Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1350 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^485 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1350, C2×#10597979, #12009551, … |
| maximal normal subgroup of | D5×#1350, C2×#10597979, #12009551, … |
| maximal quotient of | #11985987, #11985990, #11985999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 61);