Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1949 |
240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=f,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^4,d^b=dg,h^b=h^4118 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1949, C2×#10601248, #12102760, … |
| maximal normal subgroup of | D5×#1949, C2×#10601248, #12102760, … |
| maximal quotient of | #11997889, #11997906, #11997943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3330);