Finite Group DatabasebetaFinite Group Databasebeta| order | 31659 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C173 · Schur multiplier (H2) = C1 |
| direct product | C173×C61⋊C3 |
| unambiguous semidirect product | C61⋊(C3×C173) |
| unambiguous semidirect product | (C61×C173)⋊C3 |
| Fitting, socle, Hall | C61×C173 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C3×C173 |
| Frattini | C1 | G |
| Fitting, socle | C61×C173 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C173 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10553 |
3979 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31659, 1);