Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D71⋊C25) |
| unambiguous semidirect product | D639⋊C25 |
| unambiguous semidirect product | (C71⋊C25)⋊D9 |
| derived, Hall | C9×C71 ⋊ C2×C25 |
| Hall | C9×C71⋊C25 ⋊ C2 |
| Hall | C71⋊C25 ⋊ D9 |
| Hall | D639 ⋊ C25 |
| Sylow | C71 ⋊ D9×C25 |
| Sylow | C9 ⋊ D71⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊(D71⋊C5) |
| commutator, hypocenter | C9×C71 | C2×C25 |
| Frattini | C3×C5 | C3⋊(D71⋊C5) |
| Fitting, cosocle | C5×C9×C71 | C2×C5 |
| socle | C3×C5×C71 | C5×D3 |
| prime radical | C5×D639 | C5 |
| LCS | G ▷ C9×C71 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15975 |
Polycyclic presentation:
2,3,5,71,3,5|b^3=e^2,c^5=f,b^a=b^2e,d^a=d^70,e^a=e^2,d^c=d^54465 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 12);