Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2153 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^2,c^b=cg,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13026603, #13026605, #13026640, … |
| maximal normal subgroup of | #13026603, #13026605, #13026640, … |
| maximal quotient of | #13025034, #13025060, #13025090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6833);