Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×SD64 ⋊ C2 |
| Sylow | C5 ⋊ #2264 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2264, C2×#10600174, #12257442, … |
| maximal normal subgroup of | D5×#2264, C2×#10600174, #12257442, … |
| maximal quotient of | #12019736, #12019745, #12019806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2256);