diff --git a/src/GroupRings.jl b/src/GroupRings.jl
index 6f3ffaa..28df494 100644
--- a/src/GroupRings.jl
+++ b/src/GroupRings.jl
@@ -569,6 +569,7 @@ module New
 include("bases.jl")
 
 include("mstructures.jl")
+include("mtables.jl")
 
 end
 
diff --git a/src/mtables.jl b/src/mtables.jl
new file mode 100644
index 0000000..ad72c23
--- /dev/null
+++ b/src/mtables.jl
@@ -0,0 +1,73 @@
+abstract type AbstractMTable{I,Tw} <: MultiplicativeStructure{Tw,I} end
+
+Base.size(mt::AbstractMTable) = size(mt.table)
+
+_check(mt::AbstractMTable) = check(mt.table, basis(mt), _istwisted(mt))
+
+function _check(product_matrix, basis, twisted::Bool)
+    idx = findfirst(iszero, product_matrix)
+    if idx != nothing
+        i, j = Tuple(idx)
+        x = (twisted ? star(basis[i]) : basis[i])
+        throw(ProductNotDefined(i, j, "$x · $(basis[j]) =
+        $(_product(Val(twisted), x, basis[j]))"))
+    end
+    return true
+end
+
+_iscached(mt::AbstractMTable, i, j) = !iszero(mt.table[i, j])
+
+
+## MTables
+
+struct MTable{I,Twisted,M<:AbstractMatrix{I}} <: AbstractMTable{I,Twisted}
+    table::M
+end
+
+MTable{Tw}(mt::AbstractMatrix{<:Integer}) where {Tw} = MTable{eltype(mt),Tw,typeof(mt)}(mt)
+
+MTable(b::AbstractBasis; table_size) = MTable{false}(b; table_size = table_size)
+
+function MTable{Tw}(basis::AbstractBasis; table_size) where {Tw}
+    @assert length(table_size) == 2
+    @assert 1 <= first(table_size) <= length(basis)
+    @assert 1 <= last(table_size) <= length(basis)
+
+    table = zeros(SparseArrays.indtype(basis), table_size)
+
+    complete!(table, basis, Val(Tw))
+
+    _check(table, basis, Tw)
+
+    return MTable{Tw}(table)
+end
+
+function complete!(table, basis, ::Val{false})
+    Threads.@threads for j in 1:size(table, 2)
+        y = basis[j]
+        for i in 1:size(table, 1)
+            table[i, j] = basis[_product(Val(false), basis[i] ,y)]
+        end
+    end
+    return table
+end
+
+function complete!(table, basis, ::Val{true})
+    Threads.@threads for i in 1:size(table, 1)
+        x = star(basis[i])
+        for j in 1:size(table, 2)
+            # star(x)*y
+            table[i, j] = basis[_product(Val(false), x, basis[j])]
+        end
+    end
+    return table
+end
+
+basis(mt::MTable) = throw("No basis is defined for a simple $(typeof(mt))")
+
+Base.@propagate_inbounds function Base.getindex(m::MTable, i::Integer, j::Integer)
+    @boundscheck checkbounds(m, i, j)
+    @boundscheck iszero(m.table[i, j]) && throw(ProductNotDefined(i, j))
+    return m.table[i, j]
+end
+