Finite Group DatabasebetaFinite Group Databasebeta| order | 36765 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#20301353 |
| Fitting, socle, Hall | C5×C19×C43 ⋊ C9 |
| derived, Hall | C19×C43 ⋊ C5×C9 |
| Hall | C5×C43 ⋊ #4296 |
| Hall | C5×C19 ⋊ C43⋊C9 |
| Sylow | C43 ⋊ C5×#4296 |
| Sylow | C19 ⋊ C5×C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20301353 |
| commutator, hypocenter | C19×C43 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C43 | C9 |
| prime radical | C5×C43×C19⋊C3 | C3 |
| cosocle | C43×C19⋊C3 | C3×C5 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4085 |
685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36765, 8);