Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#6092 |
| Sylow | C13 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777233, #16777234, #16777242, … |
| maximal normal subgroup of | #16777233, #16777234, #16777242, … |
| maximal quotient of | C2×#13129756, C2×#13129772, #16786830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20734);