Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1452 |
196 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 88 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,b^a=bg,h^a=h^2,c^b=cf,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13016768, #13016771, #13016773, … |
| maximal normal subgroup of | #13016768, #13016771, #13016773, … |
| maximal quotient of | #13015257, #13015279, #13016669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5976);