Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,𝔽5)×Q32 |
| Fitting | C5×Q32 ⋊ C4 |
| Sylow | C5 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×SD64, AGL(1,𝔽5)×Q64, #13027854, … |
| maximal normal subgroup of | AGL(1,𝔽5)×SD64, AGL(1,𝔽5)×Q64, #13027854, … |
| maximal quotient of | Q32×#170, #13025180, #13025181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6216);