Finite Group DatabasebetaFinite Group Databasebeta| order | 31713 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C31 |
| direct product | C11×#15668333 |
| Fitting, socle, Hall | C11×C312 ⋊ C3 |
| derived, Sylow | C312 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #15668333 |
| commutator, cosocle, hypocenter | C312 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C11 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1023 |
3553 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31713, 5);