Finite Group DatabasebetaFinite Group Databasebeta| order | 32050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D5×C641⋊C5 |
| unambiguous semidirect product | C5⋊(C2×C641⋊C5) |
| unambiguous semidirect product | (D5×C641)⋊C5 |
| Fitting, socle, derived | C5×C641 ⋊ C2×C5 |
| Hall | C5×C641⋊C5 ⋊ C2 |
| Sylow | C641 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C641 | C2×C5 |
| LCS | G ▷ C5×C641 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3205 |
532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32050, 10);