Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2222 |
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^b=h^4,e^c=eg58 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2222, C2×#10601889, #12253875, … |
| maximal normal subgroup of | D5×#2222, C2×#10601889, #12253875, … |
| maximal quotient of | #12013509, #12013526, #12013560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3971);