Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D71⋊C25)) |
| unambiguous semidirect product | (C3⋊D213)⋊C25 |
| unambiguous semidirect product | (C71⋊C25)⋊(C3⋊D3) |
| derived, Hall | C32×C71 ⋊ C2×C25 |
| Hall | C32×C71⋊C25 ⋊ C2 |
| Hall | C71⋊C25 ⋊ C3⋊D3 |
| Hall | C3⋊D213 ⋊ C25 |
| Sylow | C71 ⋊ C3⋊D3×C25 |
| Sylow | C32 ⋊ D71⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊(C3⋊(D71⋊C5)) |
| commutator, hypocenter | C32×C71 | C2×C25 |
| Fitting, socle, cosocle | C32×C5×C71 | C2×C5 |
| prime radical | C5×C3⋊D213 | C5 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15975 |
Polycyclic presentation:
2,5,3^2,71,5|b^5=f,c^a=c^2,d^a=d^2,e^a=e^70,e^b=e^57465 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 17);