Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #100×#261 |
| Fitting | C13×#100 ⋊ C4 |
| Sylow | C13 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 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) = 104 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | #261×AΣL(1,𝔽16), #261×#352, #16789417, … |
| maximal normal subgroup of | #261×AΣL(1,𝔽16), #261×#352, #16789417, … |
| maximal quotient of | #261×#323, #16780363, #16780378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20261);