Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#4033 |
| Sylow | C5 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups; only the 941 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 941 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11990642, #12004727, #12004868, … |
| maximal normal subgroup of | #11990642, #12004727, #12004868, … |
| maximal quotient of | C22×#64938, C22×C4⋊C4×Dic5, C2×C4×#4033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19683);