Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#421 |
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^2,e^b=eg,h^d=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13021829, #13021831, #13021835, … |
| maximal normal subgroup of | #13021829, #13021831, #13021835, … |
| maximal quotient of | D5⋊#1478, D5⋊#1479, D5⋊#1477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19618);