Finite Group DatabasebetaFinite Group Databasebeta| order | 31713 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C961⋊C3 |
| unambiguous semidirect product | C961⋊(C3×C11) |
| unambiguous semidirect product | (C11×C961)⋊C3 |
| Fitting, Hall | C11×C961 ⋊ C3 |
| derived, Sylow | C961 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C961⋊C3 |
| commutator, cosocle, hypocenter | C961 | C3×C11 |
| Frattini | C31 | C11×C31⋊C3 |
| Fitting | C11×C961 | C3 |
| socle | C11×C31 | C31⋊C3 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10571 |
3553 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31713, 2);