Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1389 |
128 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 48 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=d,b^2=e,c^2=fg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^2,c^b=cg,h^b=h^3,h^d=h^4,h^e=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598606, #13025539, #13025908, … |
| maximal normal subgroup of | C2×#10598606, #13025539, #13025908, … |
| maximal quotient of | #13013530, #13013587, #13013591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 688);