My .45 T/C only looks like a Hawken, but it's 13/16" (across-the-flats) barrel instead of the Hawken's 15/16" barrel ID's it as an early unmarked Seneca.
The thinner barrel makes for a lighter rifle, but it also won't takes loads as hefty as a heavier Hawken. (and neither will my shoulder)
I checked it's zero last week, with T/C Maxi-Hunter pre-lubed conicals over 70gr of FFFg Holy Black, and it easily put 3 shots in a 50yd group about 2x as large as the OP's RB group - about as far as I expect to see a Whitetail, where I usually hunt.
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