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The database contains $512{,}597$ groups, including all transitive subgroups of $S_n$, up to conjugation, for $n\leq 47$ and $n\neq 32$. There is also data for groups in degree $32$ of order less than $512$ and greater than $40{,}000{,}000{,}000$.

Browse Galois groups

Browse by degree $n$: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47

Browse by type: Odd, Even, Cyclic, Non-cyclic, Solvable, Non-solvable, Primitive, Imprimitive

Browse by abstract group: $S_3$, $D_4$, $A_4$, $S_4$, $A_5$, $S_5$, $\GL(3,2)$, $A_6$, $\PSL(2,8)$, $\PSL(2,11)$, $\PSL(2,13)$, $\PSL(3,3)$, $\PSU(3,3)$, $\PSp(4,3)$, $M_{11}$, $M_{12}$

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