Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2226 |
142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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=dg,e^2=fg,f^2=g,b^a=bdg,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,e^c=ef,f^c=fg85 conjugacy classes — view the full character table.
| maximal subgroup of | #12013108, #12013111, #12013129, … |
| maximal normal subgroup of | #12013108, #12013111, #12013129, … |
| maximal quotient of | #12015341, #12015906, #12016964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3762);