
The sporadic second Janko group $J_2$ is generated by an element of order two and one of order three and hence is a quotient of the modular group $PSL_2(\mathbb{Z}) = C_2 \ast C_3$. This Janko group has a 100dimensional permutation representation and hence there is an index 100 subgroup $G$ of the modular group such… Read more »
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