Finite Group DatabasebetaFinite Group Databasebeta| order | 35050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×#31776200 |
| Fitting, socle, Hall | C2×C701 ⋊ C25 |
| derived, Sylow | C701 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31776200 |
| commutator, hypocenter | C701 | C2×C25 |
| Frattini | C1 | G |
| Fitting, socle | C2×C701 | C25 |
| prime radical | C2×C701⋊C5 | C5 |
| cosocle | C701⋊C5 | C2×C5 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1402 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35050, 9);