Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ #3414 |
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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|d^2=g,e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,h^a=h^4,e^b=ef,f^b=fg,h^b=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #12016419, #12016421, #12016440, … |
| maximal normal subgroup of | #12016419, #12016421, #12016440, … |
| maximal quotient of | #12252206, #12252339, #12252612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15822);