Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#11718304 |
| Sylow | C13 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 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 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718304, #16789312, #16789314, … |
| maximal normal subgroup of | C4×#11718304, #16789312, #16789314, … |
| maximal quotient of | C2×#13129758, #16786713, C2×#13129774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20749);