Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C19×#6875 ⋊ C3 |
| Sylow | C19 ⋊ #10624828 |
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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=e,c^3=d,e^3=f,b^a=bd,c^a=ce,d^a=df,g^b=g^7,e^c=ef^2267 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 3071);