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## G = C24.4D10order 320 = 26·5

### 4th non-split extension by C24 of D10 acting via D10/C5=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C24.4D10
 Chief series C1 — C5 — C10 — C2×C10 — C22×C10 — C22×Dic5 — C2×C4×Dic5 — C24.4D10
 Lower central C5 — C2×C10 — C24.4D10
 Upper central C1 — C23 — C2×C22⋊C4

Generators and relations for C24.4D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=b, f2=db=bd, ab=ba, eae-1=ac=ca, ad=da, faf-1=abcd, bc=cb, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e9 >

Subgroups: 590 in 190 conjugacy classes, 69 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C5, C2×C4, C2×C4, C23, C23, C23, C10, C10, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic5, C20, C2×C10, C2×C10, C2.C42, C2×C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C22×C10, C22×C10, C24.C22, C4×Dic5, C10.D4, C23.D5, C23.D5, C5×C22⋊C4, C22×Dic5, C22×C20, C23×C10, C10.10C42, C2×C4×Dic5, C2×C10.D4, C2×C23.D5, C10×C22⋊C4, C24.4D10
Quotients:

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

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

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

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

68 conjugacy classes

 class 1 2A ··· 2G 2H 2I 4A 4B 4C 4D 4E 4F 4G ··· 4N 4O 4P 4Q 4R 5A 5B 10A ··· 10N 10O ··· 10V 20A ··· 20P order 1 2 ··· 2 2 2 4 4 4 4 4 4 4 ··· 4 4 4 4 4 5 5 10 ··· 10 10 ··· 10 20 ··· 20 size 1 1 ··· 1 4 4 2 2 2 2 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 1 2 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + + + + - image C1 C2 C2 C2 C2 C2 C4 D4 D4 D5 C4○D4 D10 D10 C5⋊D4 C4×D5 C4○D20 D4×D5 D4⋊2D5 kernel C24.4D10 C10.10C42 C2×C4×Dic5 C2×C10.D4 C2×C23.D5 C10×C22⋊C4 C23.D5 C2×Dic5 C2×C20 C2×C22⋊C4 C2×C10 C22×C4 C24 C2×C4 C23 C22 C22 C22 # reps 1 2 1 1 2 1 8 2 2 2 8 4 2 8 8 8 2 6

Matrix representation of C24.4D10 in GL6(𝔽41)

 1 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 21 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 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
,
 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 1 0 0 0 0 0 0 1
,
 0 1 0 0 0 0 40 0 0 0 0 0 0 0 0 1 0 0 0 0 40 0 0 0 0 0 0 0 36 0 0 0 0 0 11 33
,
 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 32 0 0 0 0 9 0 0 0 0 0 0 0 19 6 0 0 0 0 8 22

`G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,21,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,36,11,0,0,0,0,0,33],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,0,9,0,0,0,0,32,0,0,0,0,0,0,0,19,8,0,0,0,0,6,22] >;`

C24.4D10 in GAP, Magma, Sage, TeX

`C_2^4._4D_{10}`
`% in TeX`

`G:=Group("C2^4.4D10");`
`// GroupNames label`

`G:=SmallGroup(320,572);`
`// by ID`

`G=gap.SmallGroup(320,572);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,64,926,219,12550]);`
`// Polycyclic`

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

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