Finite Group DatabasebetaFinite Group Databasebeta| order | 31465 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived, Hall | C29×C31 ⋊ C5×C7 |
| Hall | C31×C29⋊C7 ⋊ C5 |
| Hall | C29×ΓL(1,𝔽32) ⋊ C7 |
| Sylow | C31 ⋊ C5×C29⋊C7 |
| Sylow | C29 ⋊ C7×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C31 | C5×C7 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 899 |
121 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31465, 4);