Finite Group DatabasebetaFinite Group Databasebeta| order | 31017 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C7×C211⋊C7 |
| unambiguous semidirect product | (C3×C211)⋊C72 |
| unambiguous semidirect product | (C3×C7×C211)⋊C7 |
| Fitting, socle | C3×C7×C211 ⋊ C7 |
| derived, Sylow | C211 ⋊ C3×C72 |
| Hall | C3×C211 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C211⋊C7 |
| commutator, cosocle, hypocenter | C211 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C211 | C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C3×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4431 |
777 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31017, 13);