Each row represents an automorphism given by its image on a set of generators of the group (listed as the headers of the columns).
The column "Inner by" gives an element which gives rise to the automorphism as an inner automorphism if it is, in fact, inner. Otherwise, it is blank.
Elements of the group are displayed as permutations of degree 42.
| Order | Inner by | $(1,9,5,12,3)(2,8,19,17,4)(6,18,21,16,10)(7,11,13,20,14)(22,38,42,31,25)(23,40,39,28,27)(24,30,41,37,34)(26,35,32,33,29)$ | $(1,37,14,42)(2,29)(3,41,6,28)(4,33,13,38)(5,39)(7,24)(8,26,18,23)(9,30)(10,36,15,31)(11,40,19,32)(12,22,21,34)(16,25,17,35)(20,27)$ | |
|---|---|---|---|---|
| 2 | $( 1, 7)( 2, 4)( 5,14)(10,21)(11,12)(13,20)(15,16)(17,19)(22,26)(23,32)(24,30)(27,29)(28,38)(31,35)(34,37)(40,42)$ | $(1,12,20,13,5)(2,4,8,17,19)(3,7,9,14,11)(6,18,10,15,21)(22,31,23,33,27)(24,41,34,37,30)(25,26,28,40,35)(29,32,42,39,38)$ | $(1,30)(2,33,20,28)(3,41,6,38)(4,27)(5,40,7,34)(8,22,18,32)(9,24)(10,37,11,26)(12,42,17,23)(13,29)(14,39)(15,25,19,31)(16,35,21,36)$ | |
| 4 | $( 1,16,17,14)( 2, 5)( 3,19,11, 6)( 4, 8,12,10)( 7, 9)(13,15,21,18)(22,34)(23,36,41,40)(24,33,27,38)(25,35)(26,32,28,31)(29,42,39,37)$ | $(1,9,6,15,20)(2,10,19,16,7)(3,13,18,17,4)(5,12,11,14,8)(22,33,30,40,29)(23,37,31,38,36)(24,39,26,35,34)(25,28,27,42,32)$ | $(1,39,16,29)(2,37)(3,31,19,40)(4,41,21,26)(5,42)(6,23,11,28)(7,30)(8,27,15,24)(9,33)(10,34,18,22)(12,32,13,36)(14,25,17,35)(20,38)$ | |
| 2 | $( 1,17)( 3,11)( 4,12)( 6,19)( 8,10)(13,21)(14,16)(15,18)(23,41)(24,27)(26,28)(29,39)(31,32)(33,38)(36,40)(37,42)$ | $(1,12,2,10,6)(3,21,20,16,7)(4,11,17,9,5)(8,19,15,13,14)(22,33,37,32,25)(23,42,34,27,30)(24,41,36,29,26)(28,35,31,38,39)$ | $(1,35,14,25)(2,39)(3,36,6,31)(4,22,13,34)(5,29)(7,27)(8,40,18,32)(9,30)(10,28,15,41)(11,23,19,26)(12,38,21,33)(16,37,17,42)(20,24)$ | |
| 3 | $( 1,18, 7)( 2, 3, 4)( 5,17,15)( 8,21,10)( 9,11,12)(14,16,19)(23,36,32)(24,31,37)(27,29,41)(28,38,33)(30,34,35)(39,42,40)$ | $(1,12,13,20,16)(2,3,21,14,15)(4,18,11,17,9)(6,7,10,19,8)(22,33,40,37,25)(23,28,41,26,30)(24,35,31,34,27)(29,36,39,42,38)$ | $(1,31)(2,28,13,33)(3,41)(4,27,6,38)(5,37,8,32)(7,36,21,26)(9,22,10,35)(11,34)(12,39,14,23)(15,30,19,25)(16,40,18,24)(17,42)(20,29)$ | |
| 5 | $( 1,11, 4,19,12)( 2, 3, 6,17, 7)( 5,14, 9,15,18)( 8,13,10,20,21)(22,27,33,31,23)(24,29,35,28,41)(26,38,30,32,39)(34,42,36,37,40)$ | $(1,6,11,15,14)(2,4,10,21,9)(3,13,12,7,19)(5,8,16,20,17)(22,34,26,41,33)(23,25,27,30,36)(24,40,42,29,32)(28,39,31,35,38)$ | $(1,27,8,42)(2,29)(3,35)(4,34,12,39)(5,22,13,38)(6,24,17,41)(7,28,16,25)(9,36,11,40)(10,30,19,31)(14,26)(15,32)(18,23,20,37)(21,33)$ | |
| 3 | $( 1,18, 9)( 2,17,15)( 3, 4, 5)( 6,14,19)( 7,11,12)( 8,13,21)(24,28,39)(26,32,36)(27,33,31)(29,40,38)(30,34,35)(37,42,41)$ | $(1,3,7,4,18)(5,17,13,6,15)(8,16,10,14,9)(11,12,21,20,19)(22,29,41,27,25)(23,38,24,39,33)(28,34,37,42,35)(30,36,31,40,32)$ | $(1,34)(2,27,10,26)(3,24)(4,37,14,39)(5,31,21,29)(6,36,12,38)(7,22,8,35)(9,23,13,32)(11,28)(15,30,16,25)(17,40)(18,42,19,41)(20,33)$ | |
| 3 | $( 1, 2, 4)( 3, 7,18)( 5,15,11)( 6,19,14)( 8,13,10)( 9,12,17)(23,33,31)(24,40,36)(26,29,41)(28,32,42)(30,35,34)(37,38,39)$ | $(1,4,13,14,9)(2,12,15,17,7)(3,21,16,8,19)(5,10,20,6,18)(22,39,28,23,25)(26,38,30,40,35)(27,33,36,37,32)(29,34,42,31,41)$ | $(1,31,10,39)(2,38,6,28)(3,33,13,29)(4,41)(5,36,14,42)(7,26,19,32)(8,24,11,23)(9,34,16,25)(12,35)(15,37)(17,22,21,30)(18,40)(20,27)$ | |
| 4 | $( 1,37,14,42)( 2,29)( 3,41, 6,28)( 4,33,13,38)( 5,39)( 7,24)( 8,26,18,23)( 9,30)(10,36,15,31)(11,40,19,32)(12,22,21,34)(16,25,17,35)(20,27)$ | $(1,10,17,21,4)(2,18,16,11,13)(3,20,8,19,5)(6,14,12,7,9)(22,41,37,30,39)(23,34,25,36,28)(24,40,38,27,42)(26,32,35,33,29)$ | $(1,37,14,42)(2,29)(3,41,6,28)(4,33,13,38)(5,39)(7,24)(8,26,18,23)(9,30)(10,36,15,31)(11,40,19,32)(12,22,21,34)(16,25,17,35)(20,27)$ | |
| 6 | $$ | $(1,6,12,10,2)(3,16,18,21,7)(4,13,5,11,19)(8,9,17,14,15)(22,35,25,30,34)(23,31,28,42,37)(24,26,41,29,36)(27,38,32,33,39)$ | $(1,35)(2,22,13,29)(3,42,8,27)(4,33,12,34)(5,38)(6,25,9,32)(7,41,17,23)(10,30,14,26)(11,36,16,37)(15,40,20,24)(18,28)(19,31)(21,39)$ | |
| 6 | $$ | $(1,17,9,10,5)(2,6,13,14,7)(3,21,11,16,19)(4,18,20,12,15)(22,37,32,42,31)(23,28,34,27,29)(24,38,30,40,26)(25,41,33,36,39)$ | $(1,39,12,29)(2,30)(3,41,15,28)(4,22,17,25)(5,32)(6,27,10,24)(7,31)(8,35,19,34)(9,40)(11,33,18,37)(13,42,16,38)(14,26,21,23)(20,36)$ |