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G = C24.16D10order 320 = 26·5

16th non-split extension by C24 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.16D10, C23.16D20, (C2×C20)⋊7D4, C10.34C22≀C2, C2.7(C202D4), C2.8(C207D4), (C2×Dic5).65D4, (C22×D5).40D4, C22.243(D4×D5), (C22×C4).36D10, (C22×C10).70D4, C10.60(C4⋊D4), C22.127(C2×D20), C53(C23.10D4), C2.35(C22⋊D20), C10.36(C4.4D4), (C22×C20).62C22, (C23×C10).44C22, (C23×D5).17C22, C23.373(C22×D5), C10.10C4218C2, C2.11(Dic5⋊D4), C22.101(C4○D20), C22.98(D42D5), (C22×C10).335C23, C2.23(D10.12D4), C2.23(Dic5.5D4), C10.35(C22.D4), C2.17(C22.D20), (C22×Dic5).47C22, (C2×C4)⋊4(C5⋊D4), (C2×C22⋊C4)⋊9D5, (C2×C4⋊Dic5)⋊13C2, (C2×C23.D5)⋊6C2, (C2×D10⋊C4)⋊9C2, (C10×C22⋊C4)⋊12C2, (C2×C10).326(C2×D4), (C22×C5⋊D4).6C2, (C2×C10).81(C4○D4), C22.129(C2×C5⋊D4), SmallGroup(320,588)

Series: Derived Chief Lower central Upper central

C1C22×C10 — C24.16D10
C1C5C10C2×C10C22×C10C23×D5C2×D10⋊C4 — C24.16D10
C5C22×C10 — C24.16D10
C1C23C2×C22⋊C4

Generators and relations for C24.16D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=dc=cd, f2=d, ab=ba, ac=ca, eae-1=ad=da, faf-1=abd, bc=cb, bd=db, be=eb, bf=fb, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce9 >

Subgroups: 998 in 238 conjugacy classes, 63 normal (51 characteristic)
C1, C2 [×7], C2 [×4], C4 [×7], C22 [×7], C22 [×20], C5, C2×C4 [×2], C2×C4 [×15], D4 [×8], C23, C23 [×2], C23 [×14], D5 [×2], C10 [×7], C10 [×2], C22⋊C4 [×8], C4⋊C4 [×2], C22×C4 [×2], C22×C4 [×3], C2×D4 [×6], C24, C24, Dic5 [×4], C20 [×3], D10 [×10], C2×C10 [×7], C2×C10 [×10], C2.C42, C2×C22⋊C4, C2×C22⋊C4 [×3], C2×C4⋊C4, C22×D4, C2×Dic5 [×2], C2×Dic5 [×8], C5⋊D4 [×8], C2×C20 [×2], C2×C20 [×5], C22×D5 [×2], C22×D5 [×6], C22×C10, C22×C10 [×2], C22×C10 [×6], C23.10D4, C4⋊Dic5 [×2], D10⋊C4 [×4], C23.D5 [×2], C5×C22⋊C4 [×2], C22×Dic5 [×3], C2×C5⋊D4 [×6], C22×C20 [×2], C23×D5, C23×C10, C10.10C42, C2×C4⋊Dic5, C2×D10⋊C4 [×2], C2×C23.D5, C10×C22⋊C4, C22×C5⋊D4, C24.16D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×8], C23, D5, C2×D4 [×4], C4○D4 [×3], D10 [×3], C22≀C2, C4⋊D4 [×3], C22.D4 [×2], C4.4D4, D20 [×2], C5⋊D4 [×2], C22×D5, C23.10D4, C2×D20, C4○D20, D4×D5 [×2], D42D5 [×2], C2×C5⋊D4, C22⋊D20, D10.12D4, Dic5.5D4, C22.D20, C207D4, C202D4, Dic5⋊D4, C24.16D10

Smallest permutation representation of C24.16D10
On 160 points
Generators in S160
(1 138)(2 61)(3 140)(4 63)(5 122)(6 65)(7 124)(8 67)(9 126)(10 69)(11 128)(12 71)(13 130)(14 73)(15 132)(16 75)(17 134)(18 77)(19 136)(20 79)(21 55)(22 157)(23 57)(24 159)(25 59)(26 141)(27 41)(28 143)(29 43)(30 145)(31 45)(32 147)(33 47)(34 149)(35 49)(36 151)(37 51)(38 153)(39 53)(40 155)(42 89)(44 91)(46 93)(48 95)(50 97)(52 99)(54 81)(56 83)(58 85)(60 87)(62 106)(64 108)(66 110)(68 112)(70 114)(72 116)(74 118)(76 120)(78 102)(80 104)(82 156)(84 158)(86 160)(88 142)(90 144)(92 146)(94 148)(96 150)(98 152)(100 154)(101 135)(103 137)(105 139)(107 121)(109 123)(111 125)(113 127)(115 129)(117 131)(119 133)
(1 151)(2 152)(3 153)(4 154)(5 155)(6 156)(7 157)(8 158)(9 159)(10 160)(11 141)(12 142)(13 143)(14 144)(15 145)(16 146)(17 147)(18 148)(19 149)(20 150)(21 123)(22 124)(23 125)(24 126)(25 127)(26 128)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 135)(34 136)(35 137)(36 138)(37 139)(38 140)(39 121)(40 122)(41 115)(42 116)(43 117)(44 118)(45 119)(46 120)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(57 111)(58 112)(59 113)(60 114)(61 98)(62 99)(63 100)(64 81)(65 82)(66 83)(67 84)(68 85)(69 86)(70 87)(71 88)(72 89)(73 90)(74 91)(75 92)(76 93)(77 94)(78 95)(79 96)(80 97)
(1 114)(2 115)(3 116)(4 117)(5 118)(6 119)(7 120)(8 101)(9 102)(10 103)(11 104)(12 105)(13 106)(14 107)(15 108)(16 109)(17 110)(18 111)(19 112)(20 113)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 100)(30 81)(31 82)(32 83)(33 84)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 91)(41 152)(42 153)(43 154)(44 155)(45 156)(46 157)(47 158)(48 159)(49 160)(50 141)(51 142)(52 143)(53 144)(54 145)(55 146)(56 147)(57 148)(58 149)(59 150)(60 151)(61 129)(62 130)(63 131)(64 132)(65 133)(66 134)(67 135)(68 136)(69 137)(70 138)(71 139)(72 140)(73 121)(74 122)(75 123)(76 124)(77 125)(78 126)(79 127)(80 128)
(1 104)(2 105)(3 106)(4 107)(5 108)(6 109)(7 110)(8 111)(9 112)(10 113)(11 114)(12 115)(13 116)(14 117)(15 118)(16 119)(17 120)(18 101)(19 102)(20 103)(21 82)(22 83)(23 84)(24 85)(25 86)(26 87)(27 88)(28 89)(29 90)(30 91)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 81)(41 142)(42 143)(43 144)(44 145)(45 146)(46 147)(47 148)(48 149)(49 150)(50 151)(51 152)(52 153)(53 154)(54 155)(55 156)(56 157)(57 158)(58 159)(59 160)(60 141)(61 139)(62 140)(63 121)(64 122)(65 123)(66 124)(67 125)(68 126)(69 127)(70 128)(71 129)(72 130)(73 131)(74 132)(75 133)(76 134)(77 135)(78 136)(79 137)(80 138)
(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 10 104 113)(2 112 105 9)(3 8 106 111)(4 110 107 7)(5 6 108 109)(11 20 114 103)(12 102 115 19)(13 18 116 101)(14 120 117 17)(15 16 118 119)(21 64 82 122)(22 121 83 63)(23 62 84 140)(24 139 85 61)(25 80 86 138)(26 137 87 79)(27 78 88 136)(28 135 89 77)(29 76 90 134)(30 133 91 75)(31 74 92 132)(32 131 93 73)(33 72 94 130)(34 129 95 71)(35 70 96 128)(36 127 97 69)(37 68 98 126)(38 125 99 67)(39 66 100 124)(40 123 81 65)(41 149 142 48)(42 47 143 148)(43 147 144 46)(44 45 145 146)(49 141 150 60)(50 59 151 160)(51 159 152 58)(52 57 153 158)(53 157 154 56)(54 55 155 156)

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

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

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

62 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E···4J5A5B10A···10N10O···10V20A···20P
order12···2222244444···45510···1010···1020···20
size11···1442020444420···20222···24···44···4

62 irreducible representations

dim11111112222222222244
type++++++++++++++++-
imageC1C2C2C2C2C2C2D4D4D4D4D5C4○D4D10D10C5⋊D4D20C4○D20D4×D5D42D5
kernelC24.16D10C10.10C42C2×C4⋊Dic5C2×D10⋊C4C2×C23.D5C10×C22⋊C4C22×C5⋊D4C2×Dic5C2×C20C22×D5C22×C10C2×C22⋊C4C2×C10C22×C4C24C2×C4C23C22C22C22
# reps11121112222264288844

Matrix representation of C24.16D10 in GL6(𝔽41)

010000
100000
00233500
0061800
00001835
0000623
,
4000000
0400000
0040000
0004000
0000400
0000040
,
4000000
0400000
0040000
0004000
000010
000001
,
4000000
0400000
001000
000100
000010
000001
,
090000
3200000
0022500
00161600
000066
0000351
,
0320000
3200000
0025200
00161600
000066
0000135

G:=sub<GL(6,GF(41))| [0,1,0,0,0,0,1,0,0,0,0,0,0,0,23,6,0,0,0,0,35,18,0,0,0,0,0,0,18,6,0,0,0,0,35,23],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,32,0,0,0,0,9,0,0,0,0,0,0,0,2,16,0,0,0,0,25,16,0,0,0,0,0,0,6,35,0,0,0,0,6,1],[0,32,0,0,0,0,32,0,0,0,0,0,0,0,25,16,0,0,0,0,2,16,0,0,0,0,0,0,6,1,0,0,0,0,6,35] >;

C24.16D10 in GAP, Magma, Sage, TeX

C_2^4._{16}D_{10}
% in TeX

G:=Group("C2^4.16D10");
// GroupNames label

G:=SmallGroup(320,588);
// by ID

G=gap.SmallGroup(320,588);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,344,254,387,12550]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^10=d*c=c*d,f^2=d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*b*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^9>;
// generators/relations

׿
×
𝔽