Finite Group DatabasebetaFinite Group Databasebeta| order | 31775 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C31⋊C25 |
| unambiguous semidirect product | C31⋊(C25×C41) |
| derived, Sylow | C31 ⋊ C25×C41 |
| Hall | C31×C41 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C41 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C25×C41 |
| Frattini | C5 | C41×ΓL(1,𝔽32) |
| Fitting, socle, prime radical | C5×C31×C41 | C5 |
| cosocle | C5×C31 | C5×C41 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31775 |
2255 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31775, 2);