Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C9⋊(D71⋊C5)) |
| unambiguous semidirect product | C9⋊(C5⋊(D71⋊C5)) |
| unambiguous semidirect product | (C71⋊C5)⋊D45 |
| unambiguous semidirect product | D3195⋊C5 |
| Fitting, derived | C5×C9×C71 ⋊ C2×C5 |
| Hall | C5×C9×C71⋊C5 ⋊ C2 |
| Hall | C5×C71⋊C5 ⋊ D9 |
| Hall | C9×C71 ⋊ C5×D5 |
| Sylow | C71 ⋊ C5×D45 |
| Sylow | C9 ⋊ C5⋊(D71⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C71 | C2×C5 |
| Frattini | C3 | C3⋊(C5⋊(D71⋊C5)) |
| socle | C3×C5×C71 | C5×D3 |
| LCS | G ▷ C5×C9×C71 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3195 |
Polycyclic presentation:
2,5,3,5,71,3|c^3=f^2,c^a=c^2f,d^a=d^4,e^a=e^70,f^a=f^2,e^b=e^57435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 37);