Finite Group DatabasebetaFinite Group Databasebeta| order | 31465 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C31×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C5×C7×C31) |
| unambiguous semidirect product | (C5×C29)⋊(C7×C31) |
| unambiguous semidirect product | (C5×C29×C31)⋊C7 |
| Fitting, socle, Hall | C5×C29×C31 ⋊ C7 |
| derived, Sylow | C29 ⋊ C5×C7×C31 |
| Hall | C29×C31 ⋊ C5×C7 |
| Hall | C5×C29 ⋊ C7×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C31 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C5×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C31 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C5×C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4495 |
1705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31465, 2);