Show $Gl_3(\mathbb{F}_5)$ has a normal subgroup of index 4. Here is my attempt: $|Gl_3(\mathbb{F}_5)|=(5^3-1)(5^3-5)(5^3-5^2)=124*120*100=1488000=2^7*3*5^3*31$. So I'm stuck.
2026-03-29 07:19:40.1774768780
Show $Gl_3(\mathbb{F}_5)$ has a normal subgroup of index 4
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