Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting | C9×C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ #10624888 |
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^6,19|b^3=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^7699 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 3470);