Galois groups

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

Label, name, or identifier
	e.g. 8T14