Abstract groups

The database currently contains 544,831 groups from many different sources, the largest of which is $S_{47}$ of order $47!$. In addition, it contains 275,339,797 of their subgroups and 39,901,075 of their irreducible complex characters. You can browse further statistics.

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By order: 1-64  65-127  128  129-255  256  257-383  384  385-511  513-1000  1001-1500  1501-2000  2001- 

By nilpotency class: 1  2  3  4  5  6  7  8  9  (and not nilpotent)

By property: abelian  nonabelian  solvable  nonsolvable  simple  perfect  rational 

By family: $C_{{{n}}}$  $S_{{{n}}}$  $D_{{{n}}}$  $A_{{{n}}}$  $Q_{{{n}}}$  $F_{{{n}}}$  $\SD_{{{n}}}$  $\OD_{{{n}}}$  $\He_{{{n}}}$  $\Dic_{{{n}}}$  Sporadic  $\GL({n},{q})$  $\SL({n},{q})$  $\PSL({n},{q})$  $\PGL({n},{q})$  $\Sp({n},{q})$  $\SO({n},{q})$  $\SU({n},{q})$  $\PSp({n},{q})$  $\PSO({n},{q})$  $\PSU({n},{q})$  $\SOPlus({n},{q})$  $\SOMinus({n},{q})$  $\Orth({n},{q})$  $\OrthPlus({n},{q})$  $\OrthMinus({n},{q})$  $\Unitary({n},{q})$  $\Omega({n},{q})$  $\OmegaPlus({n},{q})$  $\OmegaMinus({n},{q})$  $\PSOPlus({n},{q})$  $\PSOMinus({n},{q})$  $\PO({n},{q})$  $\POPlus({n},{q})$  $\POMinus({n},{q})$  $\PU({n},{q})$  $\POmega({n},{q})$  $\POmegaPlus({n},{q})$  $\POmegaMinus({n},{q})$  $\Spin({n},{q})$  $\SpinPlus({n},{q})$  $\SpinMinus({n},{q})$  $\GSp({n},{q})$  $\GSO({n},{q})$  $\GSOPlus({n},{q})$  $\GSOMinus({n},{q})$  $\GSU({n},{q})$  $\GOrth({n},{q})$  $\GOrthPlus({n},{q})$  $\GOrthMinus({n},{q})$  $\GUnitary({n},{q})$  $\PGammaL({n},{q})$  $\PSigmaL({n},{q})$  $\PSigmaSp({n},{q})$  $\PGammaU({n},{q})$  $\AGL({n},{q})$  $\ASL({n},{q})$  $\ASp({n},{q})$  $\AGammaL({n},{q})$  $\ASigmaL({n},{q})$  $\ASigmaSp({n},{q})$  Chevalley  $A({n}, {q})$  $B({n}, {q})$  $C({n}, {q})$  $D({n}, {q})$  $E({n}, {q})$  $F({4}, {q})$  $G({2}, {q})$  Twisted Chevalley  $^{2}{A}({n},{q})$  $^{2}{B}({2},{q})$  $^{2}{D}({n},{q})$  $^{3}{D}({4},{q})$  $^{2}{E}({6},{q})$  $^{2}{F}({4},{q})$  $^{2}{G}({2},{q})$  Coxeter  $W(A_{{n}})$  $W(B_{{n}})$  $W(D_{{n}})$  $W(E_{{n}})$  $W(F_{{n}})$  $H_{{{n}}}$  $I_2({n})$ 

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Label or name
	e.g. 8.3, GL(2,3), 8T34, C3:C4, C2*A5, C16.D4, 6#1, or 12.4.2.b1.a1