Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#3958 |
| Fitting | C4×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 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 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12011019, C8×#3958, #12011048, … |
| maximal normal subgroup of | #12011019, C8×#3958, #12011048, … |
| maximal quotient of | C8×#3958, #12011193, #12011195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3758);