Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C131⋊C5 |
| unambiguous semidirect product | (C2×C131)⋊(C32×C5) |
| unambiguous semidirect product | (C2×C3×C131)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C32×C131)⋊C5 |
| Fitting, socle, Hall | C2×C32×C131 ⋊ C5 |
| derived, Sylow | C131 ⋊ C2×C32×C5 |
| Hall | C32×C131 ⋊ C2×C5 |
| Hall | C2×C131 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C131⋊C5 |
| commutator, cosocle, hypocenter | C131 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C131 | C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
558 conjugacy classes — view the full character table.
| maximal subgroup of | C32×Dic131⋊C5, C3×C3⋊(Dic131⋊C5), C3×Dic3×C131⋊C5, … |
| maximal normal subgroup of | C32×Dic131⋊C5, C3×C3⋊(Dic131⋊C5), C3×Dic3×C131⋊C5, … |
| maximal quotient of | C32×C4×C131⋊C5, C22×C32×C131⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 19);