Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊(D43⋊C9) |
| unambiguous semidirect product | (C43⋊C9)⋊D41 |
| unambiguous semidirect product | D1763⋊C9 |
| derived, Hall | C41×C43 ⋊ C2×C9 |
| Hall | C41×C43⋊C9 ⋊ C2 |
| Hall | D1763 ⋊ C9 |
| Hall | C43⋊C9 ⋊ D41 |
| Sylow | C43 ⋊ C9×D41 |
| Sylow | C41 ⋊ D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C41⋊(D43⋊C3) |
| commutator, hypocenter | C41×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C41×C43 | C2×C3 |
| prime radical | C3×D1763 | C3 |
| LCS | G ▷ C41×C43 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15867 |
Polycyclic presentation:
2,3,41,43,3|b^3=e,c^a=c^40,d^a=d^42,d^b=d^361059 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 12);