Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2090 |
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,b^2=d,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ceg,c^b=cf,f^b=fg,h^b=h^4,e^c=eg,f^c=fg82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2090, C2×#10601366, #12128421, … |
| maximal normal subgroup of | D5×#2090, C2×#10601366, #12128421, … |
| maximal quotient of | #12004227, #12004234, #12004241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3448);