Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C3×C13⋊C3)⋊C9 |
| Fitting | C3×C9×C13 ⋊ C3 |
| Sylow | C13 ⋊ C32⋊C9 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
3^4,13|a^3=d,b^a=bc,e^b=e^3141 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×C32⋊C9, C3×(C3×C13⋊C3)⋊C9, #15691554, … |
| maximal normal subgroup of | C13⋊C3×C32⋊C9, C3×(C3×C13⋊C3)⋊C9, #15691554, … |
| maximal quotient of | C13⋊#6855, (C3×C13⋊C3)⋊C27, #15691485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 18);