Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×C19×H(3,𝔽3) ⋊ C9 |
| Sylow | C19 ⋊ #10624508 |
350 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^6,19|a^3=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,d^b=df^2,g^d=g^7123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4144);