Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#358 ⋊ C2 |
| Sylow | C5 ⋊ #2237 |
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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=g,b^2=g,c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^4,e^c=ef,f^c=fg,h^c=h^473 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2237, C2×#10600007, #12254097, … |
| maximal normal subgroup of | D5×#2237, C2×#10600007, #12254097, … |
| maximal quotient of | #12015596, #12015813, #12016250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2089);