Finite Group DatabasebetaFinite Group Databasebeta| order | 11790 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C131 · Schur multiplier (H2) = C1 |
| direct product | D45×C131 |
| unambiguous semidirect product | C5⋊(D9×C131) |
| unambiguous semidirect product | C9⋊(D5×C131) |
| Fitting, Hall | C5×C9×C131 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C2×C131 |
| Hall | C9×C131 ⋊ D5 |
| Hall | C5×C131 ⋊ D9 |
| Sylow | C9 ⋊ D5×C131 |
| Sylow | C5 ⋊ D9×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C2×C131 |
| Frattini | C3 | D15×C131 |
| Fitting | C5×C9×C131 | C2 |
| socle | C3×C5×C131 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C131 | |
24 conjugacy classes of subgroups.
3144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×D131, D5×D9×C131, D45⋊D131, … |
| maximal normal subgroup of | D45×D131, D5×D9×C131, D45⋊D131, … |
| maximal quotient of | C131×Dic45, C2×D45×C131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11790, 8);