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G = C2×D4.9D10order 320 = 26·5

Direct product of C2 and D4.9D10

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

Aliases: C2×D4.9D10, C20.36C24, Dic10.31C23, C4○D4.41D10, C20.428(C2×D4), (C2×C20).219D4, C4.36(C23×D5), (C2×D4).233D10, C105(C8.C22), C52C8.15C23, D4.D518C22, (C2×Q8).191D10, C5⋊Q1617C22, D4.24(C22×D5), (C5×D4).24C23, (C5×Q8).24C23, Q8.24(C22×D5), (C2×C20).558C23, C10.161(C22×D4), (C22×C4).283D10, (C22×C10).125D4, C23.69(C5⋊D4), C4.Dic538C22, (C22×Dic10)⋊21C2, (C2×Dic10)⋊70C22, (D4×C10).273C22, (Q8×C10).238C22, (C22×C20).293C22, C56(C2×C8.C22), C4.31(C2×C5⋊D4), (C2×D4.D5)⋊31C2, (C2×C4○D4).10D5, (C2×C5⋊Q16)⋊31C2, (C2×C10).77(C2×D4), (C10×C4○D4).11C2, (C2×C4).96(C5⋊D4), (C2×C4.Dic5)⋊32C2, C2.34(C22×C5⋊D4), (C5×C4○D4).50C22, (C2×C4).247(C22×D5), C22.120(C2×C5⋊D4), (C2×C52C8).184C22, SmallGroup(320,1495)

Series: Derived Chief Lower central Upper central

C1C20 — C2×D4.9D10
C1C5C10C20Dic10C2×Dic10C22×Dic10 — C2×D4.9D10
C5C10C20 — C2×D4.9D10
C1C22C22×C4C2×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 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I4J5A5B8A8B8C8D10A···10F10G···10R20A···20H20I···20T
order12222222444444444455888810···1010···1020···2020···20
size111122442222442020202022202020202···24···42···24···4

62 irreducible representations

dim111111122222222244
type++++++++++++++--
imageC1C2C2C2C2C2C2D4D4D5D10D10D10D10C5⋊D4C5⋊D4C8.C22D4.9D10
kernelC2×D4.9D10C2×C4.Dic5C2×D4.D5C2×C5⋊Q16D4.9D10C22×Dic10C10×C4○D4C2×C20C22×C10C2×C4○D4C22×C4C2×D4C2×Q8C4○D4C2×C4C23C10C2
# reps1122811312222812428

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

10000000
01000000
004000000
000400000
000040000
000004000
000000400
000000040
,
10000000
01000000
004000000
000400000
000013200
0000234000
00002637137
00003132140
,
400000000
040000000
00100000
0017400000
000040900
00000100
0000255137
0000028040
,
135000000
66000000
004000000
000400000
000040020
0000179010
00000010
000011331332
,
10000000
640000000
0022360000
0031190000
0000119032
00003637200
000030848
000017212440

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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