Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#500 ⋊ C2 |
| Sylow | C5 ⋊ #1722 |
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1722, C2×#10602159, #12087091, … |
| maximal normal subgroup of | D5×#1722, C2×#10602159, #12087091, … |
| maximal quotient of | #11993088, #11999098, #11999103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4241);