Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1291 |
138 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 42 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=d,b^2=e,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=efg,h^a=h^2,d^b=dg,h^b=h^3,h^d=h^4,h^e=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598558, #13015986, #13015991, … |
| maximal normal subgroup of | C2×#10598558, #13015986, #13015991, … |
| maximal quotient of | #13013215, #13013221, #13013222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 640);