diff --git a/src/mtables.jl b/src/mtables.jl
index ad72c23..dbc362b 100644
--- a/src/mtables.jl
+++ b/src/mtables.jl
@@ -71,3 +71,83 @@ Base.@propagate_inbounds function Base.getindex(m::MTable, i::Integer, j::Intege
     return m.table[i, j]
 end
 
+## CachedMTables
+
+struct CachedMTable{T,I,B<:Basis{T,I},M,Twisted} <: AbstractMTable{I,Twisted}
+    basis::B
+    table::M
+end
+
+function CachedMTable{Tw}(
+    basis::AbstractBasis{T,I};
+    table_size = (l = length(basis); (l, l)),
+) where {Tw,T,I}
+    return CachedMTable{Tw}(basis, zeros(I, table_size))
+end
+
+function CachedMTable{Tw}(basis::AbstractBasis{T,I}, mt::AbstractMatrix{I}) where {Tw,T,I}
+    return CachedMTable{T,I,typeof(basis),typeof(mt),Tw}(basis, mt)
+end
+
+function CachedMTable{Tw}(
+    basis::AbstractVector;
+    table_size = (l = length(basis); (l, l)),
+) where {Tw}
+    b = Basis{UInt32}(basis)
+    cmt = zeros(UInt32, table_size)
+    return CachedMTable{Tw}(b, cmt)
+end
+
+basis(m::CachedMTable) = m.basis
+
+Base.@propagate_inbounds function Base.getindex(cmt::CachedMTable, i::Integer, j::Integer)
+    cache!(cmt, i, j)
+    return cmt.table[i, j]
+end
+
+Base.@propagate_inbounds function cache!(cmt::CachedMTable, i::Integer, j::Integer)
+    @boundscheck checkbounds(cmt, i, j)
+    if !_iscached(cmt, i, j)
+        b = basis(cmt)
+        g, h = b[i], b[j]
+        @debug "Caching $i, $j" g h
+        gh = _product(cmt, g, h)
+        gh in b || throw(ProductNotDefined(i, j, "$g · $h = $gh"))
+        cmt.table[i, j] = b[gh]
+    end
+    return cmt
+end
+
+Base.@propagate_inbounds function cache!(
+    cmt::CachedMTable{T,I,B,M,false},
+    suppX::AbstractVector{<:Integer},
+    suppY::AbstractVector{<:Integer},
+) where {T,I,B,M}
+    Threads.@threads for j in suppY
+        for i in suppX
+            if !_iscached(cmt, i, j)
+                cache!(cmt, i, j)
+            end
+        end
+    end
+    return cmt
+end
+
+Base.@propagate_inbounds function cache!(
+    cmt::CachedMTable{T,I,B,M,true},
+    suppX::AbstractVector{<:Integer},
+    suppY::AbstractVector{<:Integer},
+) where {T,I,B,M}
+    b = basis(cmt)
+    Threads.@threads for i in suppX
+        g = star(b[i])
+        for j in suppY
+            if !_iscached(cmt, i, j)
+                gh = _product(Val(false), g, b[j])
+                gh in b || throw(ProductNotDefined(i, j, "$g · $h = $gh"))
+                cmt.table[i, j] = b[gh]
+            end
+        end
+    end
+    return cmt
+end
diff --git a/test/cachedmtables.jl b/test/cachedmtables.jl
new file mode 100644
index 0000000..7a08398
--- /dev/null
+++ b/test/cachedmtables.jl
@@ -0,0 +1,32 @@
+@testset "CachedMTable" begin
+    elts = collect(SymmetricGroup(3))
+    b = New.Basis{UInt8}(elts)
+
+    mstr = New.CachedMTable{false}(b)
+    @test all(iszero, mstr.table)
+    New.cache!(mstr, 1, 2)
+    @test mstr.table[1, 2] == 2
+    @test mstr.table[1, 1] == 0
+
+    @test mstr.table[2, 3] == 0
+    @test mstr[2, 3] == 4
+    @test mstr.table[2, 3] == 4
+
+    @test b[b[2]*b[3]] == 4
+
+
+    @test mstr.table[1, 3] == 0
+    @test mstr.table[1, 4] == 0
+    New.cache!(mstr, [1], [3, 4])
+    @test mstr.table[1, 3] != 0
+    @test mstr.table[1, 4] != 0
+
+
+    tmstr = New.CachedMTable{true}(b)
+
+    @test all(iszero, tmstr.table)
+    @test tmstr[1, 2] == 2
+    @test tmstr[2, 3] == 4
+    @test tmstr[3, 2] == b[inv(b[3])*b[2]]
+end
+
diff --git a/test/runtests.jl b/test/runtests.jl
index 70b0b53..5e7a718 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,6 +4,14 @@ using AbstractAlgebra
 using GroupRings
 using SparseArrays
 
+using GroupRings.New
+
+@testset "StarAlgebras" begin
+
+   New.star(p::Generic.Perm) = inv(p)
+
+   include("cachedmtables.jl")
+end
 
 @testset "GroupRings" begin
    @testset "Constructors: SymmetricGroup" begin