Finite Group DatabasebetaFinite Group Databasebeta| order | 31775 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C41 · Schur multiplier (H2) = C5 |
| direct product | C5×C41×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊(C52×C41) |
| unambiguous semidirect product | (C5×C31)⋊(C5×C41) |
| Fitting, socle | C5×C31×C41 ⋊ C5 |
| derived, Sylow | C31 ⋊ C52×C41 |
| Hall | C31×C41 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C41 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C52×C41 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C41 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C41 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6355 |
2255 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31775, 11);