Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 108 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=d,b^2=e,d^2=f,e^2=g,c^a=cf,h^a=h^2,h^b=h^3,h^d=h^4,h^e=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #13016804, #13016809, #13016824, … |
| maximal normal subgroup of | #13016804, #13016809, #13016824, … |
| maximal quotient of | #13015245, #13015275, #13016666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5973);