Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×C22⋊D5 |
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | #12255752, #12255756, #12255758, … |
| maximal normal subgroup of | #12255752, #12255756, #12255758, … |
| maximal quotient of | #12088643, #12088648, #12088658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17651);