Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×C3⋊D129 |
| unambiguous semidirect product | C3⋊(C41×D129) |
| unambiguous semidirect product | C43⋊(C3⋊D3×C41) |
| Fitting, socle, Hall | C32×C41×C43 ⋊ C2 |
| derived, Hall | C32×C43 ⋊ C2×C41 |
| Hall | C41×C43 ⋊ C3⋊D3 |
| Hall | C32×C41 ⋊ D43 |
| Sylow | C43 ⋊ C3⋊D3×C41 |
| Sylow | C32 ⋊ C41×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C3⋊D129 |
| commutator, cosocle, hypocenter | C32×C43 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41×C43 | C2 |
| LCS | G ▷ C32×C43 | |
| UCS | C1 ◁ C41 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15867 |
7995 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 30);