Finite Group DatabasebetaFinite Group Databasebeta| order | 31722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C311 · Schur multiplier (H2) = C1 |
| direct product | D51×C311 |
| unambiguous semidirect product | C3⋊(D17×C311) |
| unambiguous semidirect product | C17⋊(D3×C311) |
| Fitting, socle, Hall | C3×C17×C311 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C2×C311 |
| Hall | C17×C311 ⋊ D3 |
| Hall | C3×C311 ⋊ D17 |
| Sylow | C17 ⋊ D3×C311 |
| Sylow | C3 ⋊ D17×C311 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C311 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C311 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C311 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C311 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15861 |
8397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31722, 7);