Finite Group DatabasebetaFinite Group Databasebeta| order | 31311 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C49⋊C9 |
| unambiguous semidirect product | C49⋊(C9×C71) |
| unambiguous semidirect product | (C49×C71)⋊C9 |
| derived, Sylow | C49 ⋊ C9×C71 |
| Hall | C49×C71 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C71 | C49⋊C3 |
| commutator, hypocenter | C49 | C9×C71 |
| Frattini | C3×C7 | ΓL(1,𝔽8)×C71 |
| Fitting | C3×C49×C71 | C3 |
| socle, prime radical | C3×C7×C71 | ΓL(1,𝔽8) |
| cosocle | C3×C49 | C3×C71 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C71 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31311 |
4047 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31311, 3);