Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | C9×C5⋊D355 |
| unambiguous semidirect product | C5⋊(C9×D355) |
| unambiguous semidirect product | C71⋊(C9×C5⋊D5) |
| Fitting, Hall | C52×C9×C71 ⋊ C2 |
| derived, Hall | C52×C71 ⋊ C2×C9 |
| Hall | C9×C71 ⋊ C5⋊D5 |
| Hall | C52×C9 ⋊ D71 |
| Sylow | C71 ⋊ C9×C5⋊D5 |
| Sylow | C52 ⋊ C9×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C5⋊D355 |
| commutator, hypocenter | C52×C71 | C2×C9 |
| Frattini | C3 | C3×C5⋊D355 |
| Fitting | C52×C9×C71 | C2 |
| socle, cosocle | C3×C52×C71 | C2×C3 |
| prime radical | C3×C5⋊D355 | C3 |
| LCS | G ▷ C52×C71 | |
| UCS | C1 ◁ C9 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15975 |
8001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 52);