Geodesic
Complex representations of the group $GL(2,Z/p^nZ)$
Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 95-103

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We obtain a description of all irreducible complex representations of the group indicated in the title ($p\ne2$ is a prime). Namely, for each $n\geqslant2$ we distinguish three series of representations of degrees $(p+I)p^{n-1}$, $(p^2-I)p^{n-2}$, $(p-I)p^{n-1}$. The other representations of $GL(2,Z_{p^n})$ are obtained from representations of $GL(2,Z_{p^{n-1}})$ by tensor multiplication by one-dimensional representations. 
@article{ZNSL_1976_64_a9,
     author = {S. V. Nagornyi},
     title = {Complex representations of the group $GL(2,Z/p^nZ)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--103},
     publisher = {mathdoc},
     volume = {64},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a9/}
}
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S. V. Nagornyi. Complex representations of the group $GL(2,Z/p^nZ)$. Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 95-103. http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a9/