Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2242 |
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,h^b=h^4,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2242, C2×#10602111, #12254599, … |
| maximal normal subgroup of | D5×#2242, C2×#10602111, #12254599, … |
| maximal quotient of | #12015682, #12017219, #12017226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4193);