Finite Group DatabasebetaFinite Group Databasebeta| order | 31317 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C11×C13) |
| unambiguous semidirect product | (C11×C73)⋊(C3×C13) |
| Fitting, socle, Hall | C11×C13×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C11×C13 |
| Hall | C13×C73 ⋊ C3×C11 |
| Hall | C11×C73 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C3×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C11×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10439 |
3861 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31317, 2);