Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#4094 |
| Sylow | C5 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12004712, #12004716, #12004732, … |
| maximal normal subgroup of | #12004712, #12004716, #12004732, … |
| maximal quotient of | C22×#65286, C2×C4×#4094, C22×#65523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21235);