Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M32 ⋊ C4 |
| Sylow | C5 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,d^b=dg,h^b=h^2,h^c=h^4,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#347, #13025409, #13025715, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#347, #13025409, #13025715, … |
| maximal quotient of | #13022987, #13022991, #13022992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6196);