Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11718128 |
| Sylow | C13 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
194 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718128, Dic13×AΣL(1,𝔽16), #15778066, … |
| maximal normal subgroup of | C4×#11718128, Dic13×AΣL(1,𝔽16), #15778066, … |
| maximal quotient of | C2×#13112764, C2×#13112784, #15772169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6142);