Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#3932 |
| Fitting | C22×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #12016363, #12016365, #12016370, … |
| maximal normal subgroup of | #12016363, #12016365, #12016370, … |
| maximal quotient of | C22×#64729, C22×#64723, C22×#64725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15815);