Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1316 |
294 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 34 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=d,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,d^b=de,h^b=h^4,d^c=dg,h^d=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #13014215, #13014216, #13014287, … |
| maximal normal subgroup of | #13014215, #13014216, #13014287, … |
| maximal quotient of | #13013301, #13013309, #13013396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 784);