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We perform the first systematic analysis of particle spectra obtained fromheterotic string compactifications on non-Abelian toroidal orbifolds. Afterdeveloping a new technique to compute the particle spectrum in the case ofstandard embedding based on higher dimensional supersymmetry, we compute theHodge numbers for all recently classified 331 non-Abelian orbifold geometrieswhich yield N=1 supersymmetry for heterotic compactifications. Surprisingly,most Hodge numbers follow the empiric pattern h^(1,1) - h^(2,1) = 0 mod 6,which might be related to the number of three standard model generations.Furthermore, we study the fundamental groups in order to identify thepossibilities for non-local gauge symmetry breaking. Three examples arediscussed in detail: the simplest non-Abelian orbifold S_3 and two moreelaborate examples, T_7 and \Delta(27), which have only one untwisted Kaehlerand no untwisted complex structure modulus. Such models might be especiallyinteresting in the context of no-scale supergravity. Finally, we brieflydiscuss the case of orbifolds with vanishing Euler numbers in the context ofenhanced (spontaneously broken) supersymmetry.

Heterotic non-Abelian orbifolds