Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D2005 |
| unambiguous semidirect product | C5⋊(C9×D401) |
| unambiguous semidirect product | C401⋊(C9×D5) |
| Fitting, Hall | C5×C9×C401 ⋊ C2 |
| derived, Hall | C5×C401 ⋊ C2×C9 |
| Hall | C9×C401 ⋊ D5 |
| Sylow | C401 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D401 |
| Sylow | C5 ⋊ C9×D401 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D2005 |
| commutator, hypocenter | C5×C401 | C2×C9 |
| Frattini | C3 | C3×D2005 |
| Fitting | C5×C9×C401 | C2 |
| socle, cosocle | C3×C5×C401 | C2×C3 |
| prime radical | C3×D2005 | C3 |
| LCS | G ▷ C5×C401 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18045 |
9036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36090, 5);