Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#442 ⋊ C2 |
| Sylow | C5 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^4,e^b=eg,h^c=h^4,h^d=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D5×AGL(1,ℤ/8), C2×#10611596, C4×#66107, … |
| maximal normal subgroup of | C4×D5×AGL(1,ℤ/8), C2×#10611596, C4×#66107, … |
| maximal quotient of | #12068717, #12068886, #12068902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13678);