Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×#685 |
| Fitting | C24×C4×C5 ⋊ C2 |
| Sylow | C5 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 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 | #11987221, #11990626, C2×#10600218, … |
| maximal normal subgroup of | #11987221, #11990626, C2×#10600218, … |
| maximal quotient of | C23×#3963, C22×C4×#685, C22×#65244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21203);