Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D655 |
| unambiguous semidirect product | C5⋊(C32×D131) |
| unambiguous semidirect product | C131⋊(C32×D5) |
| Fitting, socle, Hall | C32×C5×C131 ⋊ C2 |
| derived, Hall | C5×C131 ⋊ C2×C32 |
| Hall | C32×C131 ⋊ D5 |
| Sylow | C131 ⋊ C32×D5 |
| Hall | C32×C5 ⋊ D131 |
| Sylow | C5 ⋊ C32×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D655 |
| commutator, cosocle, hypocenter | C5×C131 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C131 | C2 |
| LCS | G ▷ C5×C131 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
2961 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D131, C3×D3×D655, C3×D15⋊D131, … |
| maximal normal subgroup of | C32×D5×D131, C3×D3×D655, C3×D15⋊D131, … |
| maximal quotient of | C32×Dic655, C2×C32×D655 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 28);