Finite Group DatabasebetaFinite Group Databasebeta| order | 31065 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#20261880 |
| Fitting, socle, Hall | C5×C19×C109 ⋊ C3 |
| derived, Hall | C19×C109 ⋊ C3×C5 |
| Hall | C5×C109 ⋊ C19⋊C3 |
| Sylow | C109 ⋊ C5×C19⋊C3 |
| Hall | C5×C19 ⋊ C109⋊C3 |
| Sylow | C19 ⋊ C5×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20261880 |
| commutator, cosocle, hypocenter | C19×C109 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C109 | C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10355 |
3465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31065, 4);