Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1451 |
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^2,h^d=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #13013705, #13013706, #13013709, … |
| maximal normal subgroup of | #13013705, #13013706, #13013709, … |
| maximal quotient of | #13015253, #13015273, #13016665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6770);