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## G = C24.9D10order 320 = 26·5

### 9th non-split extension by C24 of D10 acting via D10/C5=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22×C10 — C24.9D10
 Chief series C1 — C5 — C10 — C2×C10 — C22×C10 — C22×Dic5 — C2×C23.D5 — C24.9D10
 Lower central C5 — C22×C10 — C24.9D10
 Upper central C1 — C23 — C2×C22⋊C4

Generators and relations for C24.9D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=c, f2=bcd, 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=be9 >

Subgroups: 566 in 170 conjugacy classes, 57 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C5, C2×C4, C23, C23, C23, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic5, C20, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C22×C10, C22×C10, C23.11D4, C10.D4, C23.D5, C5×C22⋊C4, C22×Dic5, C22×C20, C23×C10, C10.10C42, C2×C10.D4, C2×C23.D5, C10×C22⋊C4, C24.9D10
Quotients:

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

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

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

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

62 conjugacy classes

 class 1 2A ··· 2G 2H 2I 4A 4B 4C 4D 4E ··· 4L 5A 5B 10A ··· 10N 10O ··· 10V 20A ··· 20P order 1 2 ··· 2 2 2 4 4 4 4 4 ··· 4 5 5 10 ··· 10 10 ··· 10 20 ··· 20 size 1 1 ··· 1 4 4 4 4 4 4 20 ··· 20 2 2 2 ··· 2 4 ··· 4 4 ··· 4

62 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + + + - image C1 C2 C2 C2 C2 D4 D4 D5 C4○D4 D10 D10 C5⋊D4 C4○D20 D4×D5 D4⋊2D5 kernel C24.9D10 C10.10C42 C2×C10.D4 C2×C23.D5 C10×C22⋊C4 C2×Dic5 C22×C10 C2×C22⋊C4 C2×C10 C22×C4 C24 C23 C22 C22 C22 # reps 1 3 1 2 1 2 2 2 10 4 2 8 16 2 6

Matrix representation of C24.9D10 in GL6(𝔽41)

 1 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 30 40 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 0 0 0 0 0 0 1 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 1 0 0 0 0 40 0 0 0 0 0 0 0 8 0 0 0 0 0 31 36 0 0 0 0 0 0 31 0 0 0 0 0 0 37
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 37 3 0 0 0 0 36 4 0 0 0 0 0 0 0 4 0 0 0 0 10 0

`G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,30,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[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],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,8,31,0,0,0,0,0,36,0,0,0,0,0,0,31,0,0,0,0,0,0,37],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,37,36,0,0,0,0,3,4,0,0,0,0,0,0,0,10,0,0,0,0,4,0] >;`

C24.9D10 in GAP, Magma, Sage, TeX

`C_2^4._9D_{10}`
`% in TeX`

`G:=Group("C2^4.9D10");`
`// GroupNames label`

`G:=SmallGroup(320,579);`
`// by ID`

`G=gap.SmallGroup(320,579);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,254,387,100,12550]);`
`// Polycyclic`

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

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