Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#6122 |
| Sylow | C13 ⋊ Q8×M16 |
388 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783570, #16783574, #16783578, … |
| maximal normal subgroup of | #16783570, #16783574, #16783578, … |
| maximal quotient of | C4⋊C4×#6122, #16797468, Q8×#88110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21309);