Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | AGL(1,𝔽5)×#124 |
| Fitting | C5×#124 ⋊ C4 |
| Sylow | C5 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#329, #13017070, #13017078, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#329, #13017070, #13017078, … |
| maximal quotient of | AGL(1,𝔽5)×#388, AGL(1,𝔽5)×#390, AGL(1,𝔽5)×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19405);