Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#66087 |
| Fitting | C2×C5×#131 ⋊ C2 |
| Sylow | C5 ⋊ C2×#578 |
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12014990, #12014993, #12015000, … |
| maximal normal subgroup of | #12014990, #12014993, #12015000, … |
| maximal quotient of | C2×#10615537, C2×#10615516, C2×#10610302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21147);