Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D9×C401⋊C5 |
| unambiguous semidirect product | C9⋊(C2×C401⋊C5) |
| unambiguous semidirect product | (D9×C401)⋊C5 |
| Fitting, derived, Hall | C9×C401 ⋊ C2×C5 |
| Hall | C9×C401⋊C5 ⋊ C2 |
| Hall | D9×C401 ⋊ C5 |
| Sylow | C401 ⋊ C5×D9 |
| Sylow | C9 ⋊ C2×C401⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C401 | C2×C5 |
| Frattini | C3 | D3×C401⋊C5 |
| socle | C3×C401 | C5×D3 |
| LCS | G ▷ C9×C401 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3609 |
510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36090, 11);