Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#66132 |
| Sylow | C5 ⋊ C2×#518 |
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 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) = 160 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #12004617, #12004620, #12004642, … |
| maximal normal subgroup of | #12004617, #12004620, #12004642, … |
| maximal quotient of | C2×#10613814, C2×#10613875, C2×#10614048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21211);