Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#3932 |
| Fitting | C4×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 | #12011026, C8×#3932, #12011038, … |
| maximal normal subgroup of | #12011026, C8×#3932, #12011038, … |
| maximal quotient of | C8×#3932, #12011204, #12011211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1938);