Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ #3169 |
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4172 conjugacy classes — view the full character table.
| maximal subgroup of | #11994520, #11994522, #11998459, … |
| maximal normal subgroup of | #11994520, #11994522, #11998459, … |
| maximal quotient of | #12099839, #12103519, #12104482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12283);