`52!` is indeed between 225 and 226 bits of information.
> 52!
= 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
> 2^225
= 53,919,893,334,301,279,589,334,030,174,039,261,347,274,288,845,081,144,962,207,220,498,432
> 2^226
= 107,839,786,668,602,559,178,668,060,348,078,522,694,548,577,690,162,289,924,414,440,996,864
