Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C32 ⋊ C4 |
| Sylow | C5 ⋊ #1423 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=ce,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,h^d=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13014584, #13014585, #13014596, … |
| maximal normal subgroup of | #13014584, #13014585, #13014596, … |
| maximal quotient of | #13014355, #13014356, #13014387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 571);