Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C19⋊C3)⋊(C81⋊C3) |
| Sylow | C19 ⋊ C3×C81⋊C3 |
164 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 87 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|a^3=d,d^3=e,e^3=f,b^a=bf,g^a=g^4,g^c=g^11,g^d=g^7459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4398);