Refine search
Elements of the group are displayed as permutations of degree 81.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $C_3^4:\Sp(4,3)$ | 1A | $1$ | $1$ | $C_3^4:\Sp(4,3)$ | 1A | 1A | 1A | $()$ |
| $C_3^4:\Sp(4,3)$ | 2A | $2$ | $81$ | $\Sp(4,3)$ | 1A | 2A | 2A | $(1,77)(2,76)(3,78)(4,74)(5,73)(6,75)(7,80)(8,79)(9,81)(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,59)(20,58)(21,60)(22,56)(23,55)(24,57)(25,62)(26,61)(27,63)(28,50)(29,49)(30,51)(31,47)(32,46)(33,48)(34,53)(35,52)(36,54)(37,41)(38,40)(39,42)(43,44)$ |
| $C_3^4:\Sp(4,3)$ | 2B | $2$ | $810$ | $C_3^2.Q_8^2.C_3^2$ | 1A | 2B | 2B | $(1,43)(2,32)(3,48)(4,67)(5,56)(6,81)(7,10)(9,24)(11,23)(13,31)(14,47)(15,45)(16,55)(17,80)(18,69)(19,79)(20,68)(21,57)(25,46)(26,44)(27,33)(28,70)(29,59)(30,75)(34,37)(36,51)(38,50)(40,58)(41,74)(42,72)(52,73)(53,71)(54,60)(61,64)(63,78)(65,77)$ |
| $C_3^4:\Sp(4,3)$ | 3A | $3$ | $80$ | $C_3^4.C_3:S_3.A_4.C_3$ | 3A | 1A | 3A | $(1,81,41)(2,79,42)(3,80,40)(4,75,44)(5,73,45)(6,74,43)(7,78,38)(8,76,39)(9,77,37)(10,63,50)(11,61,51)(12,62,49)(13,57,53)(14,55,54)(15,56,52)(16,60,47)(17,58,48)(18,59,46)(19,72,32)(20,70,33)(21,71,31)(22,66,35)(23,64,36)(24,65,34)(25,69,29)(26,67,30)(27,68,28)$ |
| $C_3^4:\Sp(4,3)$ | 3B1 | $3$ | $120$ | $C_3^4.C_3^2.Q_8.C_6$ | 3B-1 | 1A | 3B-1 | $(1,28,55)(2,56,29)(4,31,58)(5,59,32)(7,34,61)(8,62,35)(10,37,64)(11,65,38)(13,40,67)(14,68,41)(16,43,70)(17,71,44)(19,46,73)(20,74,47)(22,49,76)(23,77,50)(25,52,79)(26,80,53)$ |
| $C_3^4:\Sp(4,3)$ | 3B-1 | $3$ | $120$ | $C_3^4.C_3^2.Q_8.C_6$ | 3B1 | 1A | 3B1 | $(1,55,28)(2,29,56)(4,58,31)(5,32,59)(7,61,34)(8,35,62)(10,64,37)(11,38,65)(13,67,40)(14,41,68)(16,70,43)(17,44,71)(19,73,46)(20,47,74)(22,76,49)(23,50,77)(25,79,52)(26,53,80)$ |
| $C_3^4:\Sp(4,3)$ | 3C1 | $3$ | $960$ | $C_3^3.\He_3.C_6$ | 3C-1 | 1A | 3C-1 | $(1,36,59)(2,71,50)(3,25,14)(4,64,52)(5,21,16)(6,29,61)(7,23,12)(8,31,57)(9,69,48)(10,45,68)(11,80,32)(13,73,34)(15,38,70)(17,40,66)(18,78,30)(19,54,77)(20,62,41)(22,55,43)(24,47,79)(26,49,75)(27,60,39)(28,53,42)(33,46,44)(35,51,37)(56,81,67)(58,74,72)(63,76,65)$ |
| $C_3^4:\Sp(4,3)$ | 3C-1 | $3$ | $960$ | $C_3^3.\He_3.C_6$ | 3C1 | 1A | 3C1 | $(1,59,36)(2,50,71)(3,14,25)(4,52,64)(5,16,21)(6,61,29)(7,12,23)(8,57,31)(9,48,69)(10,68,45)(11,32,80)(13,34,73)(15,70,38)(17,66,40)(18,30,78)(19,77,54)(20,41,62)(22,43,55)(24,79,47)(26,75,49)(27,39,60)(28,42,53)(33,44,46)(35,37,51)(56,67,81)(58,72,74)(63,65,76)$ |
| $C_3^4:\Sp(4,3)$ | 3D | $3$ | $2160$ | $C_3^5:D_4$ | 3D | 1A | 3D | $(1,30,56)(2,8,5)(3,58,35)(4,33,59)(6,61,29)(7,36,62)(9,55,32)(10,71,42)(11,40,72)(13,65,45)(14,43,66)(16,68,39)(17,37,69)(19,22,25)(20,75,46)(21,53,76)(23,78,49)(24,47,79)(26,81,52)(27,50,73)(28,34,31)(48,51,54)(57,63,60)(74,77,80)$ |
| $C_3^4:\Sp(4,3)$ | 3E1 | $3$ | $2160$ | $C_3^4:\SL(2,3)$ | 3E-1 | 1A | 3E-1 | $(1,60,81)(2,42,17)(3,24,34)(4,25,29)(5,61,73)(6,43,12)(7,38,13)(8,20,33)(9,56,77)(10,69,63)(11,51,26)(14,70,55)(15,52,21)(16,47,22)(18,65,59)(19,78,72)(23,79,64)(27,74,68)(28,49,62)(30,67,45)(31,71,37)(32,53,57)(35,66,41)(36,48,58)(39,76,54)(40,80,46)(44,75,50)$ |
| $C_3^4:\Sp(4,3)$ | 3E-1 | $3$ | $2160$ | $C_3^4:\SL(2,3)$ | 3E1 | 1A | 3E1 | $(1,81,60)(2,17,42)(3,34,24)(4,29,25)(5,73,61)(6,12,43)(7,13,38)(8,33,20)(9,77,56)(10,63,69)(11,26,51)(14,55,70)(15,21,52)(16,22,47)(18,59,65)(19,72,78)(23,64,79)(27,68,74)(28,62,49)(30,45,67)(31,37,71)(32,57,53)(35,41,66)(36,58,48)(39,54,76)(40,46,80)(44,50,75)$ |
| $C_3^4:\Sp(4,3)$ | 3F | $3$ | $4320$ | $C_3^3:C_6^2$ | 3F | 1A | 3F | $(1,61,31)(3,33,63)(4,81,38)(5,19,18)(6,50,67)(7,71,54)(8,12,22)(9,40,74)(10,53,60)(11,75,28)(13,43,64)(14,65,44)(16,36,80)(17,55,51)(20,37,57)(21,68,34)(23,30,70)(24,58,41)(26,47,77)(27,78,48)(29,42,52)(35,49,39)(56,79,69)(59,72,73)$ |
| $C_3^4:\Sp(4,3)$ | 3G1 | $3$ | $8640$ | $C_3^4:C_6$ | 3G-1 | 1A | 3G-1 | $(1,52,53)(2,3,68)(4,60,18)(5,44,33)(6,19,75)(7,11,61)(8,76,22)(9,36,37)(10,23,64)(12,39,49)(13,28,29)(14,15,80)(16,72,21)(17,47,45)(20,32,48)(24,51,34)(25,40,41)(26,27,56)(30,81,79)(31,70,59)(35,62,66)(38,65,78)(42,57,55)(43,73,71)(46,58,74)(50,77,63)(54,69,67)$ |
| $C_3^4:\Sp(4,3)$ | 3G-1 | $3$ | $8640$ | $C_3^4:C_6$ | 3G1 | 1A | 3G1 | $(1,53,52)(2,68,3)(4,18,60)(5,33,44)(6,75,19)(7,61,11)(8,22,76)(9,37,36)(10,64,23)(12,49,39)(13,29,28)(14,80,15)(16,21,72)(17,45,47)(20,48,32)(24,34,51)(25,41,40)(26,56,27)(30,79,81)(31,59,70)(35,66,62)(38,78,65)(42,55,57)(43,71,73)(46,74,58)(50,63,77)(54,67,69)$ |
| $C_3^4:\Sp(4,3)$ | 3H1 | $3$ | $8640$ | $C_3^4:C_6$ | 3H-1 | 1A | 3H-1 | $(1,55,48)(2,5,25)(3,36,77)(4,78,31)(6,47,63)(7,71,44)(8,12,15)(9,40,64)(10,43,60)(11,65,28)(13,30,70)(14,58,41)(16,50,74)(17,81,54)(18,19,22)(20,53,67)(21,75,38)(23,37,80)(24,68,51)(26,33,57)(27,61,34)(29,42,45)(32,35,46)(39,49,52)(56,76,62)(59,72,66)(69,79,73)$ |
| $C_3^4:\Sp(4,3)$ | 3H-1 | $3$ | $8640$ | $C_3^4:C_6$ | 3H1 | 1A | 3H1 | $(1,48,55)(2,25,5)(3,77,36)(4,31,78)(6,63,47)(7,44,71)(8,15,12)(9,64,40)(10,60,43)(11,28,65)(13,70,30)(14,41,58)(16,74,50)(17,54,81)(18,22,19)(20,67,53)(21,38,75)(23,80,37)(24,51,68)(26,57,33)(27,34,61)(29,45,42)(32,46,35)(39,52,49)(56,62,76)(59,66,72)(69,73,79)$ |
| $C_3^4:\Sp(4,3)$ | 3I | $3$ | $17280$ | $C_3^2\times \He_3$ | 3I | 1A | 3I | $(1,34,4)(2,23,44)(3,66,75)(5,80,65)(6,42,24)(7,58,55)(8,47,14)(9,18,54)(10,70,67)(11,32,26)(12,21,30)(13,37,16)(15,78,60)(17,56,77)(19,25,49)(20,68,62)(22,73,79)(27,63,72)(28,61,31)(29,50,71)(33,69,51)(35,74,41)(36,45,81)(38,59,53)(39,48,57)(40,64,43)(46,52,76)$ |
| $C_3^4:\Sp(4,3)$ | 4A | $4$ | $4860$ | $C_4\times \PU(3,2)$ | 2B | 4A | 4A | $(1,18,43,29)(2,77,30,72)(3,28,50,22)(4,60,65,12)(5,38,58,52)(6,25,81,59)(7,48,15,73)(9,67,19,42)(10,66,80,27)(11,53,64,31)(13,36,21,61)(16,24,49,44)(17,56,45,78)(23,71,51,57)(26,32,79,37)(34,62,75,47)(35,40,68,63)(41,46,74,69)$ |
| $C_3^4:\Sp(4,3)$ | 4B | $4$ | $43740$ | $\Unitary(2,3)$ | 2A | 4B | 4B | $(1,3,49,50)(2,71,51,72)(4,32,46,21)(5,10,48,40)(6,81,47,62)(7,61,52,79)(8,42,54,11)(9,20,53,33)(12,67,41,64)(13,77,37,57)(14,28,39,22)(15,18,38,44)(16,25,43,34)(17,60,45,74)(19,66,31,68)(23,73,30,58)(24,36,29,26)(27,56,35,78)(55,75,76,59)(63,65,80,69)$ |
| $C_3^4:\Sp(4,3)$ | 4C | $4$ | $43740$ | $C_4\times \SL(2,3)$ | 2B | 4C | 4C | $(1,34,17,19)(2,7,22,40)(3,61)(4,64,66,12)(5,37,80,33)(6,10,58,81)(8,76,48,50)(9,49,35,71)(11,31,59,54)(13,16,46,23)(14,70,36,44)(15,43,41,56)(18,73)(20,55,42,29)(21,28,47,77)(24,67)(25,79,60,27)(26,52,65,39)(30,74,72,63)(38,53)(45,68,78,75)(51,62,57,69)$ |
| $C_3^4:\Sp(4,3)$ | 5A | $5$ | $419904$ | $C_{10}$ | 5A | 5A | 1A | $(1,38,80,16,52)(2,14,63,10,65)(3,71,70,13,6)(4,60,81,64,35)(5,36,61,67,75)(7,25,79,40,45)(8,73,62,43,55)(9,49,72,37,23)(11,41,12,17,19)(15,30,20,68,51)(18,76,21,44,31)(22,33,42,69,27)(24,57,32,66,59)(26,46,50,39,47)(28,77,78,54,34)(29,53,58,48,74)$ |
| $C_3^4:\Sp(4,3)$ | 6A1 | $6$ | $3240$ | $C_2\times \Unitary(3,2)$ | 3B1 | 2A | 6A-1 | $(1,23,28,77,55,50)(2,49,56,76,29,22)(3,78)(4,20,31,74,58,47)(5,46,59,73,32,19)(6,75)(7,26,34,80,61,53)(8,52,62,79,35,25)(9,81)(10,14,37,68,64,41)(11,40,65,67,38,13)(12,69)(15,66)(16,17,43,71,70,44)(18,72)(21,60)(24,57)(27,63)(30,51)(33,48)(36,54)(39,42)$ |
| $C_3^4:\Sp(4,3)$ | 6A-1 | $6$ | $3240$ | $C_2\times \Unitary(3,2)$ | 3B-1 | 2A | 6A1 | $(1,50,55,77,28,23)(2,22,29,76,56,49)(3,78)(4,47,58,74,31,20)(5,19,32,73,59,46)(6,75)(7,53,61,80,34,26)(8,25,35,79,62,52)(9,81)(10,41,64,68,37,14)(11,13,38,67,65,40)(12,69)(15,66)(16,44,70,71,43,17)(18,72)(21,60)(24,57)(27,63)(30,51)(33,48)(36,54)(39,42)$ |
| $C_3^4:\Sp(4,3)$ | 6B1 | $6$ | $3240$ | $C_6\times \PU(3,2)$ | 3B-1 | 2B | 6B-1 | $(1,66)(2,46,64,65,48,3)(4,6,50,68,69,49)(5,67)(7,54,72,70,53,8)(9,71)(10,75)(11,28,73,74,30,12)(13,15,32,77,78,31)(14,76)(16,36,81,79,35,17)(18,80)(19,57)(20,37,55,56,39,21)(22,24,41,59,60,40)(23,58)(25,45,63,61,44,26)(27,62)$ |
| $C_3^4:\Sp(4,3)$ | 6B-1 | $6$ | $3240$ | $C_6\times \PU(3,2)$ | 3B1 | 2B | 6B1 | $(1,66)(2,3,48,65,64,46)(4,49,69,68,50,6)(5,67)(7,8,53,70,72,54)(9,71)(10,75)(11,12,30,74,73,28)(13,31,78,77,32,15)(14,76)(16,17,35,79,81,36)(18,80)(19,57)(20,21,39,56,55,37)(22,40,60,59,41,24)(23,58)(25,26,44,61,63,45)(27,62)$ |
| $C_3^4:\Sp(4,3)$ | 6C | $6$ | $6480$ | $\He_3\times \SL(2,3)$ | 3A | 2B | 6C | $(1,76,81,39,41,8)(2,55,79,54,42,14)(3,70,80,33,40,20)(4,49,75,12,44,62)(5,28,73,27,45,68)(6,43,74)(7,22,78,66,38,35)(9,16,77,60,37,47)(10,50,63)(11,29,61,25,51,69)(13,23,57,64,53,36)(15,17,56,58,52,48)(18,71,59,31,46,21)(19,24,72,65,32,34)(26,30,67)$ |
| $C_3^4:\Sp(4,3)$ | 6D1 | $6$ | $9720$ | $C_3\times S_3\times \SL(2,3)$ | 3B1 | 2B | 6D-1 | $(1,23,22,17,16,2)(3,18,24)(4,66)(5,80)(6,58)(7,34,13,40,19,46)(8,42,14,48,20,36)(9,47,15,35,21,41)(10,81)(11,59)(12,64)(25,60)(26,65)(27,79)(28,56,49,77,43,71)(29,70,50,55,44,76)(30,78,51,72,45,57)(31,54)(33,37)(39,52)(61,73,67)(62,63,68,69,74,75)$ |
| $C_3^4:\Sp(4,3)$ | 6D-1 | $6$ | $9720$ | $C_3\times S_3\times \SL(2,3)$ | 3B-1 | 2B | 6D1 | $(1,2,16,17,22,23)(3,24,18)(4,66)(5,80)(6,58)(7,46,19,40,13,34)(8,36,20,48,14,42)(9,41,21,35,15,47)(10,81)(11,59)(12,64)(25,60)(26,65)(27,79)(28,71,43,77,49,56)(29,76,44,55,50,70)(30,57,45,72,51,78)(31,54)(33,37)(39,52)(61,67,73)(62,75,74,69,68,63)$ |
| $C_3^4:\Sp(4,3)$ | 6E | $6$ | $19440$ | $C_3^3:D_4$ | 3D | 2A | 6E | $(1,78,30,49,56,23)(2,48,8,51,5,54)(3,27,58,50,35,73)(4,75,33,46,59,20)(6,24,61,47,29,79)(7,81,36,52,62,26)(9,21,55,53,32,76)(10,11,71,40,42,72)(12,41)(13,17,65,37,45,69)(14,68,43,39,66,16)(15,38)(18,44)(19,34,22,31,25,28)(57,74,63,77,60,80)(64,67)$ |
| $C_3^4:\Sp(4,3)$ | 6F1 | $6$ | $19440$ | $C_3^2\times \SL(2,3)$ | 3E1 | 2B | 6F-1 | $(1,6,60,43,81,12)(2,45,42,30,17,67)(3,75,24,50,34,44)(4,18,25,65,29,59)(5,48,61,58,73,36)(7,21,38,15,13,52)(8,33,20)(9,72,56,19,77,78)(10,40,69,80,63,46)(11,79,51,64,26,23)(14,55,70)(16,28,47,49,22,62)(27,35,74,66,68,41)(31,32,71,53,37,57)(39,54,76)$ |
| $C_3^4:\Sp(4,3)$ | 6F-1 | $6$ | $19440$ | $C_3^2\times \SL(2,3)$ | 3E-1 | 2B | 6F1 | $(1,12,81,43,60,6)(2,67,17,30,42,45)(3,44,34,50,24,75)(4,59,29,65,25,18)(5,36,73,58,61,48)(7,52,13,15,38,21)(8,20,33)(9,78,77,19,56,72)(10,46,63,80,69,40)(11,23,26,64,51,79)(14,70,55)(16,62,22,49,47,28)(27,41,68,66,74,35)(31,57,37,53,71,32)(39,76,54)$ |
| $C_3^4:\Sp(4,3)$ | 6G1 | $6$ | $25920$ | $C_6\times \He_3$ | 3C-1 | 2B | 6G-1 | $(1,69,47,79,66,56)(2,28,15,74,25,12)(3,26,61,78,32,46)(4,33,17,76,21,14)(5,19,57,80,34,51)(6,71,49,75,68,58)(7,24,59,73,30,53)(8,64,54,77,70,63)(9,35,10,81,23,16)(11,40,72)(13,45,65)(18,38,67)(20,52,39,29,55,42)(22,48,41,31,60,44)(27,50,43,36,62,37)$ |
| $C_3^4:\Sp(4,3)$ | 6G-1 | $6$ | $25920$ | $C_6\times \He_3$ | 3C1 | 2B | 6G1 | $(1,56,66,79,47,69)(2,12,25,74,15,28)(3,46,32,78,61,26)(4,14,21,76,17,33)(5,51,34,80,57,19)(6,58,68,75,49,71)(7,53,30,73,59,24)(8,63,70,77,54,64)(9,16,23,81,10,35)(11,72,40)(13,65,45)(18,67,38)(20,42,55,29,39,52)(22,44,60,31,41,48)(27,37,62,36,43,50)$ |
| $C_3^4:\Sp(4,3)$ | 6H | $6$ | $38880$ | $C_3^2\times D_6$ | 3F | 2A | 6H | $(1,26,61,47,31,77)(2,46)(3,78,33,48,63,27)(4,10,81,53,38,60)(5,42,19,52,18,29)(6,71,50,54,67,7)(8,35,12,49,22,39)(9,55,40,51,74,17)(11,20,75,37,28,57)(13,65,43,44,64,14)(15,45)(16,58,36,41,80,24)(21,23,68,30,34,70)(25,32)(56,72,79,73,69,59)(62,76)$ |
| $C_3^4:\Sp(4,3)$ | 6I1 | $6$ | $38880$ | $C_3^2\times D_6$ | 3D | 2B | 6I-1 | $(1,13,25)(2,3,26,27,14,15)(4,44,5,31,6,48)(7,66,12,61,23,77)(8,62,10,78,24,64)(9,76,11,65,22,63)(16,47,17,43,18,33)(19,32,20,46,21,45)(28,56,41,55,54,57)(29,79,42,81,52,80)(30,69,40,68,53,67)(35,51)(36,38)(39,50)(58,73,70)(59,72,71,75,74,60)$ |
| $C_3^4:\Sp(4,3)$ | 6I-1 | $6$ | $38880$ | $C_3^2\times D_6$ | 3D | 2B | 6I1 | $(1,25,13)(2,15,14,27,26,3)(4,48,6,31,5,44)(7,77,23,61,12,66)(8,64,24,78,10,62)(9,63,22,65,11,76)(16,33,18,43,17,47)(19,45,21,46,20,32)(28,57,54,55,41,56)(29,80,52,81,42,79)(30,67,53,68,40,69)(35,51)(36,38)(39,50)(58,70,73)(59,60,74,75,71,72)$ |
| $C_3^4:\Sp(4,3)$ | 6J1 | $6$ | $38880$ | $C_3^2\times D_6$ | 3F | 2B | 6J-1 | $(1,67,2,69,3,68)(4,80,24,71,14,62)(5,79,22,70,15,61)(6,81,23,72,13,63)(7,57,16,64,25,74)(8,56,17,66,26,73)(9,55,18,65,27,75)(10,77,11,76,12,78)(19,60,20,59,21,58)(28,38,47,30,39,46)(29,37,48)(31,51,42,32,50,40)(33,49,41)(35,36)(43,44)(52,54)$ |
| $C_3^4:\Sp(4,3)$ | 6J-1 | $6$ | $38880$ | $C_3^2\times D_6$ | 3F | 2B | 6J1 | $(1,68,3,69,2,67)(4,62,14,71,24,80)(5,61,15,70,22,79)(6,63,13,72,23,81)(7,74,25,64,16,57)(8,73,26,66,17,56)(9,75,27,65,18,55)(10,78,12,76,11,77)(19,58,21,59,20,60)(28,46,39,30,47,38)(29,48,37)(31,40,50,32,42,51)(33,41,49)(35,36)(43,44)(52,54)$ |
| $C_3^4:\Sp(4,3)$ | 6K1 | $6$ | $77760$ | $C_3^2\times C_6$ | 3G1 | 2B | 6K-1 | $(1,71,52,43,53,73)(2,20,3,32,68,48)(4,69,60,67,18,54)(5,27,44,56,33,26)(6,30,19,81,75,79)(7,64,11,10,61,23)(8,22,76)(9,34,36,24,37,51)(12,49,39)(13,59,28,31,29,70)(14,17,15,47,80,45)(16,57,72,55,21,42)(25,74,40,46,41,58)(35,66,62)(38,63,65,50,78,77)$ |
| $C_3^4:\Sp(4,3)$ | 6K-1 | $6$ | $77760$ | $C_3^2\times C_6$ | 3G-1 | 2B | 6K1 | $(1,73,53,43,52,71)(2,48,68,32,3,20)(4,54,18,67,60,69)(5,26,33,56,44,27)(6,79,75,81,19,30)(7,23,61,10,11,64)(8,76,22)(9,51,37,24,36,34)(12,39,49)(13,70,29,31,28,59)(14,45,80,47,15,17)(16,42,21,55,72,57)(25,58,41,46,40,74)(35,62,66)(38,77,78,50,65,63)$ |
| $C_3^4:\Sp(4,3)$ | 6L1 | $6$ | $77760$ | $C_3^2\times C_6$ | 3H1 | 2B | 6L-1 | $(1,78,55,31,48,4)(2,16,5,50,25,74)(3,29,36,42,77,45)(6,72,47,66,63,59)(7,44,71)(8,57,12,26,15,33)(9,22,40,18,64,19)(10,39,43,49,60,52)(11,58,65,41,28,14)(13,79,30,73,70,69)(17,54,81)(20,46,53,32,67,35)(21,68,75,51,38,24)(23,62,37,56,80,76)(27,34,61)$ |
| $C_3^4:\Sp(4,3)$ | 6L-1 | $6$ | $77760$ | $C_3^2\times C_6$ | 3H-1 | 2B | 6L1 | $(1,4,48,31,55,78)(2,74,25,50,5,16)(3,45,77,42,36,29)(6,59,63,66,47,72)(7,71,44)(8,33,15,26,12,57)(9,19,64,18,40,22)(10,52,60,49,43,39)(11,14,28,41,65,58)(13,69,70,73,30,79)(17,81,54)(20,35,67,32,53,46)(21,24,38,51,75,68)(23,76,80,56,37,62)(27,61,34)$ |
| $C_3^4:\Sp(4,3)$ | 8A | $8$ | $524880$ | $C_8$ | 4B | 8A | 8A | $(1,69,4,71,77,12,74,16)(2,25,46,15,76,62,32,66)(3,29,70,37,78,49,17,41)(5,21,11,43,73,60,67,44)(6,31,35,68,75,47,52,10)(7,64,42,40,80,14,39,38)(8,23,57,65,79,55,24,13)(9,36,27,18,81,54,63,72)(19,51,58,26,59,30,20,61)(22,53,50,48,56,34,28,33)$ |
| $C_3^4:\Sp(4,3)$ | 9A1 | $9$ | $77760$ | $S_3\times C_9$ | 9A-1 | 3B1 | 9A-1 | $(1,10,58,28,37,4,55,64,31)(2,17,11,56,71,65,29,44,38)(3,15,54)(5,62,26,59,35,80,32,8,53)(6,60,33)(7,46,79,34,73,25,61,19,52)(9,51,39)(12,63,24)(13,49,43,40,76,70,67,22,16)(14,47,77,68,20,50,41,74,23)(21,48,75)(27,57,69)(30,42,81)(36,78,66)$ |
| $C_3^4:\Sp(4,3)$ | 9A-1 | $9$ | $77760$ | $S_3\times C_9$ | 9A1 | 3B-1 | 9A1 | $(1,31,64,55,4,37,28,58,10)(2,38,44,29,65,71,56,11,17)(3,54,15)(5,53,8,32,80,35,59,26,62)(6,33,60)(7,52,19,61,25,73,34,79,46)(9,39,51)(12,24,63)(13,16,22,67,70,76,40,43,49)(14,23,74,41,50,20,68,77,47)(21,75,48)(27,69,57)(30,81,42)(36,66,78)$ |
| $C_3^4:\Sp(4,3)$ | 9B1 | $9$ | $155520$ | $C_3\times C_9$ | 9B-1 | 3C1 | 9B-1 | $(1,21,71,36,16,50,59,5,2)(3,11,31,25,80,57,14,32,8)(4,19,81,64,54,67,52,77,56)(6,12,41,29,7,20,61,23,62)(9,10,51,69,45,37,48,68,35)(13,49,76,73,75,65,34,26,63)(15,42,39,38,28,27,70,53,60)(17,33,18,40,46,78,66,44,30)(22,79,74,55,24,72,43,47,58)$ |
| $C_3^4:\Sp(4,3)$ | 9B-1 | $9$ | $155520$ | $C_3\times C_9$ | 9B1 | 3C-1 | 9B1 | $(1,2,5,59,50,16,36,71,21)(3,8,32,14,57,80,25,31,11)(4,56,77,52,67,54,64,81,19)(6,62,23,61,20,7,29,41,12)(9,35,68,48,37,45,69,51,10)(13,63,26,34,65,75,73,76,49)(15,60,53,70,27,28,38,39,42)(17,30,44,66,78,46,40,18,33)(22,58,47,43,72,24,55,74,79)$ |
| $C_3^4:\Sp(4,3)$ | 10A | $10$ | $419904$ | $C_{10}$ | 5A | 10A | 2A | $(1,51,38,15,80,30,16,20,52,68)(2,48,14,74,63,29,10,53,65,58)(3,54,71,34,70,28,13,77,6,78)(4,75,60,5,81,36,64,61,35,67)(7,27,25,22,79,33,40,42,45,69)(8,24,73,57,62,32,43,66,55,59)(9,21,49,44,72,31,37,18,23,76)(11,50,41,39,12,47,17,26,19,46)$ |
| $C_3^4:\Sp(4,3)$ | 12A | $12$ | $38880$ | $C_4\times \He_3$ | 6C | 4A | 12A | $(1,13,76,23,81,57,39,64,41,53,8,36)(2,49,55,75,79,12,54,44,42,62,14,4)(3,58,70,52,80,48,33,15,40,17,20,56)(5,38,28,35,73,7,27,22,45,78,68,66)(6,74,43)(9,72,16,65,77,32,60,34,37,19,47,24)(10,63,50)(11,18,29,71,61,59,25,31,51,46,69,21)(26,67,30)$ |
| $C_3^4:\Sp(4,3)$ | 12B1 | $12$ | $58320$ | $S_3\times C_{12}$ | 6D1 | 4A | 12B-1 | $(1,5,13,77,53,48,29,12,69,70,81,34)(2,14,59,18,67,79,43,74,54,30,21,31)(3,23,51,28)(6,22,42,66,71,63,26,50,46,38,55,7)(8,15,68,61)(9,24,33,20,49,37,73,45,65,62,17,58)(10,78,35)(11,60,27,32)(16,76,44,56)(19,40,75,36)(25,41,57)(39,64,80,52)$ |