Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1327 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,d^b=deg,h^b=h^4,d^c=dg,h^d=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #13014263, #13014264, #13014265, … |
| maximal normal subgroup of | #13014263, #13014264, #13014265, … |
| maximal quotient of | #13013317, #13013319, #13013327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 866);