Finite Group DatabasebetaFinite Group Databasebeta| order | 31311 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| derived | C7×C71 ⋊ C7×C9 |
| Hall | C7×C71⋊C7 ⋊ C9 |
| Sylow | C71 ⋊ C7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×C71⋊C7 |
| commutator, hypocenter | C7×C71 | C7×C9 |
| Fitting, socle, cosocle | C3×C7×C71 | C3×C7 |
| prime radical | C3×C7×C71⋊C7 | C3 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4473 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31311, 8);