Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×Q32 ⋊ C4 |
| Sylow | C5 ⋊ #1416 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=g,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,c^b=ce,e^b=ef,f^b=fg,h^d=h^449 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598682, #13027765, #13027766, … |
| maximal normal subgroup of | C2×#10598682, #13027765, #13027766, … |
| maximal quotient of | #13014189, #13014190, #13014273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 764);