An almost simple group is a group that lies between a non-abelian simple group S an its automorphism group Aut S,
| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| A5 | Alternating group on 5 letters; = SL2(F4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simple | 5 | 3+ | A5 | 60,5 |
| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| S5 | Symmetric group on 5 letters; = PGL2(F5) = Aut(A5) = 5-cell symmetries; almost simple | 5 | 4+ | S5 | 120,34 |
| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| GL3(F2) | General linear group on F23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple | 7 | 3 | GL(3,2) | 168,42 |
| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| PGL2(F7) | Projective linear group on F72; = GL3(F2):C2 = Aut(GL3(F2)); almost simple | 8 | 6+ | PGL(2,7) | 336,208 |
| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| A6 | Alternating group on 6 letters; = PSL2(F9) = L2(9); 3rd non-abelian simple | 6 | 5+ | A6 | 360,118 |