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## G = C2×D4.9D10order 320 = 26·5

### Direct product of C2 and D4.9D10

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — C2×D4.9D10
 Chief series C1 — C5 — C10 — C20 — Dic10 — C2×Dic10 — C22×Dic10 — C2×D4.9D10
 Lower central C5 — C10 — C20 — C2×D4.9D10
 Upper central C1 — C22 — C22×C4 — C2×C4○D4

Generators and relations for C2×D4.9D10
G = < a,b,c,d,e | a2=b4=c2=d10=1, e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe-1=b-1, bd=db, dcd-1=b2c, ece-1=b-1c, ede-1=d-1 >

Subgroups: 734 in 258 conjugacy classes, 111 normal (27 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×2], C4 [×2], C4 [×6], C22, C22 [×2], C22 [×6], C5, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×11], D4 [×2], D4 [×5], Q8 [×2], Q8 [×11], C23, C23, C10, C10 [×2], C10 [×4], C2×C8 [×2], M4(2) [×4], SD16 [×8], Q16 [×8], C22×C4, C22×C4 [×2], C2×D4, C2×D4, C2×Q8, C2×Q8 [×9], C4○D4 [×4], C4○D4 [×2], Dic5 [×4], C20 [×2], C20 [×2], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×6], C2×M4(2), C2×SD16 [×2], C2×Q16 [×2], C8.C22 [×8], C22×Q8, C2×C4○D4, C52C8 [×4], Dic10 [×4], Dic10 [×6], C2×Dic5 [×6], C2×C20 [×2], C2×C20 [×4], C2×C20 [×5], C5×D4 [×2], C5×D4 [×5], C5×Q8 [×2], C5×Q8, C22×C10, C22×C10, C2×C8.C22, C2×C52C8 [×2], C4.Dic5 [×4], D4.D5 [×8], C5⋊Q16 [×8], C2×Dic10 [×6], C2×Dic10 [×3], C22×Dic5, C22×C20, C22×C20, D4×C10, D4×C10, Q8×C10, C5×C4○D4 [×4], C5×C4○D4 [×2], C2×C4.Dic5, C2×D4.D5 [×2], C2×C5⋊Q16 [×2], D4.9D10 [×8], C22×Dic10, C10×C4○D4, C2×D4.9D10
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C8.C22 [×2], C22×D4, C5⋊D4 [×4], C22×D5 [×7], C2×C8.C22, C2×C5⋊D4 [×6], C23×D5, D4.9D10 [×2], C22×C5⋊D4, C2×D4.9D10

Smallest permutation representation of C2×D4.9D10
On 160 points
Generators in S160
(1 47)(2 48)(3 49)(4 50)(5 41)(6 42)(7 43)(8 44)(9 45)(10 46)(11 21)(12 22)(13 23)(14 24)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(31 110)(32 101)(33 102)(34 103)(35 104)(36 105)(37 106)(38 107)(39 108)(40 109)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(61 89)(62 90)(63 81)(64 82)(65 83)(66 84)(67 85)(68 86)(69 87)(70 88)(91 116)(92 117)(93 118)(94 119)(95 120)(96 111)(97 112)(98 113)(99 114)(100 115)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 30 77 104)(2 21 78 105)(3 22 79 106)(4 23 80 107)(5 24 71 108)(6 25 72 109)(7 26 73 110)(8 27 74 101)(9 28 75 102)(10 29 76 103)(11 58 36 48)(12 59 37 49)(13 60 38 50)(14 51 39 41)(15 52 40 42)(16 53 31 43)(17 54 32 44)(18 55 33 45)(19 56 34 46)(20 57 35 47)(61 157 114 127)(62 158 115 128)(63 159 116 129)(64 160 117 130)(65 151 118 121)(66 152 119 122)(67 153 120 123)(68 154 111 124)(69 155 112 125)(70 156 113 126)(81 149 91 139)(82 150 92 140)(83 141 93 131)(84 142 94 132)(85 143 95 133)(86 144 96 134)(87 145 97 135)(88 146 98 136)(89 147 99 137)(90 148 100 138)
(1 35)(2 11)(3 37)(4 13)(5 39)(6 15)(7 31)(8 17)(9 33)(10 19)(12 79)(14 71)(16 73)(18 75)(20 77)(21 48)(22 59)(23 50)(24 51)(25 42)(26 53)(27 44)(28 55)(29 46)(30 57)(32 74)(34 76)(36 78)(38 80)(40 72)(41 108)(43 110)(45 102)(47 104)(49 106)(52 109)(54 101)(56 103)(58 105)(60 107)(61 89)(62 100)(63 81)(64 92)(65 83)(66 94)(67 85)(68 96)(69 87)(70 98)(82 117)(84 119)(86 111)(88 113)(90 115)(91 116)(93 118)(95 120)(97 112)(99 114)(121 141)(122 132)(123 143)(124 134)(125 145)(126 136)(127 147)(128 138)(129 149)(130 140)(131 151)(133 153)(135 155)(137 157)(139 159)(142 152)(144 154)(146 156)(148 158)(150 160)
(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)
(1 152 77 122)(2 151 78 121)(3 160 79 130)(4 159 80 129)(5 158 71 128)(6 157 72 127)(7 156 73 126)(8 155 74 125)(9 154 75 124)(10 153 76 123)(11 83 36 93)(12 82 37 92)(13 81 38 91)(14 90 39 100)(15 89 40 99)(16 88 31 98)(17 87 32 97)(18 86 33 96)(19 85 34 95)(20 84 35 94)(21 65 105 118)(22 64 106 117)(23 63 107 116)(24 62 108 115)(25 61 109 114)(26 70 110 113)(27 69 101 112)(28 68 102 111)(29 67 103 120)(30 66 104 119)(41 148 51 138)(42 147 52 137)(43 146 53 136)(44 145 54 135)(45 144 55 134)(46 143 56 133)(47 142 57 132)(48 141 58 131)(49 150 59 140)(50 149 60 139)

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

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

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

62 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 5A 5B 8A 8B 8C 8D 10A ··· 10F 10G ··· 10R 20A ··· 20H 20I ··· 20T order 1 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 5 5 8 8 8 8 10 ··· 10 10 ··· 10 20 ··· 20 20 ··· 20 size 1 1 1 1 2 2 4 4 2 2 2 2 4 4 20 20 20 20 2 2 20 20 20 20 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

62 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + + + + + + - - image C1 C2 C2 C2 C2 C2 C2 D4 D4 D5 D10 D10 D10 D10 C5⋊D4 C5⋊D4 C8.C22 D4.9D10 kernel C2×D4.9D10 C2×C4.Dic5 C2×D4.D5 C2×C5⋊Q16 D4.9D10 C22×Dic10 C10×C4○D4 C2×C20 C22×C10 C2×C4○D4 C22×C4 C2×D4 C2×Q8 C4○D4 C2×C4 C23 C10 C2 # reps 1 1 2 2 8 1 1 3 1 2 2 2 2 8 12 4 2 8

Matrix representation of C2×D4.9D10 in GL8(𝔽41)

 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40
,
 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 1 32 0 0 0 0 0 0 23 40 0 0 0 0 0 0 26 37 1 37 0 0 0 0 31 3 21 40
,
 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 17 40 0 0 0 0 0 0 0 0 40 9 0 0 0 0 0 0 0 1 0 0 0 0 0 0 25 5 1 37 0 0 0 0 0 28 0 40
,
 1 35 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 2 0 0 0 0 0 17 9 0 10 0 0 0 0 0 0 1 0 0 0 0 0 11 33 13 32
,
 1 0 0 0 0 0 0 0 6 40 0 0 0 0 0 0 0 0 22 36 0 0 0 0 0 0 31 19 0 0 0 0 0 0 0 0 1 19 0 32 0 0 0 0 36 37 20 0 0 0 0 0 30 8 4 8 0 0 0 0 17 21 24 40

G:=sub<GL(8,GF(41))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,23,26,31,0,0,0,0,32,40,37,3,0,0,0,0,0,0,1,21,0,0,0,0,0,0,37,40],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,17,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,25,0,0,0,0,0,9,1,5,28,0,0,0,0,0,0,1,0,0,0,0,0,0,0,37,40],[1,6,0,0,0,0,0,0,35,6,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,17,0,11,0,0,0,0,0,9,0,33,0,0,0,0,2,0,1,13,0,0,0,0,0,10,0,32],[1,6,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,22,31,0,0,0,0,0,0,36,19,0,0,0,0,0,0,0,0,1,36,30,17,0,0,0,0,19,37,8,21,0,0,0,0,0,20,4,24,0,0,0,0,32,0,8,40] >;

C2×D4.9D10 in GAP, Magma, Sage, TeX

C_2\times D_4._9D_{10}
% in TeX

G:=Group("C2xD4.9D10");
// GroupNames label

G:=SmallGroup(320,1495);
// by ID

G=gap.SmallGroup(320,1495);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,675,297,1684,235,102,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^10=1,e^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=b^2*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^-1>;
// generators/relations

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