Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11719147 |
| Sylow | C13 ⋊ C2×#408 |
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #16785383, #16785388, #16785911, … |
| maximal normal subgroup of | #16785383, #16785388, #16785911, … |
| maximal quotient of | C2×#13130102, C2×#13130106, C2×#13130109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21092);