While conducting a near-infrared ( NIR ) survey of “ Digel Clouds ” , which are thought to be located in the extreme outer Galaxy ( EOG ) , Kobayashi & Tokunaga found star formation activity in “ Cloud 2 ” , a giant molecular cloud at the Galactic radius of \sim 20 kpc . Additional infrared imaging showed two embedded young clusters at the densest regions of the molecular cloud . Because the molecular cloud is located in the vicinity of a supernova remnant ( SNR ) HI shell , GSH 138-01-94 , it was suggested that the star formation activity in Cloud 2 was triggered by this expanding HI shell . We obtained deep J ( 1.25 \mu m ) , H ( 1.65 \mu m ) and K ( 2.2 \mu m ) images of one of the embedded clusters in Cloud 2 with high spatial resolution ( FWHM \sim 0 \farcs 3 ) and high sensitivity ( K \sim 20 mag , 10 \sigma ) . We identified 52 cluster members . The estimated stellar density ( \sim 10 pc ^ { -2 } ) suggests that the cluster is a T-association . This is the deepest NIR imaging of an embedded cluster in the EOG . The observed K-band luminosity function ( KLF ) suggests that the underlying initial mass function ( IMF ) of the cluster down to the detection limit of \sim 0.1 M _ { \odot } is not significantly different from the typical IMFs in the field and in the near-by star clusters . The overall characteristics of this cluster appears to be similar to those of other embedded clusters in the far outer Galaxy . The estimated age of the cluster from the KLF , which is less than 1 Myr , is consistent with the view that the star formation was triggered by the HI shell whose age was estimated at 4.3 Myr ( Stil & Irwin ) . The 3-dimensional geometry of SNR shell , molecular cloud and the embedded cluster , which is inferred from our data , as well as the cluster age strongly suggest that the star formation in Cloud 2 was triggered by the SNR shell .