Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1179 |
| unambiguous semidirect product | C9⋊(C5×D131) |
| Fitting, Hall | C5×C9×C131 ⋊ C2 |
| derived, Hall | C9×C131 ⋊ C2×C5 |
| Hall | C5×C131 ⋊ D9 |
| Sylow | C131 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ D131 |
| Sylow | C9 ⋊ C5×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1179 |
| commutator, cosocle, hypocenter | C9×C131 | C2×C5 |
| Frattini | C3 | C5×D393 |
| Fitting | C5×C9×C131 | C2 |
| socle | C3×C5×C131 | D3 |
| LCS | G ▷ C9×C131 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
2955 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D131, D5×D1179, D45⋊D131, … |
| maximal normal subgroup of | C5×D9×D131, D5×D1179, D45⋊D131, … |
| maximal quotient of | C5×Dic1179, C2×C5×D1179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 7);