Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C41⋊(D43⋊C3)) |
| unambiguous semidirect product | C41⋊(C3⋊(D43⋊C3)) |
| unambiguous semidirect product | (C43⋊C3)⋊D123 |
| unambiguous semidirect product | D5289⋊C3 |
| Fitting, socle, derived | C3×C41×C43 ⋊ C2×C3 |
| Hall | C3×C41×C43⋊C3 ⋊ C2 |
| Hall | C41×C43 ⋊ C3×D3 |
| Hall | C3×C43⋊C3 ⋊ D41 |
| Sylow | C43 ⋊ C3×D123 |
| Sylow | C41 ⋊ C3⋊(D43⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C41×C43 | C2×C3 |
| LCS | G ▷ C3×C41×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5289 |
Polycyclic presentation:
2,3^2,41,43|c^a=c^2,d^a=d^40,e^a=e^42,e^b=e^361050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 19);