Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#4072 |
| Sylow | C5 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 421 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #11988698, #11988704, #11988738, … |
| maximal normal subgroup of | #11988698, #11988704, #11988738, … |
| maximal quotient of | C4×#65221, C42×C22⋊Dic5, C42×C4⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15869);