Finite Group DatabasebetaFinite Group Databasebeta| order | 31785 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×C13×C163⋊C3 |
| unambiguous semidirect product | C163⋊(C3×C5×C13) |
| unambiguous semidirect product | (C5×C163)⋊(C3×C13) |
| Fitting, socle, Hall | C5×C13×C163 ⋊ C3 |
| derived, Sylow | C163 ⋊ C3×C5×C13 |
| Hall | C13×C163 ⋊ C3×C5 |
| Hall | C5×C163 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | C163⋊C3 |
| commutator, cosocle, hypocenter | C163 | C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C163 | C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C5×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10595 |
3705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31785, 2);