Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1770 |
272 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^4,c^b=cg,h^b=h^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #11990089, #11990095, #11990096, … |
| maximal normal subgroup of | #11990089, #11990095, #11990096, … |
| maximal quotient of | #11990427, #11990431, #11990456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3341);