Finite Group DatabasebetaFinite Group Databasebeta| order | 32050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D641⋊C25 |
| unambiguous semidirect product | (C641⋊C25)⋊C2 |
| derived, Sylow | C641 ⋊ C2×C25 |
| Hall | C641⋊C25 ⋊ C2 |
| Hall | D641 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D641⋊C5 |
| commutator, hypocenter | C641 | C2×C25 |
| Fitting, socle, cosocle | C5×C641 | C2×C5 |
| prime radical | C5×D641 | C5 |
| LCS | G ▷ C641 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16025 |
Polycyclic presentation:
2,5,641,5|b^5=d,c^a=c^640,c^b=c^357370 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32050, 2);