Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#127 ⋊ C4 |
| Sylow | C5 ⋊ #1961 |
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=dfg,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,c^b=cg,h^b=h^3,h^f=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #13014500, #13017934, #13017935, … |
| maximal normal subgroup of | #13014500, #13017934, #13017935, … |
| maximal quotient of | #13020909, #13020910, #13020911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6699);