Finite Group DatabasebetaFinite Group Databasebeta| order | 5895 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C131⋊C5 |
| unambiguous semidirect product | C131⋊(C5×C9) |
| unambiguous semidirect product | (C9×C131)⋊C5 |
| Fitting, Hall | C9×C131 ⋊ C5 |
| derived, Sylow | C131 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C131⋊C5 |
| commutator, hypocenter | C131 | C5×C9 |
| Frattini | C3 | C3×C131⋊C5 |
| Fitting | C9×C131 | C5 |
| socle | C3×C131 | C3×C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
279 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×C131⋊C5, C9×D131⋊C5, D9×C131⋊C5, … |
| maximal normal subgroup of | C2×C9×C131⋊C5, C9×D131⋊C5, D9×C131⋊C5, … |
| maximal quotient of | C2×C9×C131⋊C5, C22⋊C9×C131⋊C5, C9×C131⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5895, 2);