Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | 3−1+2⋊#10587020 |
| Sylow | C19 ⋊ 3−1+2⋊C27 |
126 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^6,19|a^3=d,b^3=e,d^3=f,b^a=bc,c^a=ce,g^a=g^4,c^b=ce,g^d=g^7219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4047);