Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C131⋊C5 |
| unambiguous semidirect product | C3⋊(D3×C131⋊C5) |
| unambiguous semidirect product | (C3⋊D3×C131)⋊C5 |
| Fitting, socle, derived, Hall | C32×C131 ⋊ C2×C5 |
| Hall | C32×C131⋊C5 ⋊ C2 |
| Hall | C3⋊D3×C131 ⋊ C5 |
| Sylow | C131 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×C131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C131 | C2×C5 |
| LCS | G ▷ C32×C131 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
186 conjugacy classes — view the full character table.
| maximal subgroup of | (C131⋊C5)⋊#157, #157×C131⋊C5, (C3⋊D3)⋊(D131⋊C5), … |
| maximal normal subgroup of | (C131⋊C5)⋊#157, #157×C131⋊C5, (C3⋊D3)⋊(D131⋊C5), … |
| maximal quotient of | C3⋊Dic3×C131⋊C5, C2×C3⋊D3×C131⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 18);