Finite Group DatabasebetaFinite Group Databasebeta| order | 36090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D2005 |
| unambiguous semidirect product | C5⋊(C32×D401) |
| unambiguous semidirect product | C401⋊(C32×D5) |
| Fitting, socle, Hall | C32×C5×C401 ⋊ C2 |
| derived, Hall | C5×C401 ⋊ C2×C32 |
| Hall | C32×C401 ⋊ D5 |
| Sylow | C401 ⋊ C32×D5 |
| Hall | C32×C5 ⋊ D401 |
| Sylow | C5 ⋊ C32×D401 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D2005 |
| commutator, cosocle, hypocenter | C5×C401 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C401 | C2 |
| LCS | G ▷ C5×C401 | |
| UCS | C1 ◁ C32 | |
48 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, 22);