Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#338 ⋊ C2 |
| Sylow | C5 ⋊ #1341 |
110 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 31 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,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^4,d^c=dg64 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1341, C2×#10597974, #12009461, … |
| maximal normal subgroup of | D5×#1341, C2×#10597974, #12009461, … |
| maximal quotient of | #11985996, #11985999, #11986008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 56);