Finite Group DatabasebetaFinite Group Databasebeta| order | 32050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D641⋊C5 |
| unambiguous semidirect product | D641⋊C52 |
| unambiguous semidirect product | (C641⋊C5)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D641)⋊C5 |
| Fitting, socle | C5×C641 ⋊ C2×C5 |
| derived, Sylow | C641 ⋊ C2×C52 |
| Hall | C5×C641⋊C5 ⋊ C2 |
| Hall | D641 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D641⋊C5 |
| commutator, cosocle, hypocenter | C641 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C641 | C2×C5 |
| LCS | G ▷ C641 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3205 |
370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32050, 8);