Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | Dic5×H(5,𝔽2) |
| Sylow | C5 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12105169, Dic5×#453, #12105180, … |
| maximal normal subgroup of | #12105169, Dic5×#453, #12105180, … |
| maximal quotient of | Dic5×#518, Dic5×#520, Dic5×#534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21262);