Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#3961 |
| Sylow | C5 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 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) = 640 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12011031, C8×#3961, #12011043, … |
| maximal normal subgroup of | #12011031, C8×#3961, #12011043, … |
| maximal quotient of | C8×#3961, #12011214, #12011216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3783);