Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D43⋊C9 |
| unambiguous semidirect product | D43⋊(C9×C41) |
| unambiguous semidirect product | (C43⋊C9)⋊(C2×C41) |
| unambiguous semidirect product | (C41×D43)⋊C9 |
| derived, Sylow | C43 ⋊ C2×C9×C41 |
| Hall | C41×C43⋊C9 ⋊ C2 |
| Hall | C41×D43 ⋊ C9 |
| Hall | C41×C43 ⋊ C2×C9 |
| Hall | C43⋊C9 ⋊ C2×C41 |
| Hall | D43 ⋊ C9×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C9×C41 |
| Frattini | C3 | C41×D43⋊C3 |
| Fitting, socle | C3×C41×C43 | C2×C3 |
| prime radical | C3×C41×D43 | C3 |
| cosocle | C3×C43 | C2×C3×C41 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15867 |
1599 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 10);