↑

Learn more

The database current contains $512{,}614$ groups, including all transitive subgroups of $S_n$ (up to conjugacy) for $n \le 47$ and $n \ne 32$. Here are some further statistics.

Browse

By degree:	1 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
By type:	odd even cyclic noncyclic solvable nonsolvable primitive imprimitive
By group:	$S_3$ $D_4$ $A_4$ $S_4$ $A_5$ $S_5$ $\GL(3,2)$ $A_6$ $\PSL(2,8)$ $\PSL(2,11)$ $\PSL(2,13)$ $\PSL(3,3)$ $\PSU(3,3)$ $\PSp(4,3)$ $M_{11}$ $M_{12}$ $\cdots$
Some interesting Galois groups or a random Galois group

Search

Degree		e.g. 6 or 4,6 or 2..5 or 4,6..8	Parity
$T$-number		e.g. 3 or 4,6 or 2..5 or 4,6..8	Cyclic
Order		e.g. 6 or 4,6 or 2..35 or 4,6..80	Solvable
Nilpotency class		e.g. -1, or 1..3	Primitive
Group		list of GAP id's, e.g. [8,3] or 8.3, group names from the list of group labels, e.g. C5 or S12, and transitive group labels, e.g., 7T2 or 11T5
Equivalent siblings		e.g. 1 or 2,3 or 1..5 or 1,3..10
Results to display

Display:

Find