Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1354 |
140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,b^2=eg,c^2=fg,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^4,c^b=cf,d^b=defg,d^c=dg67 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1354, C2×#10598139, #12009605, … |
| maximal normal subgroup of | D5×#1354, C2×#10598139, #12009605, … |
| maximal quotient of | #11986097, #11986118, #11986422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 221);