 2);