Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5289 |
| unambiguous semidirect product | C41⋊(C3⋊D129) |
| unambiguous semidirect product | C43⋊(C3⋊D123) |
| Fitting, socle, derived, Hall | C32×C41×C43 ⋊ C2 |
| Hall | C41×C43 ⋊ C3⋊D3 |
| Hall | C32×C43 ⋊ D41 |
| Hall | C32×C41 ⋊ D43 |
| Sylow | C43 ⋊ C3⋊D123 |
| Sylow | C41 ⋊ C3⋊D129 |
| Sylow | C32 ⋊ D1763 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C41×C43 | C2 |
| LCS | G ▷ C32×C41×C43 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15867 |
Polycyclic presentation:
2,3^2,41,43|b^a=b^2,c^a=c^2,d^a=d^40,e^a=e^427935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 32);