Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2255 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=cg,h^c=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #12013304, #12013305, #12013311, … |
| maximal normal subgroup of | #12013304, #12013305, #12013311, … |
| maximal quotient of | #12015746, #12017337, #12017342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4230);