metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.552+ 1+4, C10.222- 1+4, C22⋊Q8⋊17D5, C4⋊C4.195D10, (C2×Q8).77D10, D10⋊Q8⋊23C2, D10⋊D4.2C2, C22⋊C4.20D10, Dic5⋊Q8⋊17C2, Dic5⋊3Q8⋊28C2, C20.23D4⋊15C2, (C2×C10).184C24, (C2×C20).628C23, (C22×C4).246D10, D10.13D4⋊21C2, C2.57(D4⋊6D10), Dic5.13(C4○D4), Dic5.5D4⋊26C2, (C2×D20).158C22, C23.D10⋊24C2, C4⋊Dic5.219C22, (Q8×C10).114C22, (C22×D5).75C23, C22.205(C23×D5), C23.123(C22×D5), C23.D5.35C22, D10⋊C4.26C22, C23.23D10⋊25C2, (C22×C20).383C22, (C22×C10).212C23, C5⋊5(C22.36C24), (C2×Dic5).248C23, (C4×Dic5).120C22, C10.D4.32C22, C2.23(Q8.10D10), (C2×Dic10).168C22, (C4×C5⋊D4)⋊59C2, C2.55(D5×C4○D4), C4⋊C4⋊D5⋊19C2, C4⋊C4⋊7D5⋊28C2, (C5×C22⋊Q8)⋊20C2, C10.167(C2×C4○D4), (C2×C4×D5).262C22, (C2×C4).54(C22×D5), (C5×C4⋊C4).165C22, (C2×C5⋊D4).139C22, (C5×C22⋊C4).39C22, SmallGroup(320,1312)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.552+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc-1=a5b-1, bd=db, ebe=a5b, cd=dc, ce=ec, ede=a5b2d >
Subgroups: 766 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C5, C2×C4 [×6], C2×C4 [×10], D4 [×4], Q8 [×4], C23, C23 [×2], D5 [×2], C10 [×3], C10, C42 [×4], C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4, C22×C4 [×2], C2×D4 [×3], C2×Q8, C2×Q8 [×2], Dic5 [×2], Dic5 [×5], C20 [×6], D10 [×6], C2×C10, C2×C10 [×3], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8 [×2], C22.D4 [×2], C4.4D4 [×3], C42⋊2C2 [×2], C4⋊Q8, Dic10 [×3], C4×D5 [×3], D20, C2×Dic5 [×6], C5⋊D4 [×3], C2×C20 [×6], C2×C20, C5×Q8, C22×D5 [×2], C22×C10, C22.36C24, C4×Dic5 [×4], C10.D4 [×6], C4⋊Dic5, D10⋊C4 [×8], C23.D5 [×2], C5×C22⋊C4 [×2], C5×C4⋊C4 [×3], C2×Dic10 [×2], C2×C4×D5 [×2], C2×D20, C2×C5⋊D4 [×2], C22×C20, Q8×C10, C23.D10, D10⋊D4, Dic5.5D4 [×2], Dic5⋊3Q8, C4⋊C4⋊7D5, D10.13D4, D10⋊Q8 [×2], C4⋊C4⋊D5, C4×C5⋊D4, C23.23D10, Dic5⋊Q8, C20.23D4, C5×C22⋊Q8, C10.552+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C4○D4 [×2], C24, D10 [×7], C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5 [×7], C22.36C24, C23×D5, D4⋊6D10, Q8.10D10, D5×C4○D4, C10.552+ 1+4
(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 72 30 90)(2 71 21 89)(3 80 22 88)(4 79 23 87)(5 78 24 86)(6 77 25 85)(7 76 26 84)(8 75 27 83)(9 74 28 82)(10 73 29 81)(11 110 157 92)(12 109 158 91)(13 108 159 100)(14 107 160 99)(15 106 151 98)(16 105 152 97)(17 104 153 96)(18 103 154 95)(19 102 155 94)(20 101 156 93)(31 66 49 58)(32 65 50 57)(33 64 41 56)(34 63 42 55)(35 62 43 54)(36 61 44 53)(37 70 45 52)(38 69 46 51)(39 68 47 60)(40 67 48 59)(111 133 129 141)(112 132 130 150)(113 131 121 149)(114 140 122 148)(115 139 123 147)(116 138 124 146)(117 137 125 145)(118 136 126 144)(119 135 127 143)(120 134 128 142)
(1 97 6 92)(2 98 7 93)(3 99 8 94)(4 100 9 95)(5 91 10 96)(11 85 16 90)(12 86 17 81)(13 87 18 82)(14 88 19 83)(15 89 20 84)(21 106 26 101)(22 107 27 102)(23 108 28 103)(24 109 29 104)(25 110 30 105)(31 116 36 111)(32 117 37 112)(33 118 38 113)(34 119 39 114)(35 120 40 115)(41 126 46 121)(42 127 47 122)(43 128 48 123)(44 129 49 124)(45 130 50 125)(51 136 56 131)(52 137 57 132)(53 138 58 133)(54 139 59 134)(55 140 60 135)(61 146 66 141)(62 147 67 142)(63 148 68 143)(64 149 69 144)(65 150 70 145)(71 156 76 151)(72 157 77 152)(73 158 78 153)(74 159 79 154)(75 160 80 155)
(1 45 25 32)(2 44 26 31)(3 43 27 40)(4 42 28 39)(5 41 29 38)(6 50 30 37)(7 49 21 36)(8 48 22 35)(9 47 23 34)(10 46 24 33)(11 145 152 132)(12 144 153 131)(13 143 154 140)(14 142 155 139)(15 141 156 138)(16 150 157 137)(17 149 158 136)(18 148 159 135)(19 147 160 134)(20 146 151 133)(51 86 64 73)(52 85 65 72)(53 84 66 71)(54 83 67 80)(55 82 68 79)(56 81 69 78)(57 90 70 77)(58 89 61 76)(59 88 62 75)(60 87 63 74)(91 126 104 113)(92 125 105 112)(93 124 106 111)(94 123 107 120)(95 122 108 119)(96 121 109 118)(97 130 110 117)(98 129 101 116)(99 128 102 115)(100 127 103 114)
(1 32)(2 33)(3 34)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 31)(11 137)(12 138)(13 139)(14 140)(15 131)(16 132)(17 133)(18 134)(19 135)(20 136)(21 41)(22 42)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(29 49)(30 50)(51 89)(52 90)(53 81)(54 82)(55 83)(56 84)(57 85)(58 86)(59 87)(60 88)(61 73)(62 74)(63 75)(64 76)(65 77)(66 78)(67 79)(68 80)(69 71)(70 72)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(101 121)(102 122)(103 123)(104 124)(105 125)(106 126)(107 127)(108 128)(109 129)(110 130)(141 153)(142 154)(143 155)(144 156)(145 157)(146 158)(147 159)(148 160)(149 151)(150 152)
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), (1,72,30,90)(2,71,21,89)(3,80,22,88)(4,79,23,87)(5,78,24,86)(6,77,25,85)(7,76,26,84)(8,75,27,83)(9,74,28,82)(10,73,29,81)(11,110,157,92)(12,109,158,91)(13,108,159,100)(14,107,160,99)(15,106,151,98)(16,105,152,97)(17,104,153,96)(18,103,154,95)(19,102,155,94)(20,101,156,93)(31,66,49,58)(32,65,50,57)(33,64,41,56)(34,63,42,55)(35,62,43,54)(36,61,44,53)(37,70,45,52)(38,69,46,51)(39,68,47,60)(40,67,48,59)(111,133,129,141)(112,132,130,150)(113,131,121,149)(114,140,122,148)(115,139,123,147)(116,138,124,146)(117,137,125,145)(118,136,126,144)(119,135,127,143)(120,134,128,142), (1,97,6,92)(2,98,7,93)(3,99,8,94)(4,100,9,95)(5,91,10,96)(11,85,16,90)(12,86,17,81)(13,87,18,82)(14,88,19,83)(15,89,20,84)(21,106,26,101)(22,107,27,102)(23,108,28,103)(24,109,29,104)(25,110,30,105)(31,116,36,111)(32,117,37,112)(33,118,38,113)(34,119,39,114)(35,120,40,115)(41,126,46,121)(42,127,47,122)(43,128,48,123)(44,129,49,124)(45,130,50,125)(51,136,56,131)(52,137,57,132)(53,138,58,133)(54,139,59,134)(55,140,60,135)(61,146,66,141)(62,147,67,142)(63,148,68,143)(64,149,69,144)(65,150,70,145)(71,156,76,151)(72,157,77,152)(73,158,78,153)(74,159,79,154)(75,160,80,155), (1,45,25,32)(2,44,26,31)(3,43,27,40)(4,42,28,39)(5,41,29,38)(6,50,30,37)(7,49,21,36)(8,48,22,35)(9,47,23,34)(10,46,24,33)(11,145,152,132)(12,144,153,131)(13,143,154,140)(14,142,155,139)(15,141,156,138)(16,150,157,137)(17,149,158,136)(18,148,159,135)(19,147,160,134)(20,146,151,133)(51,86,64,73)(52,85,65,72)(53,84,66,71)(54,83,67,80)(55,82,68,79)(56,81,69,78)(57,90,70,77)(58,89,61,76)(59,88,62,75)(60,87,63,74)(91,126,104,113)(92,125,105,112)(93,124,106,111)(94,123,107,120)(95,122,108,119)(96,121,109,118)(97,130,110,117)(98,129,101,116)(99,128,102,115)(100,127,103,114), (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,31)(11,137)(12,138)(13,139)(14,140)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,89)(52,90)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,71)(70,72)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(101,121)(102,122)(103,123)(104,124)(105,125)(106,126)(107,127)(108,128)(109,129)(110,130)(141,153)(142,154)(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,151)(150,152)>;
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), (1,72,30,90)(2,71,21,89)(3,80,22,88)(4,79,23,87)(5,78,24,86)(6,77,25,85)(7,76,26,84)(8,75,27,83)(9,74,28,82)(10,73,29,81)(11,110,157,92)(12,109,158,91)(13,108,159,100)(14,107,160,99)(15,106,151,98)(16,105,152,97)(17,104,153,96)(18,103,154,95)(19,102,155,94)(20,101,156,93)(31,66,49,58)(32,65,50,57)(33,64,41,56)(34,63,42,55)(35,62,43,54)(36,61,44,53)(37,70,45,52)(38,69,46,51)(39,68,47,60)(40,67,48,59)(111,133,129,141)(112,132,130,150)(113,131,121,149)(114,140,122,148)(115,139,123,147)(116,138,124,146)(117,137,125,145)(118,136,126,144)(119,135,127,143)(120,134,128,142), (1,97,6,92)(2,98,7,93)(3,99,8,94)(4,100,9,95)(5,91,10,96)(11,85,16,90)(12,86,17,81)(13,87,18,82)(14,88,19,83)(15,89,20,84)(21,106,26,101)(22,107,27,102)(23,108,28,103)(24,109,29,104)(25,110,30,105)(31,116,36,111)(32,117,37,112)(33,118,38,113)(34,119,39,114)(35,120,40,115)(41,126,46,121)(42,127,47,122)(43,128,48,123)(44,129,49,124)(45,130,50,125)(51,136,56,131)(52,137,57,132)(53,138,58,133)(54,139,59,134)(55,140,60,135)(61,146,66,141)(62,147,67,142)(63,148,68,143)(64,149,69,144)(65,150,70,145)(71,156,76,151)(72,157,77,152)(73,158,78,153)(74,159,79,154)(75,160,80,155), (1,45,25,32)(2,44,26,31)(3,43,27,40)(4,42,28,39)(5,41,29,38)(6,50,30,37)(7,49,21,36)(8,48,22,35)(9,47,23,34)(10,46,24,33)(11,145,152,132)(12,144,153,131)(13,143,154,140)(14,142,155,139)(15,141,156,138)(16,150,157,137)(17,149,158,136)(18,148,159,135)(19,147,160,134)(20,146,151,133)(51,86,64,73)(52,85,65,72)(53,84,66,71)(54,83,67,80)(55,82,68,79)(56,81,69,78)(57,90,70,77)(58,89,61,76)(59,88,62,75)(60,87,63,74)(91,126,104,113)(92,125,105,112)(93,124,106,111)(94,123,107,120)(95,122,108,119)(96,121,109,118)(97,130,110,117)(98,129,101,116)(99,128,102,115)(100,127,103,114), (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,31)(11,137)(12,138)(13,139)(14,140)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,89)(52,90)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,71)(70,72)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(101,121)(102,122)(103,123)(104,124)(105,125)(106,126)(107,127)(108,128)(109,129)(110,130)(141,153)(142,154)(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,151)(150,152) );
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)], [(1,72,30,90),(2,71,21,89),(3,80,22,88),(4,79,23,87),(5,78,24,86),(6,77,25,85),(7,76,26,84),(8,75,27,83),(9,74,28,82),(10,73,29,81),(11,110,157,92),(12,109,158,91),(13,108,159,100),(14,107,160,99),(15,106,151,98),(16,105,152,97),(17,104,153,96),(18,103,154,95),(19,102,155,94),(20,101,156,93),(31,66,49,58),(32,65,50,57),(33,64,41,56),(34,63,42,55),(35,62,43,54),(36,61,44,53),(37,70,45,52),(38,69,46,51),(39,68,47,60),(40,67,48,59),(111,133,129,141),(112,132,130,150),(113,131,121,149),(114,140,122,148),(115,139,123,147),(116,138,124,146),(117,137,125,145),(118,136,126,144),(119,135,127,143),(120,134,128,142)], [(1,97,6,92),(2,98,7,93),(3,99,8,94),(4,100,9,95),(5,91,10,96),(11,85,16,90),(12,86,17,81),(13,87,18,82),(14,88,19,83),(15,89,20,84),(21,106,26,101),(22,107,27,102),(23,108,28,103),(24,109,29,104),(25,110,30,105),(31,116,36,111),(32,117,37,112),(33,118,38,113),(34,119,39,114),(35,120,40,115),(41,126,46,121),(42,127,47,122),(43,128,48,123),(44,129,49,124),(45,130,50,125),(51,136,56,131),(52,137,57,132),(53,138,58,133),(54,139,59,134),(55,140,60,135),(61,146,66,141),(62,147,67,142),(63,148,68,143),(64,149,69,144),(65,150,70,145),(71,156,76,151),(72,157,77,152),(73,158,78,153),(74,159,79,154),(75,160,80,155)], [(1,45,25,32),(2,44,26,31),(3,43,27,40),(4,42,28,39),(5,41,29,38),(6,50,30,37),(7,49,21,36),(8,48,22,35),(9,47,23,34),(10,46,24,33),(11,145,152,132),(12,144,153,131),(13,143,154,140),(14,142,155,139),(15,141,156,138),(16,150,157,137),(17,149,158,136),(18,148,159,135),(19,147,160,134),(20,146,151,133),(51,86,64,73),(52,85,65,72),(53,84,66,71),(54,83,67,80),(55,82,68,79),(56,81,69,78),(57,90,70,77),(58,89,61,76),(59,88,62,75),(60,87,63,74),(91,126,104,113),(92,125,105,112),(93,124,106,111),(94,123,107,120),(95,122,108,119),(96,121,109,118),(97,130,110,117),(98,129,101,116),(99,128,102,115),(100,127,103,114)], [(1,32),(2,33),(3,34),(4,35),(5,36),(6,37),(7,38),(8,39),(9,40),(10,31),(11,137),(12,138),(13,139),(14,140),(15,131),(16,132),(17,133),(18,134),(19,135),(20,136),(21,41),(22,42),(23,43),(24,44),(25,45),(26,46),(27,47),(28,48),(29,49),(30,50),(51,89),(52,90),(53,81),(54,82),(55,83),(56,84),(57,85),(58,86),(59,87),(60,88),(61,73),(62,74),(63,75),(64,76),(65,77),(66,78),(67,79),(68,80),(69,71),(70,72),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(99,119),(100,120),(101,121),(102,122),(103,123),(104,124),(105,125),(106,126),(107,127),(108,128),(109,129),(110,130),(141,153),(142,154),(143,155),(144,156),(145,157),(146,158),(147,159),(148,160),(149,151),(150,152)])
50 conjugacy classes
class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | ··· | 20P |
order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
size | 1 | 1 | 1 | 1 | 4 | 20 | 20 | 2 | 2 | 4 | ··· | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
50 irreducible representations
dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4⋊6D10 | Q8.10D10 | D5×C4○D4 |
kernel | C10.552+ 1+4 | C23.D10 | D10⋊D4 | Dic5.5D4 | Dic5⋊3Q8 | C4⋊C4⋊7D5 | D10.13D4 | D10⋊Q8 | C4⋊C4⋊D5 | C4×C5⋊D4 | C23.23D10 | Dic5⋊Q8 | C20.23D4 | C5×C22⋊Q8 | C22⋊Q8 | Dic5 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C10 | C2 | C2 | C2 |
# reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 6 | 2 | 2 | 1 | 1 | 4 | 4 | 4 |
Matrix representation of C10.552+ 1+4 ►in GL6(𝔽41)
40 | 0 | 0 | 0 | 0 | 0 |
0 | 40 | 0 | 0 | 0 | 0 |
0 | 0 | 34 | 34 | 0 | 0 |
0 | 0 | 7 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 34 | 34 |
0 | 0 | 0 | 0 | 7 | 1 |
3 | 37 | 0 | 0 | 0 | 0 |
23 | 38 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 17 | 40 |
0 | 0 | 0 | 0 | 3 | 24 |
0 | 0 | 24 | 1 | 0 | 0 |
0 | 0 | 38 | 17 | 0 | 0 |
9 | 0 | 0 | 0 | 0 | 0 |
0 | 9 | 0 | 0 | 0 | 0 |
0 | 0 | 27 | 0 | 34 | 0 |
0 | 0 | 0 | 27 | 0 | 34 |
0 | 0 | 34 | 0 | 14 | 0 |
0 | 0 | 0 | 34 | 0 | 14 |
40 | 0 | 0 | 0 | 0 | 0 |
0 | 40 | 0 | 0 | 0 | 0 |
0 | 0 | 17 | 40 | 0 | 0 |
0 | 0 | 3 | 24 | 0 | 0 |
0 | 0 | 0 | 0 | 17 | 40 |
0 | 0 | 0 | 0 | 3 | 24 |
40 | 0 | 0 | 0 | 0 | 0 |
19 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 17 | 40 | 0 | 0 |
0 | 0 | 1 | 24 | 0 | 0 |
0 | 0 | 0 | 0 | 17 | 40 |
0 | 0 | 0 | 0 | 1 | 24 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,34,7,0,0,0,0,34,1,0,0,0,0,0,0,34,7,0,0,0,0,34,1],[3,23,0,0,0,0,37,38,0,0,0,0,0,0,0,0,24,38,0,0,0,0,1,17,0,0,17,3,0,0,0,0,40,24,0,0],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,27,0,34,0,0,0,0,27,0,34,0,0,34,0,14,0,0,0,0,34,0,14],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,17,3,0,0,0,0,40,24,0,0,0,0,0,0,17,3,0,0,0,0,40,24],[40,19,0,0,0,0,0,1,0,0,0,0,0,0,17,1,0,0,0,0,40,24,0,0,0,0,0,0,17,1,0,0,0,0,40,24] >;
C10.552+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{55}2_+^{1+4}
% in TeX
G:=Group("C10.55ES+(2,2)");
// GroupNames label
G:=SmallGroup(320,1312);
// by ID
G=gap.SmallGroup(320,1312);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,120,758,555,100,1571,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=a^5*b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,a*e=e*a,c*b*c^-1=a^5*b^-1,b*d=d*b,e*b*e=a^5*b,c*d=d*c,c*e=e*c,e*d*e=a^5*b^2*d>;
// generators/relations