Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ #2956 |
458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,h^c=h^3,h^f=h^455 conjugacy classes — view the full character table.
| maximal subgroup of | #13041090, #13041091, #13041094, … |
| maximal normal subgroup of | #13041090, #13041091, #13041094, … |
| maximal quotient of | #13031602, #13031603, #13031605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19531);