Finite Group DatabasebetaFinite Group Databasebeta| order | 31717 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C197⋊C7 |
| unambiguous semidirect product | C197⋊(C7×C23) |
| unambiguous semidirect product | (C23×C197)⋊C7 |
| Fitting, socle, Hall | C23×C197 ⋊ C7 |
| derived, Sylow | C197 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C197⋊C7 |
| commutator, cosocle, hypocenter | C197 | C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C197 | C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4531 |
805 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31717, 1);