Finite Group DatabasebetaFinite Group Databasebeta| order | 10769 |
| automorphism | ? |
| homology | Abelianization (H1) = C112 · Schur multiplier (H2) = C11 |
| direct product | C11×C89⋊C11 |
| unambiguous semidirect product | C89⋊C112 |
| unambiguous semidirect product | (C11×C89)⋊C11 |
| Fitting, socle | C11×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C112 |
| Frattini | C1 | G |
| Fitting, socle | C11×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C11 | |
28 conjugacy classes of subgroups.
209 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D89⋊C11, C11⋊(D89⋊C11), D11×C89⋊C11, … |
| maximal normal subgroup of | C11×D89⋊C11, C11⋊(D89⋊C11), D11×C89⋊C11, … |
| maximal quotient of | C2×C11×C89⋊C11, C3×C11×C89⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10769, 3);