Linear and projective linear groups

Over any field K, linear group usually refers to an algebraic group which is a (Zariski closed) subgroup of the general linear group GL(n,K) of invertible n×n matrices with coefficients in K. Similarly, projective linear group refers to a closed subgroup of PGL(n,K)=GL(n,K)/{scalar matrices}, the group of linear automorphisms of the projective n-space. When K=𝔽_q is a finite field, these groups are finite, and often simple or almost simple, and so they play an important role in the classification of finite simple groups.

Groups of order 6

Groups of order 8

Groups of order 12

Groups of order 18

Groups of order 20

Groups of order 24

Groups of order 36

Groups of order 42

Groups of order 48

Groups of order 50

Groups of order 56

Groups of order 60

Groups of order 64

Groups of order 72

Groups of order 81

Groups of order 96

Groups of order 98

Groups of order 110

Groups of order 120

Groups of order 144

Groups of order 156

Groups of order 160

Groups of order 168

Groups of order 180

Groups of order 192

Groups of order 216

Groups of order 240

Groups of order 242

Groups of order 272

Groups of order 288

Groups of order 300

Groups of order 324

Groups of order 336

Groups of order 338

Groups of order 342

Groups of order 360

Groups of order 375

Groups of order 432

Groups of order 480