Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | AΣL(1,𝔽16)×D67 |
| Fitting | AΣL(1,𝔽16)×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
455 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AΣL(1,𝔽16)×D67, #2120×D67, #2121×D67, … |
| maximal normal subgroup of | C2×AΣL(1,𝔽16)×D67, #2120×D67, #2121×D67, … |
| maximal quotient of | #1316×D67, #1326×D67, #30765078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6140);