Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×C22⋊D5 |
| Fitting | C22×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C42×D4 |
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 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 | C4×#65014, C4×C8×C22⋊D5, C4×#65019, … |
| maximal normal subgroup of | C4×#65014, C4×C8×C22⋊D5, C4×#65019, … |
| maximal quotient of | C42×C22⋊Dic5, C42×#685, C42×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15870);