Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C401 · Schur multiplier (H2) = C1 |
| direct product | D45×C401 |
| unambiguous semidirect product | C5⋊(D9×C401) |
| unambiguous semidirect product | C9⋊(D5×C401) |
| Fitting, Hall | C5×C9×C401 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C2×C401 |
| Hall | C9×C401 ⋊ D5 |
| Hall | C5×C401 ⋊ D9 |
| Sylow | C9 ⋊ D5×C401 |
| Sylow | C5 ⋊ D9×C401 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C401 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C2×C401 |
| Frattini | C3 | D15×C401 |
| Fitting | C5×C9×C401 | C2 |
| socle | C3×C5×C401 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C401 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18045 |
9624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36090, 8);