metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.40C24, D20.35C23, 2- 1+4⋊4D5, Dic10.35C23, C5⋊5(Q8○D8), (C5×D4).39D4, (C5×Q8).39D4, C4○D4.17D10, C20.272(C2×D4), D4⋊D5.2C22, (C2×Q8).93D10, C4.40(C23×D5), Q8⋊D5.3C22, D4.21(C5⋊D4), D4.Dic5⋊13C2, C5⋊2C8.19C23, Q8.21(C5⋊D4), (C5×D4).28C23, D4.28(C22×D5), D4.D5.3C22, D4.9D10⋊12C2, D4.8D10⋊11C2, (C5×Q8).28C23, Q8.28(C22×D5), C20.C23⋊12C2, C5⋊Q16.4C22, (C2×C20).121C23, C4○D20.34C22, C10.174(C22×D4), (C5×2- 1+4)⋊3C2, D4.10D10⋊10C2, (Q8×C10).154C22, C4.Dic5.32C22, (C2×Dic10).211C22, C4.78(C2×C5⋊D4), (C2×C5⋊Q16)⋊32C2, (C2×C10).88(C2×D4), C22.9(C2×C5⋊D4), C2.47(C22×C5⋊D4), (C5×C4○D4).30C22, (C2×C4).105(C22×D5), (C2×C5⋊2C8).185C22, SmallGroup(320,1510)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D20.35C23
G = < a,b,c,d,e | a20=b2=e2=1, c2=d2=a10, bab=a-1, ac=ca, ad=da, eae=a11, bc=cb, bd=db, ebe=a15b, dcd-1=a10c, ce=ec, de=ed >
Subgroups: 726 in 248 conjugacy classes, 107 normal (20 characteristic)
C1, C2, C2 [×5], C4, C4 [×3], C4 [×6], C22 [×3], C22 [×2], C5, C8 [×4], C2×C4 [×3], C2×C4 [×12], D4, D4 [×3], D4 [×7], Q8, Q8 [×3], Q8 [×9], D5, C10, C10 [×4], C2×C8 [×3], M4(2) [×3], D8, SD16 [×6], Q16 [×9], C2×Q8 [×3], C2×Q8 [×5], C4○D4, C4○D4 [×3], C4○D4 [×9], Dic5 [×3], C20, C20 [×3], C20 [×3], D10, C2×C10 [×3], C2×C10, C8○D4, C2×Q16 [×3], C4○D8 [×3], C8.C22 [×6], 2- 1+4, 2- 1+4, C5⋊2C8, C5⋊2C8 [×3], Dic10 [×3], Dic10 [×3], C4×D5 [×3], D20, C2×Dic5 [×3], C5⋊D4 [×3], C2×C20 [×3], C2×C20 [×6], C5×D4, C5×D4 [×3], C5×D4 [×3], C5×Q8, C5×Q8 [×3], C5×Q8 [×3], Q8○D8, C2×C5⋊2C8 [×3], C4.Dic5 [×3], D4⋊D5, D4.D5 [×3], Q8⋊D5 [×3], C5⋊Q16 [×9], C2×Dic10 [×3], C4○D20 [×3], D4⋊2D5 [×3], Q8×D5, Q8×C10 [×3], Q8×C10, C5×C4○D4, C5×C4○D4 [×3], C5×C4○D4 [×3], C20.C23 [×3], C2×C5⋊Q16 [×3], D4.Dic5, D4.8D10 [×3], D4.9D10 [×3], D4.10D10, C5×2- 1+4, D20.35C23
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C22×D4, C5⋊D4 [×4], C22×D5 [×7], Q8○D8, C2×C5⋊D4 [×6], C23×D5, C22×C5⋊D4, D20.35C23
►On 160 points
Generators in S160
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)
(1 20)(2 19)(3 18)(4 17)(5 16)(6 15)(7 14)(8 13)(9 12)(10 11)(21 27)(22 26)(23 25)(28 40)(29 39)(30 38)(31 37)(32 36)(33 35)(41 60)(42 59)(43 58)(44 57)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(61 69)(62 68)(63 67)(64 66)(70 80)(71 79)(72 78)(73 77)(74 76)(81 94)(82 93)(83 92)(84 91)(85 90)(86 89)(87 88)(95 100)(96 99)(97 98)(101 105)(102 104)(106 120)(107 119)(108 118)(109 117)(110 116)(111 115)(112 114)(121 126)(122 125)(123 124)(127 140)(128 139)(129 138)(130 137)(131 136)(132 135)(133 134)(141 151)(142 150)(143 149)(144 148)(145 147)(152 160)(153 159)(154 158)(155 157)
(1 98 11 88)(2 99 12 89)(3 100 13 90)(4 81 14 91)(5 82 15 92)(6 83 16 93)(7 84 17 94)(8 85 18 95)(9 86 19 96)(10 87 20 97)(21 120 31 110)(22 101 32 111)(23 102 33 112)(24 103 34 113)(25 104 35 114)(26 105 36 115)(27 106 37 116)(28 107 38 117)(29 108 39 118)(30 109 40 119)(41 124 51 134)(42 125 52 135)(43 126 53 136)(44 127 54 137)(45 128 55 138)(46 129 56 139)(47 130 57 140)(48 131 58 121)(49 132 59 122)(50 133 60 123)(61 152 71 142)(62 153 72 143)(63 154 73 144)(64 155 74 145)(65 156 75 146)(66 157 76 147)(67 158 77 148)(68 159 78 149)(69 160 79 150)(70 141 80 151)
(1 41 11 51)(2 42 12 52)(3 43 13 53)(4 44 14 54)(5 45 15 55)(6 46 16 56)(7 47 17 57)(8 48 18 58)(9 49 19 59)(10 50 20 60)(21 72 31 62)(22 73 32 63)(23 74 33 64)(24 75 34 65)(25 76 35 66)(26 77 36 67)(27 78 37 68)(28 79 38 69)(29 80 39 70)(30 61 40 71)(81 137 91 127)(82 138 92 128)(83 139 93 129)(84 140 94 130)(85 121 95 131)(86 122 96 132)(87 123 97 133)(88 124 98 134)(89 125 99 135)(90 126 100 136)(101 154 111 144)(102 155 112 145)(103 156 113 146)(104 157 114 147)(105 158 115 148)(106 159 116 149)(107 160 117 150)(108 141 118 151)(109 142 119 152)(110 143 120 153)
(1 32)(2 23)(3 34)(4 25)(5 36)(6 27)(7 38)(8 29)(9 40)(10 31)(11 22)(12 33)(13 24)(14 35)(15 26)(16 37)(17 28)(18 39)(19 30)(20 21)(41 63)(42 74)(43 65)(44 76)(45 67)(46 78)(47 69)(48 80)(49 71)(50 62)(51 73)(52 64)(53 75)(54 66)(55 77)(56 68)(57 79)(58 70)(59 61)(60 72)(81 104)(82 115)(83 106)(84 117)(85 108)(86 119)(87 110)(88 101)(89 112)(90 103)(91 114)(92 105)(93 116)(94 107)(95 118)(96 109)(97 120)(98 111)(99 102)(100 113)(121 141)(122 152)(123 143)(124 154)(125 145)(126 156)(127 147)(128 158)(129 149)(130 160)(131 151)(132 142)(133 153)(134 144)(135 155)(136 146)(137 157)(138 148)(139 159)(140 150)
G:=sub<Sym(160)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,27)(22,26)(23,25)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(61,69)(62,68)(63,67)(64,66)(70,80)(71,79)(72,78)(73,77)(74,76)(81,94)(82,93)(83,92)(84,91)(85,90)(86,89)(87,88)(95,100)(96,99)(97,98)(101,105)(102,104)(106,120)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(121,126)(122,125)(123,124)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,151)(142,150)(143,149)(144,148)(145,147)(152,160)(153,159)(154,158)(155,157), (1,98,11,88)(2,99,12,89)(3,100,13,90)(4,81,14,91)(5,82,15,92)(6,83,16,93)(7,84,17,94)(8,85,18,95)(9,86,19,96)(10,87,20,97)(21,120,31,110)(22,101,32,111)(23,102,33,112)(24,103,34,113)(25,104,35,114)(26,105,36,115)(27,106,37,116)(28,107,38,117)(29,108,39,118)(30,109,40,119)(41,124,51,134)(42,125,52,135)(43,126,53,136)(44,127,54,137)(45,128,55,138)(46,129,56,139)(47,130,57,140)(48,131,58,121)(49,132,59,122)(50,133,60,123)(61,152,71,142)(62,153,72,143)(63,154,73,144)(64,155,74,145)(65,156,75,146)(66,157,76,147)(67,158,77,148)(68,159,78,149)(69,160,79,150)(70,141,80,151), (1,41,11,51)(2,42,12,52)(3,43,13,53)(4,44,14,54)(5,45,15,55)(6,46,16,56)(7,47,17,57)(8,48,18,58)(9,49,19,59)(10,50,20,60)(21,72,31,62)(22,73,32,63)(23,74,33,64)(24,75,34,65)(25,76,35,66)(26,77,36,67)(27,78,37,68)(28,79,38,69)(29,80,39,70)(30,61,40,71)(81,137,91,127)(82,138,92,128)(83,139,93,129)(84,140,94,130)(85,121,95,131)(86,122,96,132)(87,123,97,133)(88,124,98,134)(89,125,99,135)(90,126,100,136)(101,154,111,144)(102,155,112,145)(103,156,113,146)(104,157,114,147)(105,158,115,148)(106,159,116,149)(107,160,117,150)(108,141,118,151)(109,142,119,152)(110,143,120,153), (1,32)(2,23)(3,34)(4,25)(5,36)(6,27)(7,38)(8,29)(9,40)(10,31)(11,22)(12,33)(13,24)(14,35)(15,26)(16,37)(17,28)(18,39)(19,30)(20,21)(41,63)(42,74)(43,65)(44,76)(45,67)(46,78)(47,69)(48,80)(49,71)(50,62)(51,73)(52,64)(53,75)(54,66)(55,77)(56,68)(57,79)(58,70)(59,61)(60,72)(81,104)(82,115)(83,106)(84,117)(85,108)(86,119)(87,110)(88,101)(89,112)(90,103)(91,114)(92,105)(93,116)(94,107)(95,118)(96,109)(97,120)(98,111)(99,102)(100,113)(121,141)(122,152)(123,143)(124,154)(125,145)(126,156)(127,147)(128,158)(129,149)(130,160)(131,151)(132,142)(133,153)(134,144)(135,155)(136,146)(137,157)(138,148)(139,159)(140,150)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,27)(22,26)(23,25)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(61,69)(62,68)(63,67)(64,66)(70,80)(71,79)(72,78)(73,77)(74,76)(81,94)(82,93)(83,92)(84,91)(85,90)(86,89)(87,88)(95,100)(96,99)(97,98)(101,105)(102,104)(106,120)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(121,126)(122,125)(123,124)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,151)(142,150)(143,149)(144,148)(145,147)(152,160)(153,159)(154,158)(155,157), (1,98,11,88)(2,99,12,89)(3,100,13,90)(4,81,14,91)(5,82,15,92)(6,83,16,93)(7,84,17,94)(8,85,18,95)(9,86,19,96)(10,87,20,97)(21,120,31,110)(22,101,32,111)(23,102,33,112)(24,103,34,113)(25,104,35,114)(26,105,36,115)(27,106,37,116)(28,107,38,117)(29,108,39,118)(30,109,40,119)(41,124,51,134)(42,125,52,135)(43,126,53,136)(44,127,54,137)(45,128,55,138)(46,129,56,139)(47,130,57,140)(48,131,58,121)(49,132,59,122)(50,133,60,123)(61,152,71,142)(62,153,72,143)(63,154,73,144)(64,155,74,145)(65,156,75,146)(66,157,76,147)(67,158,77,148)(68,159,78,149)(69,160,79,150)(70,141,80,151), (1,41,11,51)(2,42,12,52)(3,43,13,53)(4,44,14,54)(5,45,15,55)(6,46,16,56)(7,47,17,57)(8,48,18,58)(9,49,19,59)(10,50,20,60)(21,72,31,62)(22,73,32,63)(23,74,33,64)(24,75,34,65)(25,76,35,66)(26,77,36,67)(27,78,37,68)(28,79,38,69)(29,80,39,70)(30,61,40,71)(81,137,91,127)(82,138,92,128)(83,139,93,129)(84,140,94,130)(85,121,95,131)(86,122,96,132)(87,123,97,133)(88,124,98,134)(89,125,99,135)(90,126,100,136)(101,154,111,144)(102,155,112,145)(103,156,113,146)(104,157,114,147)(105,158,115,148)(106,159,116,149)(107,160,117,150)(108,141,118,151)(109,142,119,152)(110,143,120,153), (1,32)(2,23)(3,34)(4,25)(5,36)(6,27)(7,38)(8,29)(9,40)(10,31)(11,22)(12,33)(13,24)(14,35)(15,26)(16,37)(17,28)(18,39)(19,30)(20,21)(41,63)(42,74)(43,65)(44,76)(45,67)(46,78)(47,69)(48,80)(49,71)(50,62)(51,73)(52,64)(53,75)(54,66)(55,77)(56,68)(57,79)(58,70)(59,61)(60,72)(81,104)(82,115)(83,106)(84,117)(85,108)(86,119)(87,110)(88,101)(89,112)(90,103)(91,114)(92,105)(93,116)(94,107)(95,118)(96,109)(97,120)(98,111)(99,102)(100,113)(121,141)(122,152)(123,143)(124,154)(125,145)(126,156)(127,147)(128,158)(129,149)(130,160)(131,151)(132,142)(133,153)(134,144)(135,155)(136,146)(137,157)(138,148)(139,159)(140,150) );
G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)], [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,27),(22,26),(23,25),(28,40),(29,39),(30,38),(31,37),(32,36),(33,35),(41,60),(42,59),(43,58),(44,57),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(61,69),(62,68),(63,67),(64,66),(70,80),(71,79),(72,78),(73,77),(74,76),(81,94),(82,93),(83,92),(84,91),(85,90),(86,89),(87,88),(95,100),(96,99),(97,98),(101,105),(102,104),(106,120),(107,119),(108,118),(109,117),(110,116),(111,115),(112,114),(121,126),(122,125),(123,124),(127,140),(128,139),(129,138),(130,137),(131,136),(132,135),(133,134),(141,151),(142,150),(143,149),(144,148),(145,147),(152,160),(153,159),(154,158),(155,157)], [(1,98,11,88),(2,99,12,89),(3,100,13,90),(4,81,14,91),(5,82,15,92),(6,83,16,93),(7,84,17,94),(8,85,18,95),(9,86,19,96),(10,87,20,97),(21,120,31,110),(22,101,32,111),(23,102,33,112),(24,103,34,113),(25,104,35,114),(26,105,36,115),(27,106,37,116),(28,107,38,117),(29,108,39,118),(30,109,40,119),(41,124,51,134),(42,125,52,135),(43,126,53,136),(44,127,54,137),(45,128,55,138),(46,129,56,139),(47,130,57,140),(48,131,58,121),(49,132,59,122),(50,133,60,123),(61,152,71,142),(62,153,72,143),(63,154,73,144),(64,155,74,145),(65,156,75,146),(66,157,76,147),(67,158,77,148),(68,159,78,149),(69,160,79,150),(70,141,80,151)], [(1,41,11,51),(2,42,12,52),(3,43,13,53),(4,44,14,54),(5,45,15,55),(6,46,16,56),(7,47,17,57),(8,48,18,58),(9,49,19,59),(10,50,20,60),(21,72,31,62),(22,73,32,63),(23,74,33,64),(24,75,34,65),(25,76,35,66),(26,77,36,67),(27,78,37,68),(28,79,38,69),(29,80,39,70),(30,61,40,71),(81,137,91,127),(82,138,92,128),(83,139,93,129),(84,140,94,130),(85,121,95,131),(86,122,96,132),(87,123,97,133),(88,124,98,134),(89,125,99,135),(90,126,100,136),(101,154,111,144),(102,155,112,145),(103,156,113,146),(104,157,114,147),(105,158,115,148),(106,159,116,149),(107,160,117,150),(108,141,118,151),(109,142,119,152),(110,143,120,153)], [(1,32),(2,23),(3,34),(4,25),(5,36),(6,27),(7,38),(8,29),(9,40),(10,31),(11,22),(12,33),(13,24),(14,35),(15,26),(16,37),(17,28),(18,39),(19,30),(20,21),(41,63),(42,74),(43,65),(44,76),(45,67),(46,78),(47,69),(48,80),(49,71),(50,62),(51,73),(52,64),(53,75),(54,66),(55,77),(56,68),(57,79),(58,70),(59,61),(60,72),(81,104),(82,115),(83,106),(84,117),(85,108),(86,119),(87,110),(88,101),(89,112),(90,103),(91,114),(92,105),(93,116),(94,107),(95,118),(96,109),(97,120),(98,111),(99,102),(100,113),(121,141),(122,152),(123,143),(124,154),(125,145),(126,156),(127,147),(128,158),(129,149),(130,160),(131,151),(132,142),(133,153),(134,144),(135,155),(136,146),(137,157),(138,148),(139,159),(140,150)])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 10A | 10B | 10C | ··· | 10L | 20A | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 2 | 2 | 2 | 4 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 20 | 20 | 20 | 2 | 2 | 10 | 10 | 20 | 20 | 20 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | D10 | D10 | C5⋊D4 | C5⋊D4 | Q8○D8 | D20.35C23 |
| kernel | D20.35C23 | C20.C23 | C2×C5⋊Q16 | D4.Dic5 | D4.8D10 | D4.9D10 | D4.10D10 | C5×2- 1+4 | C5×D4 | C5×Q8 | 2- 1+4 | C2×Q8 | C4○D4 | D4 | Q8 | C5 | C1 |
| # reps | 1 | 3 | 3 | 1 | 3 | 3 | 1 | 1 | 3 | 1 | 2 | 6 | 8 | 12 | 4 | 2 | 2 |
Matrix representation of D20.35C23 ►in GL6(𝔽41)
| 34 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 21 | 0 | 0 |
| 0 | 0 | 37 | 40 | 0 | 0 |
| 0 | 0 | 10 | 33 | 1 | 18 |
| 0 | 0 | 29 | 2 | 9 | 40 |
| 1 | 34 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 21 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 33 | 1 | 18 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 12 | 13 | 0 |
| 0 | 0 | 0 | 4 | 0 | 17 |
| 0 | 0 | 29 | 37 | 27 | 19 |
| 0 | 0 | 0 | 40 | 0 | 37 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 30 | 2 | 9 | 0 |
| 0 | 0 | 0 | 1 | 0 | 37 |
| 0 | 0 | 32 | 25 | 11 | 10 |
| 0 | 0 | 0 | 21 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 6 | 0 | 0 |
| 0 | 0 | 34 | 17 | 0 | 0 |
| 0 | 0 | 38 | 5 | 24 | 11 |
| 0 | 0 | 20 | 24 | 26 | 17 |
G:=sub<GL(6,GF(41))| [34,40,0,0,0,0,1,0,0,0,0,0,0,0,1,37,10,29,0,0,21,40,33,2,0,0,0,0,1,9,0,0,0,0,18,40],[1,0,0,0,0,0,34,40,0,0,0,0,0,0,1,0,0,0,0,0,21,40,33,0,0,0,0,0,1,0,0,0,0,0,18,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,14,0,29,0,0,0,12,4,37,40,0,0,13,0,27,0,0,0,0,17,19,37],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,30,0,32,0,0,0,2,1,25,21,0,0,9,0,11,0,0,0,0,37,10,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,24,34,38,20,0,0,6,17,5,24,0,0,0,0,24,26,0,0,0,0,11,17] >;
D20.35C23 in GAP, Magma, Sage, TeX
D_{20}._{35}C_2^3 % in TeX
G:=Group("D20.35C2^3"); // GroupNames label
G:=SmallGroup(320,1510);
// by ID
G=gap.SmallGroup(320,1510);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,387,184,675,1684,235,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^20=b^2=e^2=1,c^2=d^2=a^10,b*a*b=a^-1,a*c=c*a,a*d=d*a,e*a*e=a^11,b*c=c*b,b*d=d*b,e*b*e=a^15*b,d*c*d^-1=a^10*c,c*e=e*c,d*e=e*d>;
// generators/relations