Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#497 ⋊ C2 |
| Sylow | C5 ⋊ #3400 |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,c^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^4,h^d=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3400, C2×#10613596, #12980339, … |
| maximal normal subgroup of | D5×#3400, C2×#10613596, #12980339, … |
| maximal quotient of | #12116144, #12116155, #12118160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15678);