Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D131⋊C5 |
| unambiguous semidirect product | D131⋊(C5×C9) |
| unambiguous semidirect product | (C131⋊C5)⋊(C2×C9) |
| unambiguous semidirect product | (C9×D131)⋊C5 |
| Fitting, Hall | C9×C131 ⋊ C2×C5 |
| derived, Sylow | C131 ⋊ C2×C5×C9 |
| Hall | C9×C131⋊C5 ⋊ C2 |
| Hall | C9×D131 ⋊ C5 |
| Hall | C131⋊C5 ⋊ C2×C9 |
| Hall | D131 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D131⋊C5 |
| commutator, hypocenter | C131 | C2×C5×C9 |
| Frattini | C3 | C3×D131⋊C5 |
| Fitting | C9×C131 | C2×C5 |
| socle, cosocle | C3×C131 | C2×C3×C5 |
| prime radical | C3×D131⋊C5 | C3 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
207 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D131⋊C5, C2×C9×D131⋊C5 |
| maximal normal subgroup of | D9×D131⋊C5, C2×C9×D131⋊C5 |
| maximal quotient of | C9×Dic131⋊C5, C2×C9×D131⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 10);