Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | AΣL(1,𝔽16)×D271 |
| Fitting | AΣL(1,𝔽16)×C271 ⋊ C2 |
| Sylow | C271 ⋊ 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.
| transitive degree | μt(G) = 2168 |
1781 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 6140);