Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| unambiguous semidirect product | D5⋊#410 |
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=g,b^a=be,e^a=eg,h^a=h^2,f^b=fg,h^d=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13021731, #13021733, #13021750, … |
| maximal normal subgroup of | #13021731, #13021733, #13021750, … |
| maximal quotient of | D5⋊#1458, D5⋊#1460, D5⋊#1461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19619);