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G = C2×SD16⋊3D5  order 320 = 26·5

Direct product of C2 and SD16⋊3D5

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

Aliases: C2×SD16⋊3D5, C20.8C24, SD16⋊12D10, C40.44C23, D20.4C23, Dic10.4C23, C4.45(D4×D5), C10⋊3(C4○D8), (C4×D5).68D4, C20.83(C2×D4), C4.8(C23×D5), D4⋊D5⋊11C22, (C2×SD16)⋊16D5, D10.22(C2×D4), (C2×C8).265D10, (C8×D5)⋊18C22, C5⋊Q16⋊7C22, D4.6(C22×D5), (C5×D4).6C23, C8.41(C22×D5), (C10×SD16)⋊11C2, (C2×D4).184D10, (C5×Q8).2C23, Q8.2(C22×D5), D4⋊2D5⋊7C22, C40⋊C2⋊18C22, C5⋊2C8.21C23, (C2×Q8).151D10, Q8⋊2D5⋊6C22, (C22×D5).93D4, (C4×D5).62C23, C22.141(D4×D5), (C2×C20).525C23, (C2×C40).166C22, Dic5.124(C2×D4), (C2×Dic5).284D4, (C5×SD16)⋊13C22, C10.109(C22×D4), (D4×C10).166C22, (C2×D20).184C22, (Q8×C10).148C22, (C2×Dic10).203C22, C5⋊3(C2×C4○D8), (D5×C2×C8)⋊10C2, C2.82(C2×D4×D5), (C2×D4⋊D5)⋊28C2, (C2×C40⋊C2)⋊32C2, (C2×C5⋊Q16)⋊26C2, (C2×D4⋊2D5)⋊25C2, (C2×Q8⋊2D5)⋊15C2, (C2×C10).398(C2×D4), (C2×C4×D5).328C22, (C2×C4).614(C22×D5), (C2×C5⋊2C8).292C22, SmallGroup(320,1433)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C20 — C2×SD16⋊3D5
Chief series
C1 — C5 — C10 — C20 — C4×D5 — C2×C4×D5 — C2×D4⋊2D5 — C2×SD16⋊3D5
Lower central
C5 — C10 — C20 — C2×SD16⋊3D5

Subgroups: 990 in 266 conjugacy classes, 103 normal (33 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×2], C4 [×6], C22, C22 [×12], C5, C8 [×2], C8 [×2], C2×C4, C2×C4 [×15], D4 [×2], D4 [×12], Q8 [×2], Q8 [×4], C23 [×3], D5 [×4], C10, C10 [×2], C10 [×2], C2×C8, C2×C8 [×5], D8 [×4], SD16 [×4], SD16 [×4], Q16 [×4], C22×C4 [×3], C2×D4, C2×D4 [×3], C2×Q8, C2×Q8, C4○D4 [×12], Dic5 [×2], Dic5 [×2], C20 [×2], C20 [×2], D10 [×2], D10 [×6], C2×C10, C2×C10 [×4], C22×C8, C2×D8, C2×SD16, C2×SD16, C2×Q16, C4○D8 [×8], C2×C4○D4 [×2], C5⋊2C8 [×2], C40 [×2], Dic10 [×2], Dic10, C4×D5 [×4], C4×D5 [×4], D20 [×2], D20 [×5], C2×Dic5, C2×Dic5 [×5], C5⋊D4 [×4], C2×C20, C2×C20, C5×D4 [×2], C5×D4, C5×Q8 [×2], C5×Q8, C22×D5, C22×D5, C22×C10, C2×C4○D8, C8×D5 [×4], C40⋊C2 [×4], C2×C5⋊2C8, D4⋊D5 [×4], C5⋊Q16 [×4], C2×C40, C5×SD16 [×4], C2×Dic10, C2×C4×D5, C2×C4×D5, C2×D20, C2×D20, D4⋊2D5 [×4], D4⋊2D5 [×2], Q8⋊2D5 [×4], Q8⋊2D5 [×2], C22×Dic5, C2×C5⋊D4, D4×C10, Q8×C10, D5×C2×C8, C2×C40⋊C2, SD16⋊3D5 [×8], C2×D4⋊D5, C2×C5⋊Q16, C10×SD16, C2×D4⋊2D5, C2×Q8⋊2D5, C2×SD16⋊3D5

Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C4○D8 [×2], C22×D4, C22×D5 [×7], C2×C4○D8, D4×D5 [×2], C23×D5, SD16⋊3D5 [×2], C2×D4×D5, C2×SD16⋊3D5

Generators and relations
 G = < a,b,c,d,e | a2=b8=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b3, bd=db, be=eb, cd=dc, ece=b4c, ede=d-1 >

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

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

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

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

Matrix representation ►G ⊆ GL5(𝔽41)

400000
01000
00100
00010
00001
,
10000
001100
0151100
00010
00001
,
10000
001700
029000
00010
00001
,
10000
01000
00100
000040
000134
,
400000
092300
093200
000740
000734

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],[1,0,0,0,0,0,0,15,0,0,0,11,11,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,29,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,40,34],[40,0,0,0,0,0,9,9,0,0,0,23,32,0,0,0,0,0,7,7,0,0,0,40,34] >;
 

56 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A4B4C4D4E4F4G4H4I4J5A5B8A8B8C8D8E8F8G8H10A···10F10G10H10I10J20A20B20C20D20E20F20G20H40A···40H
order12222222224444444444558888888810···1010101010202020202020202040···40
size11114410102020224455552020222222101010102···28888444488884···4

56 irreducible representations

dim111111111222222222444
type+++++++++++++++++++
imageC1C2C2C2C2C2C2C2C2D4D4D4D5D10D10D10D10C4○D8D4×D5D4×D5SD16⋊3D5
kernelC2×SD16⋊3D5D5×C2×C8C2×C40⋊C2SD16⋊3D5C2×D4⋊D5C2×C5⋊Q16C10×SD16C2×D4⋊2D5C2×Q8⋊2D5C4×D5C2×Dic5C22×D5C2×SD16C2×C8SD16C2×D4C2×Q8C10C4C22C2
# reps111811111211228228228

In GAP, Magma, Sage, TeX 

C_2\times SD_{16}\rtimes_3D_5
 
% in TeX
 
G:=Group("C2xSD16:3D5");
 
// GroupNames label
 
G:=SmallGroup(320,1433);
 
// by ID
 
G=gap.SmallGroup(320,1433);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,1123,185,136,438,235,102,12550]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^8=c^2=d^5=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^3,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
 
// generators/relations
 

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