Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1493 |
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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=e,b^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,c^b=cg,d^b=df,h^b=h^4,h^c=h^4,h^e=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13017794, #13017795, #13017798, … |
| maximal normal subgroup of | #13017794, #13017795, #13017798, … |
| maximal quotient of | #13014977, #13014980, #13014983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6734);