Finite Group DatabasebetaFinite Group Databasebeta| order | 32050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D3205 |
| unambiguous semidirect product | C641⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C641 ⋊ C2 |
| Sylow | C641 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C641 | C2 |
| LCS | G ▷ C52×C641 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16025 |
Polycyclic presentation:
2,5^2,641|b^a=b^4,c^a=c^4,d^a=d^6408014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32050, 16);