Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#131 ⋊ C2 |
| Sylow | C5 ⋊ #2880 |
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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|a^2=f,f^2=g,b^a=be,h^b=h^4,d^c=dg130 conjugacy classes — view the full character table.
| maximal subgroup of | #12115173, #12115174, #12115181, … |
| maximal normal subgroup of | #12115173, #12115174, #12115181, … |
| maximal quotient of | #12065482, #12065491, #12065501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17606);