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## G = C24.18D10order 320 = 26·5

### 18th non-split extension by C24 of D10 acting via D10/C5=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C24.18D10
 Chief series C1 — C5 — C10 — C2×C10 — C22×C10 — C22×Dic5 — C23×Dic5 — C24.18D10
 Lower central C5 — C2×C10 — C24.18D10
 Upper central C1 — C23 — C22×D4

Generators and relations for C24.18D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=b, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e-1 >

Subgroups: 862 in 286 conjugacy classes, 91 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, C10, C10, C10, C22⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, Dic5, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C23×C4, C22×D4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C22×C10, C23.23D4, C23.D5, C22×Dic5, C22×Dic5, C22×C20, D4×C10, D4×C10, C23×C10, C10.10C42, C2×C23.D5, C2×C23.D5, C23×Dic5, D4×C2×C10, C24.18D10
Quotients:

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

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

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

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

68 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 2L 2M 4A 4B 4C ··· 4J 4K 4L 4M 4N 5A 5B 10A ··· 10N 10O ··· 10AD 20A ··· 20H order 1 2 ··· 2 2 2 2 2 2 2 4 4 4 ··· 4 4 4 4 4 5 5 10 ··· 10 10 ··· 10 20 ··· 20 size 1 1 ··· 1 2 2 2 2 4 4 4 4 10 ··· 10 20 20 20 20 2 2 2 ··· 2 4 ··· 4 4 ··· 4

68 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + - + + - image C1 C2 C2 C2 C2 C4 D4 D4 D5 C4○D4 D10 Dic5 D10 C5⋊D4 D4×D5 D4⋊2D5 kernel C24.18D10 C10.10C42 C2×C23.D5 C23×Dic5 D4×C2×C10 D4×C10 C2×Dic5 C22×C10 C22×D4 C2×C10 C22×C4 C2×D4 C24 C23 C22 C22 # reps 1 2 3 1 1 8 4 4 2 4 2 8 4 16 4 4

Matrix representation of C24.18D10 in GL5(𝔽41)

 40 0 0 0 0 0 1 0 0 0 0 0 40 0 0 0 0 0 1 0 0 0 0 33 40
,
 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
,
 1 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 40
,
 1 0 0 0 0 0 40 0 0 0 0 0 40 0 0 0 0 0 1 0 0 0 0 0 1
,
 40 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 26 31
,
 9 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 2 21 0 0 0 31 39

`G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,1,33,0,0,0,0,40],[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],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,4,26,0,0,0,0,31],[9,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,2,31,0,0,0,21,39] >;`

C24.18D10 in GAP, Magma, Sage, TeX

`C_2^4._{18}D_{10}`
`% in TeX`

`G:=Group("C2^4.18D10");`
`// GroupNames label`

`G:=SmallGroup(320,847);`
`// by ID`

`G=gap.SmallGroup(320,847);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,12550]);`
`// Polycyclic`

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

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