direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C23.18D10, C24.58D10, (C2×D4).228D10, (C23×Dic5)⋊8C2, (C22×D4).10D5, (C2×C20).642C23, (C2×C10).291C24, C10.139(C22×D4), (C22×C4).269D10, (C22×C10).121D4, C23.67(C5⋊D4), C23.D5⋊57C22, (D4×C10).311C22, C10.D4⋊72C22, C10⋊5(C22.D4), (C23×C10).73C22, C22.305(C23×D5), C23.133(C22×D5), C22.77(D4⋊2D5), (C22×C20).437C22, (C22×C10).227C23, (C2×Dic5).291C23, (C22×Dic5)⋊48C22, (D4×C2×C10).21C2, (C2×C10).73(C2×D4), C5⋊6(C2×C22.D4), C10.103(C2×C4○D4), C2.67(C2×D4⋊2D5), (C2×C23.D5)⋊24C2, C2.12(C22×C5⋊D4), (C2×C10.D4)⋊47C2, (C2×C4).236(C22×D5), C22.108(C2×C5⋊D4), (C2×C10).175(C4○D4), SmallGroup(320,1468)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C23.18D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=dc=cd, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, ebe-1=fbf-1=bd=db, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >
Subgroups: 958 in 342 conjugacy classes, 127 normal (19 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, Dic5, C20, C2×C10, C2×C10, C2×C10, C2×C22⋊C4, C2×C4⋊C4, C22.D4, C23×C4, C22×D4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C22×C10, C2×C22.D4, C10.D4, C23.D5, C22×Dic5, C22×Dic5, C22×C20, D4×C10, D4×C10, C23×C10, C2×C10.D4, C23.18D10, C2×C23.D5, C2×C23.D5, C23×Dic5, D4×C2×C10, C2×C23.18D10
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C22.D4, C22×D4, C2×C4○D4, C5⋊D4, C22×D5, C2×C22.D4, D4⋊2D5, C2×C5⋊D4, C23×D5, C23.18D10, C2×D4⋊2D5, C22×C5⋊D4, C2×C23.18D10
►On 160 points
Generators in S160
(1 27)(2 28)(3 29)(4 30)(5 26)(6 24)(7 25)(8 21)(9 22)(10 23)(11 36)(12 37)(13 38)(14 39)(15 40)(16 31)(17 32)(18 33)(19 34)(20 35)(41 62)(42 63)(43 64)(44 65)(45 66)(46 67)(47 68)(48 69)(49 70)(50 61)(51 76)(52 77)(53 78)(54 79)(55 80)(56 71)(57 72)(58 73)(59 74)(60 75)(81 115)(82 116)(83 117)(84 118)(85 119)(86 120)(87 111)(88 112)(89 113)(90 114)(91 107)(92 108)(93 109)(94 110)(95 101)(96 102)(97 103)(98 104)(99 105)(100 106)(121 159)(122 160)(123 151)(124 152)(125 153)(126 154)(127 155)(128 156)(129 157)(130 158)(131 143)(132 144)(133 145)(134 146)(135 147)(136 148)(137 149)(138 150)(139 141)(140 142)
(1 41)(2 47)(3 43)(4 49)(5 45)(6 48)(7 44)(8 50)(9 46)(10 42)(11 51)(12 57)(13 53)(14 59)(15 55)(16 56)(17 52)(18 58)(19 54)(20 60)(21 61)(22 67)(23 63)(24 69)(25 65)(26 66)(27 62)(28 68)(29 64)(30 70)(31 71)(32 77)(33 73)(34 79)(35 75)(36 76)(37 72)(38 78)(39 74)(40 80)(81 122)(82 144)(83 124)(84 146)(85 126)(86 148)(87 128)(88 150)(89 130)(90 142)(91 149)(92 129)(93 141)(94 121)(95 143)(96 123)(97 145)(98 125)(99 147)(100 127)(101 131)(102 151)(103 133)(104 153)(105 135)(106 155)(107 137)(108 157)(109 139)(110 159)(111 156)(112 138)(113 158)(114 140)(115 160)(116 132)(117 152)(118 134)(119 154)(120 136)
(1 17)(2 18)(3 19)(4 20)(5 16)(6 14)(7 15)(8 11)(9 12)(10 13)(21 36)(22 37)(23 38)(24 39)(25 40)(26 31)(27 32)(28 33)(29 34)(30 35)(41 52)(42 53)(43 54)(44 55)(45 56)(46 57)(47 58)(48 59)(49 60)(50 51)(61 76)(62 77)(63 78)(64 79)(65 80)(66 71)(67 72)(68 73)(69 74)(70 75)(81 100)(82 91)(83 92)(84 93)(85 94)(86 95)(87 96)(88 97)(89 98)(90 99)(101 120)(102 111)(103 112)(104 113)(105 114)(106 115)(107 116)(108 117)(109 118)(110 119)(121 126)(122 127)(123 128)(124 129)(125 130)(131 136)(132 137)(133 138)(134 139)(135 140)(141 146)(142 147)(143 148)(144 149)(145 150)(151 156)(152 157)(153 158)(154 159)(155 160)
(1 9)(2 10)(3 6)(4 7)(5 8)(11 16)(12 17)(13 18)(14 19)(15 20)(21 26)(22 27)(23 28)(24 29)(25 30)(31 36)(32 37)(33 38)(34 39)(35 40)(41 46)(42 47)(43 48)(44 49)(45 50)(51 56)(52 57)(53 58)(54 59)(55 60)(61 66)(62 67)(63 68)(64 69)(65 70)(71 76)(72 77)(73 78)(74 79)(75 80)(81 95)(82 96)(83 97)(84 98)(85 99)(86 100)(87 91)(88 92)(89 93)(90 94)(101 115)(102 116)(103 117)(104 118)(105 119)(106 120)(107 111)(108 112)(109 113)(110 114)(121 142)(122 143)(123 144)(124 145)(125 146)(126 147)(127 148)(128 149)(129 150)(130 141)(131 160)(132 151)(133 152)(134 153)(135 154)(136 155)(137 156)(138 157)(139 158)(140 159)
(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)
(1 150 12 124)(2 144 13 128)(3 148 14 122)(4 142 15 126)(5 146 11 130)(6 127 19 143)(7 121 20 147)(8 125 16 141)(9 129 17 145)(10 123 18 149)(21 153 31 139)(22 157 32 133)(23 151 33 137)(24 155 34 131)(25 159 35 135)(26 134 36 158)(27 138 37 152)(28 132 38 156)(29 136 39 160)(30 140 40 154)(41 92 57 97)(42 82 58 87)(43 100 59 95)(44 90 60 85)(45 98 51 93)(46 88 52 83)(47 96 53 91)(48 86 54 81)(49 94 55 99)(50 84 56 89)(61 118 71 113)(62 108 72 103)(63 116 73 111)(64 106 74 101)(65 114 75 119)(66 104 76 109)(67 112 77 117)(68 102 78 107)(69 120 79 115)(70 110 80 105)
G:=sub<Sym(160)| (1,27)(2,28)(3,29)(4,30)(5,26)(6,24)(7,25)(8,21)(9,22)(10,23)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,61)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(81,115)(82,116)(83,117)(84,118)(85,119)(86,120)(87,111)(88,112)(89,113)(90,114)(91,107)(92,108)(93,109)(94,110)(95,101)(96,102)(97,103)(98,104)(99,105)(100,106)(121,159)(122,160)(123,151)(124,152)(125,153)(126,154)(127,155)(128,156)(129,157)(130,158)(131,143)(132,144)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,141)(140,142), (1,41)(2,47)(3,43)(4,49)(5,45)(6,48)(7,44)(8,50)(9,46)(10,42)(11,51)(12,57)(13,53)(14,59)(15,55)(16,56)(17,52)(18,58)(19,54)(20,60)(21,61)(22,67)(23,63)(24,69)(25,65)(26,66)(27,62)(28,68)(29,64)(30,70)(31,71)(32,77)(33,73)(34,79)(35,75)(36,76)(37,72)(38,78)(39,74)(40,80)(81,122)(82,144)(83,124)(84,146)(85,126)(86,148)(87,128)(88,150)(89,130)(90,142)(91,149)(92,129)(93,141)(94,121)(95,143)(96,123)(97,145)(98,125)(99,147)(100,127)(101,131)(102,151)(103,133)(104,153)(105,135)(106,155)(107,137)(108,157)(109,139)(110,159)(111,156)(112,138)(113,158)(114,140)(115,160)(116,132)(117,152)(118,134)(119,154)(120,136), (1,17)(2,18)(3,19)(4,20)(5,16)(6,14)(7,15)(8,11)(9,12)(10,13)(21,36)(22,37)(23,38)(24,39)(25,40)(26,31)(27,32)(28,33)(29,34)(30,35)(41,52)(42,53)(43,54)(44,55)(45,56)(46,57)(47,58)(48,59)(49,60)(50,51)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,100)(82,91)(83,92)(84,93)(85,94)(86,95)(87,96)(88,97)(89,98)(90,99)(101,120)(102,111)(103,112)(104,113)(105,114)(106,115)(107,116)(108,117)(109,118)(110,119)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140)(141,146)(142,147)(143,148)(144,149)(145,150)(151,156)(152,157)(153,158)(154,159)(155,160), (1,9)(2,10)(3,6)(4,7)(5,8)(11,16)(12,17)(13,18)(14,19)(15,20)(21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)(41,46)(42,47)(43,48)(44,49)(45,50)(51,56)(52,57)(53,58)(54,59)(55,60)(61,66)(62,67)(63,68)(64,69)(65,70)(71,76)(72,77)(73,78)(74,79)(75,80)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,91)(88,92)(89,93)(90,94)(101,115)(102,116)(103,117)(104,118)(105,119)(106,120)(107,111)(108,112)(109,113)(110,114)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,148)(128,149)(129,150)(130,141)(131,160)(132,151)(133,152)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159), (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), (1,150,12,124)(2,144,13,128)(3,148,14,122)(4,142,15,126)(5,146,11,130)(6,127,19,143)(7,121,20,147)(8,125,16,141)(9,129,17,145)(10,123,18,149)(21,153,31,139)(22,157,32,133)(23,151,33,137)(24,155,34,131)(25,159,35,135)(26,134,36,158)(27,138,37,152)(28,132,38,156)(29,136,39,160)(30,140,40,154)(41,92,57,97)(42,82,58,87)(43,100,59,95)(44,90,60,85)(45,98,51,93)(46,88,52,83)(47,96,53,91)(48,86,54,81)(49,94,55,99)(50,84,56,89)(61,118,71,113)(62,108,72,103)(63,116,73,111)(64,106,74,101)(65,114,75,119)(66,104,76,109)(67,112,77,117)(68,102,78,107)(69,120,79,115)(70,110,80,105)>;
G:=Group( (1,27)(2,28)(3,29)(4,30)(5,26)(6,24)(7,25)(8,21)(9,22)(10,23)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,61)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(81,115)(82,116)(83,117)(84,118)(85,119)(86,120)(87,111)(88,112)(89,113)(90,114)(91,107)(92,108)(93,109)(94,110)(95,101)(96,102)(97,103)(98,104)(99,105)(100,106)(121,159)(122,160)(123,151)(124,152)(125,153)(126,154)(127,155)(128,156)(129,157)(130,158)(131,143)(132,144)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,141)(140,142), (1,41)(2,47)(3,43)(4,49)(5,45)(6,48)(7,44)(8,50)(9,46)(10,42)(11,51)(12,57)(13,53)(14,59)(15,55)(16,56)(17,52)(18,58)(19,54)(20,60)(21,61)(22,67)(23,63)(24,69)(25,65)(26,66)(27,62)(28,68)(29,64)(30,70)(31,71)(32,77)(33,73)(34,79)(35,75)(36,76)(37,72)(38,78)(39,74)(40,80)(81,122)(82,144)(83,124)(84,146)(85,126)(86,148)(87,128)(88,150)(89,130)(90,142)(91,149)(92,129)(93,141)(94,121)(95,143)(96,123)(97,145)(98,125)(99,147)(100,127)(101,131)(102,151)(103,133)(104,153)(105,135)(106,155)(107,137)(108,157)(109,139)(110,159)(111,156)(112,138)(113,158)(114,140)(115,160)(116,132)(117,152)(118,134)(119,154)(120,136), (1,17)(2,18)(3,19)(4,20)(5,16)(6,14)(7,15)(8,11)(9,12)(10,13)(21,36)(22,37)(23,38)(24,39)(25,40)(26,31)(27,32)(28,33)(29,34)(30,35)(41,52)(42,53)(43,54)(44,55)(45,56)(46,57)(47,58)(48,59)(49,60)(50,51)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,100)(82,91)(83,92)(84,93)(85,94)(86,95)(87,96)(88,97)(89,98)(90,99)(101,120)(102,111)(103,112)(104,113)(105,114)(106,115)(107,116)(108,117)(109,118)(110,119)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140)(141,146)(142,147)(143,148)(144,149)(145,150)(151,156)(152,157)(153,158)(154,159)(155,160), (1,9)(2,10)(3,6)(4,7)(5,8)(11,16)(12,17)(13,18)(14,19)(15,20)(21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)(41,46)(42,47)(43,48)(44,49)(45,50)(51,56)(52,57)(53,58)(54,59)(55,60)(61,66)(62,67)(63,68)(64,69)(65,70)(71,76)(72,77)(73,78)(74,79)(75,80)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,91)(88,92)(89,93)(90,94)(101,115)(102,116)(103,117)(104,118)(105,119)(106,120)(107,111)(108,112)(109,113)(110,114)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,148)(128,149)(129,150)(130,141)(131,160)(132,151)(133,152)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159), (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), (1,150,12,124)(2,144,13,128)(3,148,14,122)(4,142,15,126)(5,146,11,130)(6,127,19,143)(7,121,20,147)(8,125,16,141)(9,129,17,145)(10,123,18,149)(21,153,31,139)(22,157,32,133)(23,151,33,137)(24,155,34,131)(25,159,35,135)(26,134,36,158)(27,138,37,152)(28,132,38,156)(29,136,39,160)(30,140,40,154)(41,92,57,97)(42,82,58,87)(43,100,59,95)(44,90,60,85)(45,98,51,93)(46,88,52,83)(47,96,53,91)(48,86,54,81)(49,94,55,99)(50,84,56,89)(61,118,71,113)(62,108,72,103)(63,116,73,111)(64,106,74,101)(65,114,75,119)(66,104,76,109)(67,112,77,117)(68,102,78,107)(69,120,79,115)(70,110,80,105) );
G=PermutationGroup([[(1,27),(2,28),(3,29),(4,30),(5,26),(6,24),(7,25),(8,21),(9,22),(10,23),(11,36),(12,37),(13,38),(14,39),(15,40),(16,31),(17,32),(18,33),(19,34),(20,35),(41,62),(42,63),(43,64),(44,65),(45,66),(46,67),(47,68),(48,69),(49,70),(50,61),(51,76),(52,77),(53,78),(54,79),(55,80),(56,71),(57,72),(58,73),(59,74),(60,75),(81,115),(82,116),(83,117),(84,118),(85,119),(86,120),(87,111),(88,112),(89,113),(90,114),(91,107),(92,108),(93,109),(94,110),(95,101),(96,102),(97,103),(98,104),(99,105),(100,106),(121,159),(122,160),(123,151),(124,152),(125,153),(126,154),(127,155),(128,156),(129,157),(130,158),(131,143),(132,144),(133,145),(134,146),(135,147),(136,148),(137,149),(138,150),(139,141),(140,142)], [(1,41),(2,47),(3,43),(4,49),(5,45),(6,48),(7,44),(8,50),(9,46),(10,42),(11,51),(12,57),(13,53),(14,59),(15,55),(16,56),(17,52),(18,58),(19,54),(20,60),(21,61),(22,67),(23,63),(24,69),(25,65),(26,66),(27,62),(28,68),(29,64),(30,70),(31,71),(32,77),(33,73),(34,79),(35,75),(36,76),(37,72),(38,78),(39,74),(40,80),(81,122),(82,144),(83,124),(84,146),(85,126),(86,148),(87,128),(88,150),(89,130),(90,142),(91,149),(92,129),(93,141),(94,121),(95,143),(96,123),(97,145),(98,125),(99,147),(100,127),(101,131),(102,151),(103,133),(104,153),(105,135),(106,155),(107,137),(108,157),(109,139),(110,159),(111,156),(112,138),(113,158),(114,140),(115,160),(116,132),(117,152),(118,134),(119,154),(120,136)], [(1,17),(2,18),(3,19),(4,20),(5,16),(6,14),(7,15),(8,11),(9,12),(10,13),(21,36),(22,37),(23,38),(24,39),(25,40),(26,31),(27,32),(28,33),(29,34),(30,35),(41,52),(42,53),(43,54),(44,55),(45,56),(46,57),(47,58),(48,59),(49,60),(50,51),(61,76),(62,77),(63,78),(64,79),(65,80),(66,71),(67,72),(68,73),(69,74),(70,75),(81,100),(82,91),(83,92),(84,93),(85,94),(86,95),(87,96),(88,97),(89,98),(90,99),(101,120),(102,111),(103,112),(104,113),(105,114),(106,115),(107,116),(108,117),(109,118),(110,119),(121,126),(122,127),(123,128),(124,129),(125,130),(131,136),(132,137),(133,138),(134,139),(135,140),(141,146),(142,147),(143,148),(144,149),(145,150),(151,156),(152,157),(153,158),(154,159),(155,160)], [(1,9),(2,10),(3,6),(4,7),(5,8),(11,16),(12,17),(13,18),(14,19),(15,20),(21,26),(22,27),(23,28),(24,29),(25,30),(31,36),(32,37),(33,38),(34,39),(35,40),(41,46),(42,47),(43,48),(44,49),(45,50),(51,56),(52,57),(53,58),(54,59),(55,60),(61,66),(62,67),(63,68),(64,69),(65,70),(71,76),(72,77),(73,78),(74,79),(75,80),(81,95),(82,96),(83,97),(84,98),(85,99),(86,100),(87,91),(88,92),(89,93),(90,94),(101,115),(102,116),(103,117),(104,118),(105,119),(106,120),(107,111),(108,112),(109,113),(110,114),(121,142),(122,143),(123,144),(124,145),(125,146),(126,147),(127,148),(128,149),(129,150),(130,141),(131,160),(132,151),(133,152),(134,153),(135,154),(136,155),(137,156),(138,157),(139,158),(140,159)], [(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)], [(1,150,12,124),(2,144,13,128),(3,148,14,122),(4,142,15,126),(5,146,11,130),(6,127,19,143),(7,121,20,147),(8,125,16,141),(9,129,17,145),(10,123,18,149),(21,153,31,139),(22,157,32,133),(23,151,33,137),(24,155,34,131),(25,159,35,135),(26,134,36,158),(27,138,37,152),(28,132,38,156),(29,136,39,160),(30,140,40,154),(41,92,57,97),(42,82,58,87),(43,100,59,95),(44,90,60,85),(45,98,51,93),(46,88,52,83),(47,96,53,91),(48,86,54,81),(49,94,55,99),(50,84,56,89),(61,118,71,113),(62,108,72,103),(63,116,73,111),(64,106,74,101),(65,114,75,119),(66,104,76,109),(67,112,77,117),(68,102,78,107),(69,120,79,115),(70,110,80,105)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | 4B | 4C | ··· | 4J | 4K | 4L | 4M | 4N | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C5⋊D4 | D4⋊2D5 |
| kernel | C2×C23.18D10 | C2×C10.D4 | C23.18D10 | C2×C23.D5 | C23×Dic5 | D4×C2×C10 | C22×C10 | C22×D4 | C2×C10 | C22×C4 | C2×D4 | C24 | C23 | C22 |
| # reps | 1 | 2 | 8 | 3 | 1 | 1 | 4 | 2 | 8 | 2 | 8 | 4 | 16 | 8 |
Matrix representation of C2×C23.18D10 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 26 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 10 | 0 | 0 | 0 |
| 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 22 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 19 | 12 | 0 | 0 |
| 0 | 4 | 22 | 0 | 0 |
| 0 | 0 | 0 | 32 | 12 |
| 0 | 0 | 0 | 7 | 9 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,26,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,10,11,0,0,0,0,4,0,0,0,0,0,1,22,0,0,0,0,40],[40,0,0,0,0,0,19,4,0,0,0,12,22,0,0,0,0,0,32,7,0,0,0,12,9] >;
C2×C23.18D10 in GAP, Magma, Sage, TeX
C_2\times C_2^3._{18}D_{10} % in TeX
G:=Group("C2xC2^3.18D10"); // GroupNames label
G:=SmallGroup(320,1468);
// by ID
G=gap.SmallGroup(320,1468);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,675,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=d*c=c*d,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,e*b*e^-1=f*b*f^-1=b*d=d*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^-1>;
// generators/relations