Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#64907 |
| Fitting | C2×C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | #13025895, C4×#64907, #13025926, … |
| maximal normal subgroup of | #13025895, C4×#64907, #13025926, … |
| maximal quotient of | C2×#10598607, C2×#10598807, #13023712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6911);