Finite Group DatabasebetaFinite Group Databasebeta| order | 31017 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17984522⋊C7 |
| Fitting, socle, derived | C7×C211 ⋊ C3×C7 |
| Hall | C7×C211⋊C7 ⋊ C3 |
| Sylow | C211 ⋊ C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C211 | C3×C7 |
| LCS | G ▷ C7×C211 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1477 |
Polycyclic presentation:
3,7^2,211|c^a=c^2,d^a=d^196,d^b=d^171105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31017, 11);