Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#170 |
| Sylow | C5 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 378 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598821, #13015529, #13015546, … |
| maximal normal subgroup of | C2×#10598821, #13015529, #13015546, … |
| maximal quotient of | C22×#64933, C22×#64913, C2×#10604877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19646);