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A Lie Group which has a simply connected covering group Homeomorphic to 
. The prototype is any
connected closed subgroup of upper triangular Complex matrices with 1s on the diagonal. The
Heisenberg Group is such a group.
References
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.