Finite Group DatabasebetaFinite Group Databasebeta| order | 31065 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C5×C19) |
| unambiguous semidirect product | (C5×C109)⋊(C3×C19) |
| Fitting, socle, Hall | C5×C19×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C5×C19 |
| Hall | C19×C109 ⋊ C3×C5 |
| Hall | C5×C109 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C3×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C5×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10355 |
3705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31065, 2);