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The database current contains $512{,}613$ groups, including all transitive subgroups of $S_n$ (up to conjugacy) for $n \le 47$ and $n \ne 32$. Here are some further statistics.

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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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e.g. 8T14