  A remarkable result at the intersection of number theory and group theory
states that the order of a finite group $G$ (denoted $|G|$) is divisible by the
dimension $d_R$ of any irreducible complex representation of $G$. We show that
the integer ratios ${ |G|^2 / d_R^2 } $ are combinatorially constructible using
finite algorithms which take as input the amplitudes of combinatoric
topological strings ($G$-CTST) of finite groups based on 2D Dijkgraaf-Witten
topological field theories ($G$-TQFT2). The ratios are also shown to be
eigenvalues of handle creation operators in $G$-TQFT2/$G$-CTST. These strings
have recently been discussed as toy models of wormholes and baby universes by
Marolf and Maxfield, and Gardiner and Megas. Boundary amplitudes of the
$G$-TQFT2/$G$-CTST provide algorithms for combinatoric constructions of
normalized characters. Stringy S-duality for closed $G$-CTST gives a dual
expansion generated by disconnected entangled surfaces. There are universal
relations between $G$-TQFT2 amplitudes due to the finiteness of the number $K $
of conjugacy classes. These relations can be labelled by Young diagrams and are
captured by null states in an inner product constructed by coupling the
$G$-TQFT2 to a universal TQFT2 based on symmetric group algebras. We discuss
the scenario of a 3D holographic dual for this coupled theory and the
implications of the scenario for the factorization puzzle of 2D/3D holography
raised by wormholes in 3D.
