Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#365 ⋊ C2 |
| Sylow | C5 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,d^b=dfg,e^b=eg,f^b=fg,h^b=h^4,d^c=dg,h^c=h^455 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,ℤ/16), C2×#10600103, #12252745, … |
| maximal normal subgroup of | D5×AGL(1,ℤ/16), C2×#10600103, #12252745, … |
| maximal quotient of | #12011172, #12011184, #12011250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2185);