Jim Caprioli at The Finland Station

      

      StructureDescription(<G>) ::=
      

      1                                 ; trivial group
      

      | C<size>                           ; cyclic group
      

      | A<degree>                         ; alternating group
      

      | S<degree>                         ; symmetric group
      

      | D<size>                           ; dihedral group
      

      | Q<size>                           ; quaternion group
      

      | QD<size>                          ; quasidihedral group
      

      | PSL(<n>,<q>)                      ; projective special linear group
      

      | SL(<n>,<q>)                       ; special linear group
      

      | GL(<n>,<q>)                       ; general linear group
      

      | PSU(<n>,<q>)                      ; proj. special unitary group
      

      | O(2<n>+1,<q>)                     ; orthogonal group, type B
      

      | O+(2<n>,<q>)                      ; orthogonal group, type D
      

      | O-(2<n>,<q>)                      ; orthogonal group, type 2D
      

      | PSp(2<n>,<q>)                     ; proj. special symplectic group
      

      | Sz(<q>)                           ; Suzuki group
      

      | Ree(<q>)                          ; Ree group (type 2F or 2G)
      

      | E(6,<q>) | E(7,<q>) | E(8,<q>)    ; Lie group of exceptional type
      

      | 2E(6,<q>) | F(4,<q>) | G(2,<q>)
      

      | 3D(4,<q>)                         ; Steinberg triality group
      

      | M11 | M12 | M22 | M23 | M24
      

      | J1 | J2 | J3 | J4 | Co1 | Co2
      

      | Co3 | Fi22 | Fi23 | Fi24' | Suz
      

      | HS | McL | He | HN | Th | B
      

      | M | ON | Ly | Ru                  ; sporadic simple group
      

      | 2F(4,2)'                          ; Tits group
      

      | PerfectGroup(<size>,<id>)         ; the indicated group from the
      

      ; library of perfect groups
      

      | A x B                             ; direct product
      

      | N : H                             ; semidirect product
      

      | C(G) . G/C(G) = G' . G/G'         ; non-split extension
      

      ; (equal alternatives and
      

      ; trivial extensions omitted)
      

      | Phi(G) . G/Phi(G)                 ; non-split extension:
      

      ; Frattini subgroup and
      

      ; Frattini factor group