Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2066 |
248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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=d,b^2=deg,c^2=g,e^2=g,f^2=g,b^a=bdeg,c^a=ce,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,e^c=eg,f^c=fg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2066, C2×#10601281, #12127910, … |
| maximal normal subgroup of | D5×#2066, C2×#10601281, #12127910, … |
| maximal quotient of | #12003823, #12003830, #12003879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3363);