Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C9×C13 ⋊ C3 |
| Sylow | C13 ⋊ #732 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
3^4,13|b^3=d^2,b^a=bc,c^a=cd,e^a=e^3125 conjugacy classes — view the full character table.
| maximal subgroup of | #15691520, #15691521, #15691522, … |
| maximal normal subgroup of | #15691520, #15691521, #15691522, … |
| maximal quotient of | #15691461, #15691470, #15691474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 35);