diff --git a/src/bases_dirac.jl b/src/bases_dirac.jl
index 75d7918..54ece3e 100644
--- a/src/bases_dirac.jl
+++ b/src/bases_dirac.jl
@@ -38,8 +38,8 @@ function Base.IteratorSize(::Type{<:DiracBasis{T,S}}) where {T,S}
 end
 
 function Base.size(db::DiracBasis)
-    @assert Base.haslength(object(db))
-    return size(object(db))
+    # Some object such as `PermGroup` do not define `size`
+    return (length(db),)
 end
 
 function Base.length(db::DiracBasis)
@@ -53,6 +53,7 @@ Base.iterate(db::DiracBasis, st) = iterate(object(db), st)
 Base.in(g, db::DiracBasis) = g in object(db)
 Base.haskey(db::DiracBasis, g) = in(g, db)
 
+Base.firstindex(db::DiracBasis) = Base.first(object(db))
 function Base.getindex(db::DiracBasis{T}, x::T) where {T}
     @assert x in object(db)
     return x
diff --git a/src/bases_fixed.jl b/src/bases_fixed.jl
index 5273279..76ac973 100644
--- a/src/bases_fixed.jl
+++ b/src/bases_fixed.jl
@@ -75,6 +75,8 @@ end
 FixedBasis(basis::AbstractBasis{T}; n::Integer) where {T} = FixedBasis{T,typeof(n)}(basis; n)
 
 Base.in(x, b::FixedBasis) = haskey(b.relts, x)
+Base.firstindex(b::FixedBasis) = firstindex(b.elts)
+Base.lastindex(b::FixedBasis) = lastindex(b.elts)
 Base.getindex(b::FixedBasis{T}, x::T) where {T} = b.relts[x]
 Base.getindex(b::FixedBasis, i::Integer) = b.elts[i]
 
@@ -138,6 +140,8 @@ end
 Base.in(x::T, b::SubBasis{T}) where T = !isnothing(get(b, x, nothing))
 Base.haskey(b::SubBasis, i::Integer) = i in eachindex(b.keys)
 
+Base.firstindex(b::SubBasis) = firstindex(b.keys)
+Base.lastindex(b::SubBasis) = lastindex(b.keys)
 Base.getindex(b::SubBasis, i::Integer) = parent(b)[b.keys[i]]
 function Base.getindex(b::SubBasis{T,I}, x::T) where {T,I}
     i = get(b, x, nothing)
diff --git a/test/quadratic_form.jl b/test/quadratic_form.jl
index 85f1b0c..8afcb69 100644
--- a/test/quadratic_form.jl
+++ b/test/quadratic_form.jl
@@ -110,7 +110,9 @@ end
     mstr = ChebyMStruct(implicit)
     mt = SA.MTable(implicit, mstr, (0, 0))
     sub = SA.SubBasis(implicit, 1:3)
+    test_vector_interface(sub)
     fixed = SA.FixedBasis(implicit; n = 3)
+    test_vector_interface(fixed)
     a = ChebyPoly(2)
     b = ChebyPoly(3)
     expected = SA.SparseCoefficients((ChebyPoly(1), ChebyPoly(5)), (1 // 2, 1 // 2))
diff --git a/test/runtests.jl b/test/runtests.jl
index 07f31bd..b27be3c 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -28,6 +28,23 @@ for file in readdir(joinpath(@__DIR__, "..", "examples"))
     end
 end
 
+# Test that `basis` implements the vector interface
+# returns the same as `vector`
+function test_vector_interface(basis, vector = collect(basis))
+    @test length(basis) == length(vector)
+    @test size(basis) == size(vector)
+    @test eltype(basis) == eltype(vector)
+    @test eltype(basis) == eltype(typeof(basis))
+    @test last(basis) == last(vector)
+    i = lastindex(basis)
+    @test i == lastindex(vector)
+    @test getindex(basis, i) == last(vector)
+    @test first(basis) == first(vector)
+    i = firstindex(basis)
+    @test i == firstindex(vector)
+    @test getindex(basis, i) == first(vector)
+end
+
 @testset "StarAlgebras" begin
     include("basic.jl")
     # proof of concept