Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#65533 |
| Fitting | C2×C5×H(5,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12016557, #12016563, #12016571, … |
| maximal normal subgroup of | #12016557, #12016563, #12016571, … |
| maximal quotient of | C2×#10602638, C2×#10602639, C2×#10602685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17922);