Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C5×C32 ⋊ C4 |
| Sylow | C5 ⋊ #1398 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=h^2,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598487, #13027533, #13027537, … |
| maximal normal subgroup of | C2×#10598487, #13027533, #13027537, … |
| maximal quotient of | #13014067, #13014075, #13014369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 569);