Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2970 |
406 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 168 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,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^2,d^c=dg,h^c=h^2,h^d=h^4,h^f=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13019724, #13019726, #13019732, … |
| maximal normal subgroup of | #13019724, #13019726, #13019732, … |
| maximal quotient of | #13033694, #13033700, #13033758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19239);