Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1392 |
158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=g,e^2=g,b^a=bc,c^a=cf,f^a=fg,d^b=df,h^b=h^2,d^c=dg,h^e=h^437 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598574, #13025571, #13025575, … |
| maximal normal subgroup of | C2×#10598574, #13025571, #13025575, … |
| maximal quotient of | #13013628, #13013675, #13013678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 656);