Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | AΣL(1,𝔽16)×#6157 |
| Fitting | C53×AΣL(1,𝔽16) ⋊ C4 |
| Sylow | C53 ⋊ C4×AΣL(1,𝔽16) |
844 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 424 |
221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1096056);