Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×#672 |
| Sylow | C5 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #12011002, D8×#672, #12011007, … |
| maximal normal subgroup of | #12011002, D8×#672, #12011007, … |
| maximal quotient of | D8×#672, SD16×#672, Q16×#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3731);