Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#65221 |
| Sylow | C5 ⋊ C2×#376 |
840 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598228, #11988701, #11988890, … |
| maximal normal subgroup of | C2×#10598228, #11988701, #11988890, … |
| maximal quotient of | C2×C4×#3963, C4×#65221, C2×#10600194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15865);