Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C3×H(3,𝔽3)⋊#4296 |
| unambiguous semidirect product | (C19⋊C3)⋊(H(3,𝔽3)⋊C9) |
| Fitting | C3×C19×H(3,𝔽3) ⋊ C9 |
| Sylow | C19 ⋊ C3×H(3,𝔽3)⋊C9 |
680 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 513 |
219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4275);