Finite Group DatabasebetaFinite Group Databasebeta| order | 31786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C691⋊C23 |
| unambiguous semidirect product | (C2×C691)⋊C23 |
| Fitting, socle, Hall | C2×C691 ⋊ C23 |
| derived, Sylow | C691 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C691⋊C23 |
| commutator, cosocle, hypocenter | C691 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C691 | C23 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1382 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31786, 2);