Finite Group DatabasebetaFinite Group Databasebeta| order | 35050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #31776200⋊C2 |
| Fitting, socle, derived, Sylow | C701 ⋊ C2×C25 |
| Hall | #31776200 ⋊ C2 |
| Hall | D701 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C701 | C2×C25 |
| prime radical | D701⋊C5 | C5 |
| cosocle | C701⋊C5 | C2×C5 |
| LCS | G ▷ C701 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 701 |
Polycyclic presentation:
2,5^2,701|b^5=c,d^a=d^700,d^b=d^569,d^c=d^8964 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35050, 8);