Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2064 |
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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|a^2=d,b^2=de,c^2=g,d^2=g,f^2=g,b^a=bde,c^a=ce,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,d^c=dg,f^c=fg,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2064, C2×#10601337, #12127844, … |
| maximal normal subgroup of | D5×#2064, C2×#10601337, #12127844, … |
| maximal quotient of | #12003823, #12003837, #12003851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3419);