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G = C22×D4.D5order 320 = 26·5

Direct product of C22 and D4.D5

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22×D4.D5, C20.29C24, Dic107C23, C52C89C23, C103(C2×SD16), C53(C22×SD16), (C2×C10)⋊12SD16, C20.250(C2×D4), (C2×C20).208D4, (C22×D4).9D5, C4.29(C23×D5), (C2×D4).227D10, (C5×D4).21C23, D4.21(C22×D5), (C2×C20).538C23, C10.138(C22×D4), (C22×C4).376D10, (C22×C10).208D4, (C22×Dic10)⋊19C2, (C2×Dic10)⋊66C22, (D4×C10).267C22, C23.105(C5⋊D4), (C22×C20).271C22, (D4×C2×C10).6C2, C4.22(C2×C5⋊D4), (C2×C52C8)⋊39C22, (C22×C52C8)⋊12C2, (C2×C10).578(C2×D4), C2.11(C22×C5⋊D4), (C2×C4).152(C5⋊D4), (C2×C4).621(C22×D5), C22.107(C2×C5⋊D4), SmallGroup(320,1466)

Series: Derived Chief Lower central Upper central

C1C20 — C22×D4.D5
C1C5C10C20Dic10C2×Dic10C22×Dic10 — C22×D4.D5
C5C10C20 — C22×D4.D5
C1C23C22×C4C22×D4

Generators and relations for C22×D4.D5
 G = < a,b,c,d,e,f | a2=b2=c4=d2=e5=1, f2=c2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, dcd=fcf-1=c-1, ce=ec, de=ed, fdf-1=cd, fef-1=e-1 >

Subgroups: 862 in 298 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2 [×6], C2 [×4], C4, C4 [×3], C4 [×4], C22 [×7], C22 [×16], C5, C8 [×4], C2×C4 [×6], C2×C4 [×6], D4 [×4], D4 [×6], Q8 [×10], C23, C23 [×10], C10, C10 [×6], C10 [×4], C2×C8 [×6], SD16 [×16], C22×C4, C22×C4, C2×D4 [×6], C2×D4 [×3], C2×Q8 [×9], C24, Dic5 [×4], C20, C20 [×3], C2×C10 [×7], C2×C10 [×16], C22×C8, C2×SD16 [×12], C22×D4, C22×Q8, C52C8 [×4], Dic10 [×4], Dic10 [×6], C2×Dic5 [×6], C2×C20 [×6], C5×D4 [×4], C5×D4 [×6], C22×C10, C22×C10 [×10], C22×SD16, C2×C52C8 [×6], D4.D5 [×16], C2×Dic10 [×6], C2×Dic10 [×3], C22×Dic5, C22×C20, D4×C10 [×6], D4×C10 [×3], C23×C10, C22×C52C8, C2×D4.D5 [×12], C22×Dic10, D4×C2×C10, C22×D4.D5
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, SD16 [×4], C2×D4 [×6], C24, D10 [×7], C2×SD16 [×6], C22×D4, C5⋊D4 [×4], C22×D5 [×7], C22×SD16, D4.D5 [×4], C2×C5⋊D4 [×6], C23×D5, C2×D4.D5 [×6], C22×C5⋊D4, C22×D4.D5

Smallest permutation representation of C22×D4.D5
On 160 points
Generators in S160
(1 66)(2 67)(3 68)(4 69)(5 70)(6 61)(7 62)(8 63)(9 64)(10 65)(11 71)(12 72)(13 73)(14 74)(15 75)(16 76)(17 77)(18 78)(19 79)(20 80)(21 46)(22 47)(23 48)(24 49)(25 50)(26 41)(27 42)(28 43)(29 44)(30 45)(31 51)(32 52)(33 53)(34 54)(35 55)(36 56)(37 57)(38 58)(39 59)(40 60)(81 146)(82 147)(83 148)(84 149)(85 150)(86 141)(87 142)(88 143)(89 144)(90 145)(91 151)(92 152)(93 153)(94 154)(95 155)(96 156)(97 157)(98 158)(99 159)(100 160)(101 126)(102 127)(103 128)(104 129)(105 130)(106 121)(107 122)(108 123)(109 124)(110 125)(111 131)(112 132)(113 133)(114 134)(115 135)(116 136)(117 137)(118 138)(119 139)(120 140)
(1 41)(2 42)(3 43)(4 44)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 55)(16 56)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(81 121)(82 122)(83 123)(84 124)(85 125)(86 126)(87 127)(88 128)(89 129)(90 130)(91 131)(92 132)(93 133)(94 134)(95 135)(96 136)(97 137)(98 138)(99 139)(100 140)(101 141)(102 142)(103 143)(104 144)(105 145)(106 146)(107 147)(108 148)(109 149)(110 150)(111 151)(112 152)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)
(1 16 6 11)(2 17 7 12)(3 18 8 13)(4 19 9 14)(5 20 10 15)(21 31 26 36)(22 32 27 37)(23 33 28 38)(24 34 29 39)(25 35 30 40)(41 56 46 51)(42 57 47 52)(43 58 48 53)(44 59 49 54)(45 60 50 55)(61 71 66 76)(62 72 67 77)(63 73 68 78)(64 74 69 79)(65 75 70 80)(81 91 86 96)(82 92 87 97)(83 93 88 98)(84 94 89 99)(85 95 90 100)(101 116 106 111)(102 117 107 112)(103 118 108 113)(104 119 109 114)(105 120 110 115)(121 131 126 136)(122 132 127 137)(123 133 128 138)(124 134 129 139)(125 135 130 140)(141 156 146 151)(142 157 147 152)(143 158 148 153)(144 159 149 154)(145 160 150 155)
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 36)(22 37)(23 38)(24 39)(25 40)(26 31)(27 32)(28 33)(29 34)(30 35)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(61 76)(62 77)(63 78)(64 79)(65 80)(66 71)(67 72)(68 73)(69 74)(70 75)(81 86)(82 87)(83 88)(84 89)(85 90)(101 106)(102 107)(103 108)(104 109)(105 110)(121 126)(122 127)(123 128)(124 129)(125 130)(141 146)(142 147)(143 148)(144 149)(145 150)
(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)
(1 148 6 143)(2 147 7 142)(3 146 8 141)(4 150 9 145)(5 149 10 144)(11 153 16 158)(12 152 17 157)(13 151 18 156)(14 155 19 160)(15 154 20 159)(21 128 26 123)(22 127 27 122)(23 126 28 121)(24 130 29 125)(25 129 30 124)(31 133 36 138)(32 132 37 137)(33 131 38 136)(34 135 39 140)(35 134 40 139)(41 108 46 103)(42 107 47 102)(43 106 48 101)(44 110 49 105)(45 109 50 104)(51 113 56 118)(52 112 57 117)(53 111 58 116)(54 115 59 120)(55 114 60 119)(61 88 66 83)(62 87 67 82)(63 86 68 81)(64 90 69 85)(65 89 70 84)(71 93 76 98)(72 92 77 97)(73 91 78 96)(74 95 79 100)(75 94 80 99)

G:=sub<Sym(160)| (1,66)(2,67)(3,68)(4,69)(5,70)(6,61)(7,62)(8,63)(9,64)(10,65)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,80)(21,46)(22,47)(23,48)(24,49)(25,50)(26,41)(27,42)(28,43)(29,44)(30,45)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(81,146)(82,147)(83,148)(84,149)(85,150)(86,141)(87,142)(88,143)(89,144)(90,145)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,126)(102,127)(103,128)(104,129)(105,130)(106,121)(107,122)(108,123)(109,124)(110,125)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(81,121)(82,122)(83,123)(84,124)(85,125)(86,126)(87,127)(88,128)(89,129)(90,130)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160), (1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)(41,56,46,51)(42,57,47,52)(43,58,48,53)(44,59,49,54)(45,60,50,55)(61,71,66,76)(62,72,67,77)(63,73,68,78)(64,74,69,79)(65,75,70,80)(81,91,86,96)(82,92,87,97)(83,93,88,98)(84,94,89,99)(85,95,90,100)(101,116,106,111)(102,117,107,112)(103,118,108,113)(104,119,109,114)(105,120,110,115)(121,131,126,136)(122,132,127,137)(123,133,128,138)(124,134,129,139)(125,135,130,140)(141,156,146,151)(142,157,147,152)(143,158,148,153)(144,159,149,154)(145,160,150,155), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,36)(22,37)(23,38)(24,39)(25,40)(26,31)(27,32)(28,33)(29,34)(30,35)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90)(101,106)(102,107)(103,108)(104,109)(105,110)(121,126)(122,127)(123,128)(124,129)(125,130)(141,146)(142,147)(143,148)(144,149)(145,150), (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), (1,148,6,143)(2,147,7,142)(3,146,8,141)(4,150,9,145)(5,149,10,144)(11,153,16,158)(12,152,17,157)(13,151,18,156)(14,155,19,160)(15,154,20,159)(21,128,26,123)(22,127,27,122)(23,126,28,121)(24,130,29,125)(25,129,30,124)(31,133,36,138)(32,132,37,137)(33,131,38,136)(34,135,39,140)(35,134,40,139)(41,108,46,103)(42,107,47,102)(43,106,48,101)(44,110,49,105)(45,109,50,104)(51,113,56,118)(52,112,57,117)(53,111,58,116)(54,115,59,120)(55,114,60,119)(61,88,66,83)(62,87,67,82)(63,86,68,81)(64,90,69,85)(65,89,70,84)(71,93,76,98)(72,92,77,97)(73,91,78,96)(74,95,79,100)(75,94,80,99)>;

G:=Group( (1,66)(2,67)(3,68)(4,69)(5,70)(6,61)(7,62)(8,63)(9,64)(10,65)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,80)(21,46)(22,47)(23,48)(24,49)(25,50)(26,41)(27,42)(28,43)(29,44)(30,45)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(81,146)(82,147)(83,148)(84,149)(85,150)(86,141)(87,142)(88,143)(89,144)(90,145)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,126)(102,127)(103,128)(104,129)(105,130)(106,121)(107,122)(108,123)(109,124)(110,125)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(81,121)(82,122)(83,123)(84,124)(85,125)(86,126)(87,127)(88,128)(89,129)(90,130)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160), (1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)(41,56,46,51)(42,57,47,52)(43,58,48,53)(44,59,49,54)(45,60,50,55)(61,71,66,76)(62,72,67,77)(63,73,68,78)(64,74,69,79)(65,75,70,80)(81,91,86,96)(82,92,87,97)(83,93,88,98)(84,94,89,99)(85,95,90,100)(101,116,106,111)(102,117,107,112)(103,118,108,113)(104,119,109,114)(105,120,110,115)(121,131,126,136)(122,132,127,137)(123,133,128,138)(124,134,129,139)(125,135,130,140)(141,156,146,151)(142,157,147,152)(143,158,148,153)(144,159,149,154)(145,160,150,155), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,36)(22,37)(23,38)(24,39)(25,40)(26,31)(27,32)(28,33)(29,34)(30,35)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,86)(82,87)(83,88)(84,89)(85,90)(101,106)(102,107)(103,108)(104,109)(105,110)(121,126)(122,127)(123,128)(124,129)(125,130)(141,146)(142,147)(143,148)(144,149)(145,150), (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), (1,148,6,143)(2,147,7,142)(3,146,8,141)(4,150,9,145)(5,149,10,144)(11,153,16,158)(12,152,17,157)(13,151,18,156)(14,155,19,160)(15,154,20,159)(21,128,26,123)(22,127,27,122)(23,126,28,121)(24,130,29,125)(25,129,30,124)(31,133,36,138)(32,132,37,137)(33,131,38,136)(34,135,39,140)(35,134,40,139)(41,108,46,103)(42,107,47,102)(43,106,48,101)(44,110,49,105)(45,109,50,104)(51,113,56,118)(52,112,57,117)(53,111,58,116)(54,115,59,120)(55,114,60,119)(61,88,66,83)(62,87,67,82)(63,86,68,81)(64,90,69,85)(65,89,70,84)(71,93,76,98)(72,92,77,97)(73,91,78,96)(74,95,79,100)(75,94,80,99) );

G=PermutationGroup([(1,66),(2,67),(3,68),(4,69),(5,70),(6,61),(7,62),(8,63),(9,64),(10,65),(11,71),(12,72),(13,73),(14,74),(15,75),(16,76),(17,77),(18,78),(19,79),(20,80),(21,46),(22,47),(23,48),(24,49),(25,50),(26,41),(27,42),(28,43),(29,44),(30,45),(31,51),(32,52),(33,53),(34,54),(35,55),(36,56),(37,57),(38,58),(39,59),(40,60),(81,146),(82,147),(83,148),(84,149),(85,150),(86,141),(87,142),(88,143),(89,144),(90,145),(91,151),(92,152),(93,153),(94,154),(95,155),(96,156),(97,157),(98,158),(99,159),(100,160),(101,126),(102,127),(103,128),(104,129),(105,130),(106,121),(107,122),(108,123),(109,124),(110,125),(111,131),(112,132),(113,133),(114,134),(115,135),(116,136),(117,137),(118,138),(119,139),(120,140)], [(1,41),(2,42),(3,43),(4,44),(5,45),(6,46),(7,47),(8,48),(9,49),(10,50),(11,51),(12,52),(13,53),(14,54),(15,55),(16,56),(17,57),(18,58),(19,59),(20,60),(21,61),(22,62),(23,63),(24,64),(25,65),(26,66),(27,67),(28,68),(29,69),(30,70),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(81,121),(82,122),(83,123),(84,124),(85,125),(86,126),(87,127),(88,128),(89,129),(90,130),(91,131),(92,132),(93,133),(94,134),(95,135),(96,136),(97,137),(98,138),(99,139),(100,140),(101,141),(102,142),(103,143),(104,144),(105,145),(106,146),(107,147),(108,148),(109,149),(110,150),(111,151),(112,152),(113,153),(114,154),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160)], [(1,16,6,11),(2,17,7,12),(3,18,8,13),(4,19,9,14),(5,20,10,15),(21,31,26,36),(22,32,27,37),(23,33,28,38),(24,34,29,39),(25,35,30,40),(41,56,46,51),(42,57,47,52),(43,58,48,53),(44,59,49,54),(45,60,50,55),(61,71,66,76),(62,72,67,77),(63,73,68,78),(64,74,69,79),(65,75,70,80),(81,91,86,96),(82,92,87,97),(83,93,88,98),(84,94,89,99),(85,95,90,100),(101,116,106,111),(102,117,107,112),(103,118,108,113),(104,119,109,114),(105,120,110,115),(121,131,126,136),(122,132,127,137),(123,133,128,138),(124,134,129,139),(125,135,130,140),(141,156,146,151),(142,157,147,152),(143,158,148,153),(144,159,149,154),(145,160,150,155)], [(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(21,36),(22,37),(23,38),(24,39),(25,40),(26,31),(27,32),(28,33),(29,34),(30,35),(41,51),(42,52),(43,53),(44,54),(45,55),(46,56),(47,57),(48,58),(49,59),(50,60),(61,76),(62,77),(63,78),(64,79),(65,80),(66,71),(67,72),(68,73),(69,74),(70,75),(81,86),(82,87),(83,88),(84,89),(85,90),(101,106),(102,107),(103,108),(104,109),(105,110),(121,126),(122,127),(123,128),(124,129),(125,130),(141,146),(142,147),(143,148),(144,149),(145,150)], [(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)], [(1,148,6,143),(2,147,7,142),(3,146,8,141),(4,150,9,145),(5,149,10,144),(11,153,16,158),(12,152,17,157),(13,151,18,156),(14,155,19,160),(15,154,20,159),(21,128,26,123),(22,127,27,122),(23,126,28,121),(24,130,29,125),(25,129,30,124),(31,133,36,138),(32,132,37,137),(33,131,38,136),(34,135,39,140),(35,134,40,139),(41,108,46,103),(42,107,47,102),(43,106,48,101),(44,110,49,105),(45,109,50,104),(51,113,56,118),(52,112,57,117),(53,111,58,116),(54,115,59,120),(55,114,60,119),(61,88,66,83),(62,87,67,82),(63,86,68,81),(64,90,69,85),(65,89,70,84),(71,93,76,98),(72,92,77,97),(73,91,78,96),(74,95,79,100),(75,94,80,99)])

68 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E4F4G4H5A5B8A···8H10A···10N10O···10AD20A···20H
order12···2222244444444558···810···1010···1020···20
size11···144442222202020202210···102···24···44···4

68 irreducible representations

dim11111222222224
type++++++++++-
imageC1C2C2C2C2D4D4D5SD16D10D10C5⋊D4C5⋊D4D4.D5
kernelC22×D4.D5C22×C52C8C2×D4.D5C22×Dic10D4×C2×C10C2×C20C22×C10C22×D4C2×C10C22×C4C2×D4C2×C4C23C22
# reps11121131282121248

Matrix representation of C22×D4.D5 in GL5(𝔽41)

400000
01000
00100
000400
000040
,
400000
040000
004000
00010
00001
,
10000
00100
040000
000400
000040
,
400000
00100
01000
000400
00041
,
10000
01000
00100
000180
0003716
,
400000
0261500
0151500
000126
0002429

G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,40,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,40,4,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,18,37,0,0,0,0,16],[40,0,0,0,0,0,26,15,0,0,0,15,15,0,0,0,0,0,12,24,0,0,0,6,29] >;

C22×D4.D5 in GAP, Magma, Sage, TeX

C_2^2\times D_4.D_5
% in TeX

G:=Group("C2^2xD4.D5");
// GroupNames label

G:=SmallGroup(320,1466);
// by ID

G=gap.SmallGroup(320,1466);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,675,1684,235,102,12550]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^4=d^2=e^5=1,f^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,d*c*d=f*c*f^-1=c^-1,c*e=e*c,d*e=e*d,f*d*f^-1=c*d,f*e*f^-1=e^-1>;
// generators/relations

׿
×
𝔽