Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^4,c^b=cg,h^b=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #12012794, #12012795, #12012801, … |
| maximal normal subgroup of | #12012794, #12012795, #12012801, … |
| maximal quotient of | #12013973, #12013978, #12013998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4197);