Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊#170 |
| Sylow | C5 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013207, #13013208, #13013224, … |
| maximal normal subgroup of | #13013207, #13013208, #13013224, … |
| maximal quotient of | C8×C4⋊#170, #13017238, #13017248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6260);