Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ #2296 |
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,d^2=f,b^a=be,c^a=cf,h^a=h^2,h^b=h^3,h^g=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13022148, #13022150, #13022167, … |
| maximal normal subgroup of | #13022148, #13022150, #13022167, … |
| maximal quotient of | #13027906, #13027913, C4×#65699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19210);