Finite Group DatabasebetaFinite Group Databasebeta| order | 31017 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C211 · Schur multiplier (H2) = C1 |
| direct product | C49⋊C3×C211 |
| unambiguous semidirect product | C49⋊(C3×C211) |
| Fitting, Hall | C49×C211 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C211 |
| Frattini | C7 | ΓL(1,𝔽8)×C211 |
| Fitting | C49×C211 | C3 |
| socle | C7×C211 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C211 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10339 |
4009 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31017, 4);