Finite Group DatabasebetaFinite Group Databasebeta| order | 31017 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×(C211⋊C3)⋊C7 |
| unambiguous semidirect product | (C211⋊C3)⋊C72 |
| unambiguous semidirect product | (C211⋊C7)⋊(C3×C7) |
| unambiguous semidirect product | (C7×C211⋊C3)⋊C7 |
| Fitting, socle | C7×C211 ⋊ C3×C7 |
| derived, Sylow | C211 ⋊ C3×C72 |
| Hall | C7×C211⋊C7 ⋊ C3 |
| Hall | C211⋊C3 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C211⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C211 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C211 | C3×C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1477 |
217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31017, 9);