The Sanhedrin was also referred to as the Great Sanhedrin because there was also a Lesser Sanhedrin. Not only did the Great Sanhedrin have more members (71 as opposed to 23), but it also had fewer councils (there was only one Great Sanhedrin while there was a Lesser Sanhedrin in every city).
The Sanhedrin Religious ruled on religious matters (Num. 11: 16). The Sanhedrin Political, made up of priests, Levites, and what we would call aristocrats, ruled on political matters. This is where Jesus ended up.
The Lesser Sanhedrin ruled on most cases with capital punishment. Still, neither could sentence someone to death penalty. (That is why Jesus had to go before Pilate and Herod.) They would have gotten in T-R-O-U-B-L-E if they would have sentenced Him to die.
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