Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #3246 |
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^4,c^b=ce,f^c=fg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #12000238, #12000240, #12000250, … |
| maximal normal subgroup of | #12000238, #12000240, #12000250, … |
| maximal quotient of | #12109181, #12109188, #12109672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12840);