Finite Group DatabasebetaFinite Group Databasebeta| order | 36165 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C2411⋊C5 |
| unambiguous semidirect product | C2411⋊(C3×C5) |
| unambiguous semidirect product | (C3×C2411)⋊C5 |
| Fitting, socle, Hall | C3×C2411 ⋊ C5 |
| derived, Sylow | C2411 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C2411⋊C5 |
| commutator, cosocle, hypocenter | C2411 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2411 | C5 |
| LCS | G ▷ C2411 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7233 |
1461 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36165, 1);