Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ #1746 |
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^b=cg,h^b=h^2,h^f=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13013483, #13013486, #13016688, … |
| maximal normal subgroup of | #13013483, #13013486, #13016688, … |
| maximal quotient of | #13016665, #13016667, #13016668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5922);