Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#495 ⋊ C2 |
| Sylow | C5 ⋊ #2212 |
154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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|b^2=d,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^467 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2212, C2×#10602118, #12253688, … |
| maximal normal subgroup of | D5×#2212, C2×#10602118, #12253688, … |
| maximal quotient of | #12013413, #12013420, #12013441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4200);