Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×D71⋊C25 |
| unambiguous semidirect product | D71⋊(C9×C25) |
| unambiguous semidirect product | (C9×D71)⋊C25 |
| unambiguous semidirect product | (C71⋊C25)⋊(C2×C9) |
| derived, Sylow | C71 ⋊ C2×C9×C25 |
| Hall | C9×C71⋊C25 ⋊ C2 |
| Hall | C71⋊C25 ⋊ C2×C9 |
| Hall | C9×D71 ⋊ C25 |
| Hall | C9×C71 ⋊ C2×C25 |
| Hall | D71 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C9 | D71⋊C5 |
| commutator, hypocenter | C71 | C2×C9×C25 |
| Frattini | C3×C5 | C3×D71⋊C5 |
| Fitting | C5×C9×C71 | C2×C5 |
| socle, cosocle | C3×C5×C71 | C2×C3×C5 |
| prime radical | C3×C5×D71 | C3×C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C5×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15975 |
765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 10);