Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D131⋊C5) |
| unambiguous semidirect product | (C131⋊C5)⋊D9 |
| unambiguous semidirect product | D1179⋊C5 |
| Fitting, derived, Hall | C9×C131 ⋊ C2×C5 |
| Hall | C9×C131⋊C5 ⋊ C2 |
| Hall | D1179 ⋊ C5 |
| Hall | C131⋊C5 ⋊ D9 |
| Sylow | C131 ⋊ C5×D9 |
| Sylow | C9 ⋊ D131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C131 | C2×C5 |
| Frattini | C3 | C3⋊(D131⋊C5) |
| socle | C3×C131 | C5×D3 |
| LCS | G ▷ C9×C131 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,131,3|b^3=e^2,b^a=b^2e,d^a=d^130,e^a=e^2,d^c=d^53147 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, 12);