Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2255 |
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 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) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,c^b=cg,h^b=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2255, C2×#10600115, #12254799, … |
| maximal normal subgroup of | D5×#2255, C2×#10600115, #12254799, … |
| maximal quotient of | #12015742, #12017338, #12017339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2197);