Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #3356 |
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^4,c^b=cg,d^b=de,h^b=h^4,f^c=fg,h^d=h^485 conjugacy classes — view the full character table.
| maximal subgroup of | #12090297, #12090299, #12090312, … |
| maximal normal subgroup of | #12090297, #12090299, #12090312, … |
| maximal quotient of | #12115751, #12115773, #12117056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13558);