Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#568 ⋊ C2 |
| Sylow | C5 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,e^a=eg,f^b=fg,h^b=h^4,d^c=dg109 conjugacy classes — view the full character table.
| maximal subgroup of | #12108459, #12108461, #12108465, … |
| maximal normal subgroup of | #12108459, #12108461, #12108465, … |
| maximal quotient of | #12065116, #12065131, #12065203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17626);