Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#536 ⋊ C2 |
| Sylow | C5 ⋊ #3225 |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^4,c^b=ce,d^b=dg,f^c=fg70 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3225, C2×#10615141, #12970711, … |
| maximal normal subgroup of | D5×#3225, C2×#10615141, #12970711, … |
| maximal quotient of | #12108685, #12109073, #12109913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17223);