Finite Group DatabasebetaFinite Group Databasebeta| order | 10769 |
| automorphism | ? |
| homology | Abelianization (H1) = C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C89⋊C121 |
| derived, Sylow | C89 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | C89⋊C11 |
| commutator, hypocenter | C89 | C121 |
| Fitting, socle, prime radical, cosocle | C11×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C11 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
11^2,89|a^11=b,c^a=c^64209 conjugacy classes — view the full character table.
| maximal subgroup of | D89⋊C121, C2×C89⋊C121, C3×C89⋊C121 |
| maximal normal subgroup of | D89⋊C121, C2×C89⋊C121, C3×C89⋊C121 |
| maximal quotient of | C2×C89⋊C121, C3×C89⋊C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10769, 1);