Relating back to recent events a study from Finland shows transgender and non binary youths are more likely to be bullies than cisgender individuals. Unadjusted odds ratio of 4.45 and 5.25 respectively and initial regression modelling actually increases the OR.

https://www.frontiersin.org/articles/10.3389/fpsyg.2020.612424/full#h4

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I wonder how much of that is because the system protects them so their targets can't fight back. I can believe trannys would want to be bullies but I feel like they'd do a bad job at it in a vacuum.

They are (in school at least) bullied more as well as you can see from the table but the odds ratios are smaller. A few factors to consider:

1) most trans and non binary kids, particularly outside the US aren't on blockers or hormones so you can still get a 6'6' 300lb boy in a dress clotheslining you.

2) While transgenderism isn't officially a mental illness (LOL) other studies such as https://doi.org/10.1007/s10508-009-9570-y have shown high rates of antisocial personality disorder which predicts both bullying and their infamously high crime rates.