Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#64691 |
| Fitting | C2×C5×#99 ⋊ C2 |
| Sylow | C5 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #12014431, C4×#64691, #12014446, … |
| maximal normal subgroup of | #12014431, C4×#64691, #12014446, … |
| maximal quotient of | C2×#10597935, C2×#10597937, #12008548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2889);