Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1664 |
184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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=f,b^2=g,c^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^4,d^b=df,e^b=eg,h^b=h^4,d^c=dg,e^c=efg,h^c=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1664, C2×#10599152, #12080474, … |
| maximal normal subgroup of | D5×#1664, C2×#10599152, #12080474, … |
| maximal quotient of | #11988173, #11988179, #11988186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1234);