/usr/bin/git-delete-branch is in git-extras 1.9.1-2.
This file is owned by root:root, with mode 0o755.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 | #!/bin/sh
branch=$1
test -z $branch && echo "branch required." 1>&2 && exit 1
git branch -D $branch
git branch -d -r origin/$branch
git push origin :refs/heads/$branch
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