Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1331 |
110 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 38 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,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ce,e^b=eg,h^b=h^4,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#1331, C2×#10598609, #13023687, … |
| maximal normal subgroup of | D5⋊#1331, C2×#10598609, #13023687, … |
| maximal quotient of | #13013329, #13013337, #13013414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 691);