Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#417 ⋊ C2 |
| Sylow | C5 ⋊ #2037 |
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 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) = 160 |
Polycyclic presentation:
2^7,5|c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,h^b=h^4,e^c=eg70 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2037, C2×#10601099, #12126899, … |
| maximal normal subgroup of | D5×#2037, C2×#10601099, #12126899, … |
| maximal quotient of | #12002566, #12002573, #12002594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3181);