Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1381 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^2,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13014275, #13014276, #13014277, … |
| maximal normal subgroup of | #13014275, #13014276, #13014277, … |
| maximal quotient of | #13013518, #13013577, #13013740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 749);