Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×#6092 |
| Sylow | C13 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#6092, #16788782, #16788784, … |
| maximal normal subgroup of | D8×#6092, #16788782, #16788784, … |
| maximal quotient of | D8×#6092, SD16×#6092, Q16×#6092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20887);