Finite Group DatabasebetaFinite Group Databasebeta| order | 31775 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#20263758 |
| Fitting, socle | C5×C31×C41 ⋊ C5 |
| derived, Hall | C31×C41 ⋊ C52 |
| Sylow | C41 ⋊ C5×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20263758 |
| commutator, cosocle, hypocenter | C31×C41 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C41 | C5 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6355 |
1295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31775, 14);