Finite Group DatabasebetaFinite Group Databasebeta| order | 32631 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C149 · Schur multiplier (H2) = C1 |
| direct product | C149×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C149) |
| unambiguous semidirect product | (C73×C149)⋊C3 |
| Fitting, socle, Hall | C73×C149 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C149 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C3×C149 |
| Frattini | C1 | G |
| Fitting, socle | C73×C149 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C149 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10877 |
4023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32631, 1);