Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C5×#124 ⋊ C4 |
| Sylow | C5 ⋊ #2379 |
520 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 152 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=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^2,c^b=cef,d^b=de,h^g=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13019036, #13019037, #13019040, … |
| maximal normal subgroup of | #13019036, #13019037, #13019040, … |
| maximal quotient of | #13028052, #13028056, #13028058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19410);