Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2151 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^b=cg,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11986700, #12015435, #12015440, … |
| maximal normal subgroup of | #11986700, #12015435, #12015440, … |
| maximal quotient of | #12010847, #12010873, #12010906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4276);