Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2210 |
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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|b^2=dg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^4,e^c=ef,f^c=fg73 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2210, C2×#10602256, #12253560, … |
| maximal normal subgroup of | D5×#2210, C2×#10602256, #12253560, … |
| maximal quotient of | #12013428, #12013460, #12013490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4338);