Finite Group DatabasebetaFinite Group Databasebeta| order | 36765 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×C43×#4296 |
| Fitting, socle, Hall | C5×C19×C43 ⋊ C9 |
| derived, Sylow | C19 ⋊ C5×C9×C43 |
| Hall | C19×C43 ⋊ C5×C9 |
| Hall | C5×C19 ⋊ C9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C43 | #4296 |
| commutator, hypocenter | C19 | C5×C9×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C43 | C9 |
| prime radical | C5×C43×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C3×C5×C43 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4085 |
2365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36765, 7);