Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#3998 |
| Sylow | C5 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #13013468, #13013470, #13013472, … |
| maximal normal subgroup of | #13013468, #13013470, #13013472, … |
| maximal quotient of | C8×#3998, #13022980, #13023025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6230);