Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#65027 |
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#448 |
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #11994422, #11994424, #11995767, … |
| maximal normal subgroup of | #11994422, #11994424, #11995767, … |
| maximal quotient of | C2×#10598907, C2×#10598909, C2×#10598931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12428);