Finite Group DatabasebetaFinite Group Databasebeta| order | 32431 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C113⋊C7 |
| unambiguous semidirect product | C113⋊(C7×C41) |
| unambiguous semidirect product | (C41×C113)⋊C7 |
| Fitting, socle, Hall | C41×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C7×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C113⋊C7 |
| commutator, cosocle, hypocenter | C113 | C7×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C41 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4633 |
943 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32431, 1);