Finite Group DatabasebetaFinite Group Databasebeta| order | 8822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D401 |
| unambiguous semidirect product | C401⋊(C2×C11) |
| Fitting, socle, Hall | C11×C401 ⋊ C2 |
| derived, Sylow | C401 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D401 |
| commutator, hypocenter | C401 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C401 | C2 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#13107944, C11⋊#13107944, D11×D401, … |
| maximal normal subgroup of | C11×#13107944, C11⋊#13107944, D11×D401, … |
| maximal quotient of | C11×Dic401, C2×C11×D401, C3×C11×D401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8822, 2);