Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #2884 |
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^2,f^b=fg,h^b=h^4,d^c=dg,h^f=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | #13027040, #13027042, #13027048, … |
| maximal normal subgroup of | #13027040, #13027042, #13027048, … |
| maximal quotient of | #13029215, #13029216, #13029218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19621);