metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.38D20, C22⋊C8⋊9D5, C40⋊6C4⋊8C2, (C2×C20).44D4, (C2×C4).33D20, (C2×C8).109D10, C20⋊7D4.2C2, D20⋊5C4⋊10C2, C10.8(C2×SD16), (C2×C10).14SD16, (C22×C4).85D10, (C22×C10).55D4, C20.282(C4○D4), C2.14(C8⋊D10), C10.11(C8⋊C22), (C2×C40).120C22, (C2×C20).745C23, (C2×D20).12C22, C22.108(C2×D20), C22.3(C40⋊C2), C5⋊1(C23.46D4), C4.106(D4⋊2D5), C4⋊Dic5.270C22, (C22×C20).52C22, C10.17(C22.D4), C2.13(C22.D20), (C2×C4⋊Dic5)⋊5C2, (C5×C22⋊C8)⋊11C2, C2.11(C2×C40⋊C2), (C2×C10).128(C2×D4), (C2×C4).690(C22×D5), SmallGroup(320,362)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.38D20
G = < a,b,c,d,e | a2=b2=c2=1, d20=c, e2=cb=bc, dad-1=ab=ba, ac=ca, ae=ea, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd19 >
Subgroups: 542 in 114 conjugacy classes, 43 normal (25 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×5], C5, C8 [×2], C2×C4 [×2], C2×C4 [×7], D4 [×4], C23, C23, D5, C10 [×3], C10 [×2], C22⋊C4, C4⋊C4 [×4], C2×C8 [×2], C22×C4, C22×C4, C2×D4 [×2], Dic5 [×3], C20 [×2], C20, D10 [×3], C2×C10, C2×C10 [×2], C2×C10 [×2], C22⋊C8, D4⋊C4 [×2], C4.Q8 [×2], C2×C4⋊C4, C4⋊D4, C40 [×2], D20 [×2], C2×Dic5 [×5], C5⋊D4 [×2], C2×C20 [×2], C2×C20 [×2], C22×D5, C22×C10, C23.46D4, C4⋊Dic5, C4⋊Dic5 [×2], C4⋊Dic5, D10⋊C4, C2×C40 [×2], C2×D20, C22×Dic5, C2×C5⋊D4, C22×C20, C40⋊6C4 [×2], D20⋊5C4 [×2], C5×C22⋊C8, C2×C4⋊Dic5, C20⋊7D4, C23.38D20
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D5, SD16 [×2], C2×D4, C4○D4 [×2], D10 [×3], C22.D4, C2×SD16, C8⋊C22, D20 [×2], C22×D5, C23.46D4, C40⋊C2 [×2], C2×D20, D4⋊2D5 [×2], C22.D20, C2×C40⋊C2, C8⋊D10, C23.38D20
►On 160 points
Generators in S160
(1 159)(2 88)(3 121)(4 90)(5 123)(6 92)(7 125)(8 94)(9 127)(10 96)(11 129)(12 98)(13 131)(14 100)(15 133)(16 102)(17 135)(18 104)(19 137)(20 106)(21 139)(22 108)(23 141)(24 110)(25 143)(26 112)(27 145)(28 114)(29 147)(30 116)(31 149)(32 118)(33 151)(34 120)(35 153)(36 82)(37 155)(38 84)(39 157)(40 86)(41 136)(42 105)(43 138)(44 107)(45 140)(46 109)(47 142)(48 111)(49 144)(50 113)(51 146)(52 115)(53 148)(54 117)(55 150)(56 119)(57 152)(58 81)(59 154)(60 83)(61 156)(62 85)(63 158)(64 87)(65 160)(66 89)(67 122)(68 91)(69 124)(70 93)(71 126)(72 95)(73 128)(74 97)(75 130)(76 99)(77 132)(78 101)(79 134)(80 103)
(1 64)(2 65)(3 66)(4 67)(5 68)(6 69)(7 70)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 80)(18 41)(19 42)(20 43)(21 44)(22 45)(23 46)(24 47)(25 48)(26 49)(27 50)(28 51)(29 52)(30 53)(31 54)(32 55)(33 56)(34 57)(35 58)(36 59)(37 60)(38 61)(39 62)(40 63)(81 153)(82 154)(83 155)(84 156)(85 157)(86 158)(87 159)(88 160)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 139)(108 140)(109 141)(110 142)(111 143)(112 144)(113 145)(114 146)(115 147)(116 148)(117 149)(118 150)(119 151)(120 152)
(1 21)(2 22)(3 23)(4 24)(5 25)(6 26)(7 27)(8 28)(9 29)(10 30)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(41 61)(42 62)(43 63)(44 64)(45 65)(46 66)(47 67)(48 68)(49 69)(50 70)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(121 141)(122 142)(123 143)(124 144)(125 145)(126 146)(127 147)(128 148)(129 149)(130 150)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(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 43 44 40)(2 39 45 42)(3 41 46 38)(4 37 47 80)(5 79 48 36)(6 35 49 78)(7 77 50 34)(8 33 51 76)(9 75 52 32)(10 31 53 74)(11 73 54 30)(12 29 55 72)(13 71 56 28)(14 27 57 70)(15 69 58 26)(16 25 59 68)(17 67 60 24)(18 23 61 66)(19 65 62 22)(20 21 63 64)(81 112 133 124)(82 123 134 111)(83 110 135 122)(84 121 136 109)(85 108 137 160)(86 159 138 107)(87 106 139 158)(88 157 140 105)(89 104 141 156)(90 155 142 103)(91 102 143 154)(92 153 144 101)(93 100 145 152)(94 151 146 99)(95 98 147 150)(96 149 148 97)(113 120 125 132)(114 131 126 119)(115 118 127 130)(116 129 128 117)
G:=sub<Sym(160)| (1,159)(2,88)(3,121)(4,90)(5,123)(6,92)(7,125)(8,94)(9,127)(10,96)(11,129)(12,98)(13,131)(14,100)(15,133)(16,102)(17,135)(18,104)(19,137)(20,106)(21,139)(22,108)(23,141)(24,110)(25,143)(26,112)(27,145)(28,114)(29,147)(30,116)(31,149)(32,118)(33,151)(34,120)(35,153)(36,82)(37,155)(38,84)(39,157)(40,86)(41,136)(42,105)(43,138)(44,107)(45,140)(46,109)(47,142)(48,111)(49,144)(50,113)(51,146)(52,115)(53,148)(54,117)(55,150)(56,119)(57,152)(58,81)(59,154)(60,83)(61,156)(62,85)(63,158)(64,87)(65,160)(66,89)(67,122)(68,91)(69,124)(70,93)(71,126)(72,95)(73,128)(74,97)(75,130)(76,99)(77,132)(78,101)(79,134)(80,103), (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,41)(19,42)(20,43)(21,44)(22,45)(23,46)(24,47)(25,48)(26,49)(27,50)(28,51)(29,52)(30,53)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(81,153)(82,154)(83,155)(84,156)(85,157)(86,158)(87,159)(88,160)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)(113,145)(114,146)(115,147)(116,148)(117,149)(118,150)(119,151)(120,152), (1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,43,44,40)(2,39,45,42)(3,41,46,38)(4,37,47,80)(5,79,48,36)(6,35,49,78)(7,77,50,34)(8,33,51,76)(9,75,52,32)(10,31,53,74)(11,73,54,30)(12,29,55,72)(13,71,56,28)(14,27,57,70)(15,69,58,26)(16,25,59,68)(17,67,60,24)(18,23,61,66)(19,65,62,22)(20,21,63,64)(81,112,133,124)(82,123,134,111)(83,110,135,122)(84,121,136,109)(85,108,137,160)(86,159,138,107)(87,106,139,158)(88,157,140,105)(89,104,141,156)(90,155,142,103)(91,102,143,154)(92,153,144,101)(93,100,145,152)(94,151,146,99)(95,98,147,150)(96,149,148,97)(113,120,125,132)(114,131,126,119)(115,118,127,130)(116,129,128,117)>;
G:=Group( (1,159)(2,88)(3,121)(4,90)(5,123)(6,92)(7,125)(8,94)(9,127)(10,96)(11,129)(12,98)(13,131)(14,100)(15,133)(16,102)(17,135)(18,104)(19,137)(20,106)(21,139)(22,108)(23,141)(24,110)(25,143)(26,112)(27,145)(28,114)(29,147)(30,116)(31,149)(32,118)(33,151)(34,120)(35,153)(36,82)(37,155)(38,84)(39,157)(40,86)(41,136)(42,105)(43,138)(44,107)(45,140)(46,109)(47,142)(48,111)(49,144)(50,113)(51,146)(52,115)(53,148)(54,117)(55,150)(56,119)(57,152)(58,81)(59,154)(60,83)(61,156)(62,85)(63,158)(64,87)(65,160)(66,89)(67,122)(68,91)(69,124)(70,93)(71,126)(72,95)(73,128)(74,97)(75,130)(76,99)(77,132)(78,101)(79,134)(80,103), (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,41)(19,42)(20,43)(21,44)(22,45)(23,46)(24,47)(25,48)(26,49)(27,50)(28,51)(29,52)(30,53)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(81,153)(82,154)(83,155)(84,156)(85,157)(86,158)(87,159)(88,160)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)(113,145)(114,146)(115,147)(116,148)(117,149)(118,150)(119,151)(120,152), (1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,43,44,40)(2,39,45,42)(3,41,46,38)(4,37,47,80)(5,79,48,36)(6,35,49,78)(7,77,50,34)(8,33,51,76)(9,75,52,32)(10,31,53,74)(11,73,54,30)(12,29,55,72)(13,71,56,28)(14,27,57,70)(15,69,58,26)(16,25,59,68)(17,67,60,24)(18,23,61,66)(19,65,62,22)(20,21,63,64)(81,112,133,124)(82,123,134,111)(83,110,135,122)(84,121,136,109)(85,108,137,160)(86,159,138,107)(87,106,139,158)(88,157,140,105)(89,104,141,156)(90,155,142,103)(91,102,143,154)(92,153,144,101)(93,100,145,152)(94,151,146,99)(95,98,147,150)(96,149,148,97)(113,120,125,132)(114,131,126,119)(115,118,127,130)(116,129,128,117) );
G=PermutationGroup([(1,159),(2,88),(3,121),(4,90),(5,123),(6,92),(7,125),(8,94),(9,127),(10,96),(11,129),(12,98),(13,131),(14,100),(15,133),(16,102),(17,135),(18,104),(19,137),(20,106),(21,139),(22,108),(23,141),(24,110),(25,143),(26,112),(27,145),(28,114),(29,147),(30,116),(31,149),(32,118),(33,151),(34,120),(35,153),(36,82),(37,155),(38,84),(39,157),(40,86),(41,136),(42,105),(43,138),(44,107),(45,140),(46,109),(47,142),(48,111),(49,144),(50,113),(51,146),(52,115),(53,148),(54,117),(55,150),(56,119),(57,152),(58,81),(59,154),(60,83),(61,156),(62,85),(63,158),(64,87),(65,160),(66,89),(67,122),(68,91),(69,124),(70,93),(71,126),(72,95),(73,128),(74,97),(75,130),(76,99),(77,132),(78,101),(79,134),(80,103)], [(1,64),(2,65),(3,66),(4,67),(5,68),(6,69),(7,70),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,80),(18,41),(19,42),(20,43),(21,44),(22,45),(23,46),(24,47),(25,48),(26,49),(27,50),(28,51),(29,52),(30,53),(31,54),(32,55),(33,56),(34,57),(35,58),(36,59),(37,60),(38,61),(39,62),(40,63),(81,153),(82,154),(83,155),(84,156),(85,157),(86,158),(87,159),(88,160),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,131),(100,132),(101,133),(102,134),(103,135),(104,136),(105,137),(106,138),(107,139),(108,140),(109,141),(110,142),(111,143),(112,144),(113,145),(114,146),(115,147),(116,148),(117,149),(118,150),(119,151),(120,152)], [(1,21),(2,22),(3,23),(4,24),(5,25),(6,26),(7,27),(8,28),(9,29),(10,30),(11,31),(12,32),(13,33),(14,34),(15,35),(16,36),(17,37),(18,38),(19,39),(20,40),(41,61),(42,62),(43,63),(44,64),(45,65),(46,66),(47,67),(48,68),(49,69),(50,70),(51,71),(52,72),(53,73),(54,74),(55,75),(56,76),(57,77),(58,78),(59,79),(60,80),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(99,119),(100,120),(121,141),(122,142),(123,143),(124,144),(125,145),(126,146),(127,147),(128,148),(129,149),(130,150),(131,151),(132,152),(133,153),(134,154),(135,155),(136,156),(137,157),(138,158),(139,159),(140,160)], [(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)], [(1,43,44,40),(2,39,45,42),(3,41,46,38),(4,37,47,80),(5,79,48,36),(6,35,49,78),(7,77,50,34),(8,33,51,76),(9,75,52,32),(10,31,53,74),(11,73,54,30),(12,29,55,72),(13,71,56,28),(14,27,57,70),(15,69,58,26),(16,25,59,68),(17,67,60,24),(18,23,61,66),(19,65,62,22),(20,21,63,64),(81,112,133,124),(82,123,134,111),(83,110,135,122),(84,121,136,109),(85,108,137,160),(86,159,138,107),(87,106,139,158),(88,157,140,105),(89,104,141,156),(90,155,142,103),(91,102,143,154),(92,153,144,101),(93,100,145,152),(94,151,146,99),(95,98,147,150),(96,149,148,97),(113,120,125,132),(114,131,126,119),(115,118,127,130),(116,129,128,117)])
59 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | 20J | 20K | 20L | 40A | ··· | 40P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 40 | 2 | 2 | 4 | 20 | 20 | 20 | 20 | 40 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
59 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | SD16 | D10 | D10 | D20 | D20 | C40⋊C2 | C8⋊C22 | D4⋊2D5 | C8⋊D10 |
| kernel | C23.38D20 | C40⋊6C4 | D20⋊5C4 | C5×C22⋊C8 | C2×C4⋊Dic5 | C20⋊7D4 | C2×C20 | C22×C10 | C22⋊C8 | C20 | C2×C10 | C2×C8 | C22×C4 | C2×C4 | C23 | C22 | C10 | C4 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 4 | 2 | 4 | 4 | 16 | 1 | 4 | 4 |
Matrix representation of C23.38D20 ►in GL4(𝔽41) generated by
| 40 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 40 | 0 |
| 0 | 0 | 5 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 13 | 14 | 0 | 0 |
| 27 | 29 | 0 | 0 |
| 0 | 0 | 32 | 21 |
| 0 | 0 | 0 | 9 |
| 29 | 16 | 0 | 0 |
| 14 | 12 | 0 | 0 |
| 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 32 |
G:=sub<GL(4,GF(41))| [40,0,0,0,0,40,0,0,0,0,40,5,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,40,0,0,0,0,40],[40,0,0,0,0,40,0,0,0,0,1,0,0,0,0,1],[13,27,0,0,14,29,0,0,0,0,32,0,0,0,21,9],[29,14,0,0,16,12,0,0,0,0,32,0,0,0,0,32] >;
C23.38D20 in GAP, Magma, Sage, TeX
C_2^3._{38}D_{20} % in TeX
G:=Group("C2^3.38D20"); // GroupNames label
G:=SmallGroup(320,362);
// by ID
G=gap.SmallGroup(320,362);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,254,219,142,1123,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^20=c,e^2=c*b=b*c,d*a*d^-1=a*b=b*a,a*c=c*a,a*e=e*a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b*d^19>;
// generators/relations