metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×D4).7F5, (D4×C10).5C4, D10⋊C8⋊3C2, C23.13(C2×F5), C10.17(C8○D4), (C2×Dic10).9C4, C2.17(D4.F5), Dic5.109(C2×D4), (C2×Dic5).119D4, C23.2F5⋊11C2, C22.2(C22⋊F5), C22.93(C22×F5), Dic5.11(C22⋊C4), (C2×Dic5).354C23, (C22×Dic5).187C22, (C22×C5⋊C8)⋊6C2, (C2×C5⋊D4).7C4, (C2×C4).37(C2×F5), (C2×C20).24(C2×C4), (C2×C5⋊C8).11C22, (C2×C4×D5).60C22, (C2×C22.F5)⋊6C2, C2.20(C2×C22⋊F5), C5⋊1((C22×C8)⋊C2), (C2×D4⋊2D5).7C2, C10.19(C2×C22⋊C4), (C2×C10).2(C22⋊C4), (C2×C10).78(C22×C4), (C22×C10).26(C2×C4), (C2×Dic5).73(C2×C4), (C22×D5).55(C2×C4), SmallGroup(320,1113)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×D4).7F5
G = < a,b,c,d,e | a2=b4=c2=d5=1, e4=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, ebe-1=ab-1, cd=dc, ce=ec, ede-1=d3 >
Subgroups: 586 in 158 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C10, C2×C8, M4(2), C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C22⋊C8, C22×C8, C2×M4(2), C2×C4○D4, C5⋊C8, Dic10, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C5×D4, C22×D5, C22×C10, (C22×C8)⋊C2, C2×C5⋊C8, C2×C5⋊C8, C22.F5, C2×Dic10, C2×C4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, D4×C10, D10⋊C8, C23.2F5, C22×C5⋊C8, C2×C22.F5, C2×D4⋊2D5, (C2×D4).7F5
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, C22⋊C4, C22×C4, C2×D4, F5, C2×C22⋊C4, C8○D4, C2×F5, (C22×C8)⋊C2, C22⋊F5, C22×F5, D4.F5, C2×C22⋊F5, (C2×D4).7F5
►On 160 points
Generators in S160
(1 141)(2 142)(3 143)(4 144)(5 137)(6 138)(7 139)(8 140)(9 19)(10 20)(11 21)(12 22)(13 23)(14 24)(15 17)(16 18)(25 147)(26 148)(27 149)(28 150)(29 151)(30 152)(31 145)(32 146)(33 98)(34 99)(35 100)(36 101)(37 102)(38 103)(39 104)(40 97)(41 52)(42 53)(43 54)(44 55)(45 56)(46 49)(47 50)(48 51)(57 105)(58 106)(59 107)(60 108)(61 109)(62 110)(63 111)(64 112)(65 136)(66 129)(67 130)(68 131)(69 132)(70 133)(71 134)(72 135)(73 94)(74 95)(75 96)(76 89)(77 90)(78 91)(79 92)(80 93)(81 122)(82 123)(83 124)(84 125)(85 126)(86 127)(87 128)(88 121)(113 155)(114 156)(115 157)(116 158)(117 159)(118 160)(119 153)(120 154)
(1 7 5 3)(2 144 6 140)(4 138 8 142)(9 17 13 21)(10 12 14 16)(11 19 15 23)(18 20 22 24)(25 104 29 100)(26 36 30 40)(27 98 31 102)(28 38 32 34)(33 145 37 149)(35 147 39 151)(41 69 45 65)(42 129 46 133)(43 71 47 67)(44 131 48 135)(49 70 53 66)(50 130 54 134)(51 72 55 68)(52 132 56 136)(57 127 61 123)(58 83 62 87)(59 121 63 125)(60 85 64 81)(73 155 77 159)(74 118 78 114)(75 157 79 153)(76 120 80 116)(82 105 86 109)(84 107 88 111)(89 154 93 158)(90 117 94 113)(91 156 95 160)(92 119 96 115)(97 148 101 152)(99 150 103 146)(106 124 110 128)(108 126 112 122)(137 143 141 139)
(1 24)(2 17)(3 18)(4 19)(5 20)(6 21)(7 22)(8 23)(9 144)(10 137)(11 138)(12 139)(13 140)(14 141)(15 142)(16 143)(25 71)(26 72)(27 65)(28 66)(29 67)(30 68)(31 69)(32 70)(33 56)(34 49)(35 50)(36 51)(37 52)(38 53)(39 54)(40 55)(41 102)(42 103)(43 104)(44 97)(45 98)(46 99)(47 100)(48 101)(57 73)(58 74)(59 75)(60 76)(61 77)(62 78)(63 79)(64 80)(81 120)(82 113)(83 114)(84 115)(85 116)(86 117)(87 118)(88 119)(89 108)(90 109)(91 110)(92 111)(93 112)(94 105)(95 106)(96 107)(121 153)(122 154)(123 155)(124 156)(125 157)(126 158)(127 159)(128 160)(129 150)(130 151)(131 152)(132 145)(133 146)(134 147)(135 148)(136 149)
(1 92 132 50 113)(2 51 93 114 133)(3 115 52 134 94)(4 135 116 95 53)(5 96 136 54 117)(6 55 89 118 129)(7 119 56 130 90)(8 131 120 91 49)(9 26 126 58 103)(10 59 27 104 127)(11 97 60 128 28)(12 121 98 29 61)(13 30 122 62 99)(14 63 31 100 123)(15 101 64 124 32)(16 125 102 25 57)(17 36 112 83 146)(18 84 37 147 105)(19 148 85 106 38)(20 107 149 39 86)(21 40 108 87 150)(22 88 33 151 109)(23 152 81 110 34)(24 111 145 35 82)(41 71 73 143 157)(42 144 72 158 74)(43 159 137 75 65)(44 76 160 66 138)(45 67 77 139 153)(46 140 68 154 78)(47 155 141 79 69)(48 80 156 70 142)
(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)
G:=sub<Sym(160)| (1,141)(2,142)(3,143)(4,144)(5,137)(6,138)(7,139)(8,140)(9,19)(10,20)(11,21)(12,22)(13,23)(14,24)(15,17)(16,18)(25,147)(26,148)(27,149)(28,150)(29,151)(30,152)(31,145)(32,146)(33,98)(34,99)(35,100)(36,101)(37,102)(38,103)(39,104)(40,97)(41,52)(42,53)(43,54)(44,55)(45,56)(46,49)(47,50)(48,51)(57,105)(58,106)(59,107)(60,108)(61,109)(62,110)(63,111)(64,112)(65,136)(66,129)(67,130)(68,131)(69,132)(70,133)(71,134)(72,135)(73,94)(74,95)(75,96)(76,89)(77,90)(78,91)(79,92)(80,93)(81,122)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,121)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,153)(120,154), (1,7,5,3)(2,144,6,140)(4,138,8,142)(9,17,13,21)(10,12,14,16)(11,19,15,23)(18,20,22,24)(25,104,29,100)(26,36,30,40)(27,98,31,102)(28,38,32,34)(33,145,37,149)(35,147,39,151)(41,69,45,65)(42,129,46,133)(43,71,47,67)(44,131,48,135)(49,70,53,66)(50,130,54,134)(51,72,55,68)(52,132,56,136)(57,127,61,123)(58,83,62,87)(59,121,63,125)(60,85,64,81)(73,155,77,159)(74,118,78,114)(75,157,79,153)(76,120,80,116)(82,105,86,109)(84,107,88,111)(89,154,93,158)(90,117,94,113)(91,156,95,160)(92,119,96,115)(97,148,101,152)(99,150,103,146)(106,124,110,128)(108,126,112,122)(137,143,141,139), (1,24)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,144)(10,137)(11,138)(12,139)(13,140)(14,141)(15,142)(16,143)(25,71)(26,72)(27,65)(28,66)(29,67)(30,68)(31,69)(32,70)(33,56)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,102)(42,103)(43,104)(44,97)(45,98)(46,99)(47,100)(48,101)(57,73)(58,74)(59,75)(60,76)(61,77)(62,78)(63,79)(64,80)(81,120)(82,113)(83,114)(84,115)(85,116)(86,117)(87,118)(88,119)(89,108)(90,109)(91,110)(92,111)(93,112)(94,105)(95,106)(96,107)(121,153)(122,154)(123,155)(124,156)(125,157)(126,158)(127,159)(128,160)(129,150)(130,151)(131,152)(132,145)(133,146)(134,147)(135,148)(136,149), (1,92,132,50,113)(2,51,93,114,133)(3,115,52,134,94)(4,135,116,95,53)(5,96,136,54,117)(6,55,89,118,129)(7,119,56,130,90)(8,131,120,91,49)(9,26,126,58,103)(10,59,27,104,127)(11,97,60,128,28)(12,121,98,29,61)(13,30,122,62,99)(14,63,31,100,123)(15,101,64,124,32)(16,125,102,25,57)(17,36,112,83,146)(18,84,37,147,105)(19,148,85,106,38)(20,107,149,39,86)(21,40,108,87,150)(22,88,33,151,109)(23,152,81,110,34)(24,111,145,35,82)(41,71,73,143,157)(42,144,72,158,74)(43,159,137,75,65)(44,76,160,66,138)(45,67,77,139,153)(46,140,68,154,78)(47,155,141,79,69)(48,80,156,70,142), (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)>;
G:=Group( (1,141)(2,142)(3,143)(4,144)(5,137)(6,138)(7,139)(8,140)(9,19)(10,20)(11,21)(12,22)(13,23)(14,24)(15,17)(16,18)(25,147)(26,148)(27,149)(28,150)(29,151)(30,152)(31,145)(32,146)(33,98)(34,99)(35,100)(36,101)(37,102)(38,103)(39,104)(40,97)(41,52)(42,53)(43,54)(44,55)(45,56)(46,49)(47,50)(48,51)(57,105)(58,106)(59,107)(60,108)(61,109)(62,110)(63,111)(64,112)(65,136)(66,129)(67,130)(68,131)(69,132)(70,133)(71,134)(72,135)(73,94)(74,95)(75,96)(76,89)(77,90)(78,91)(79,92)(80,93)(81,122)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,121)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,153)(120,154), (1,7,5,3)(2,144,6,140)(4,138,8,142)(9,17,13,21)(10,12,14,16)(11,19,15,23)(18,20,22,24)(25,104,29,100)(26,36,30,40)(27,98,31,102)(28,38,32,34)(33,145,37,149)(35,147,39,151)(41,69,45,65)(42,129,46,133)(43,71,47,67)(44,131,48,135)(49,70,53,66)(50,130,54,134)(51,72,55,68)(52,132,56,136)(57,127,61,123)(58,83,62,87)(59,121,63,125)(60,85,64,81)(73,155,77,159)(74,118,78,114)(75,157,79,153)(76,120,80,116)(82,105,86,109)(84,107,88,111)(89,154,93,158)(90,117,94,113)(91,156,95,160)(92,119,96,115)(97,148,101,152)(99,150,103,146)(106,124,110,128)(108,126,112,122)(137,143,141,139), (1,24)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,144)(10,137)(11,138)(12,139)(13,140)(14,141)(15,142)(16,143)(25,71)(26,72)(27,65)(28,66)(29,67)(30,68)(31,69)(32,70)(33,56)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,102)(42,103)(43,104)(44,97)(45,98)(46,99)(47,100)(48,101)(57,73)(58,74)(59,75)(60,76)(61,77)(62,78)(63,79)(64,80)(81,120)(82,113)(83,114)(84,115)(85,116)(86,117)(87,118)(88,119)(89,108)(90,109)(91,110)(92,111)(93,112)(94,105)(95,106)(96,107)(121,153)(122,154)(123,155)(124,156)(125,157)(126,158)(127,159)(128,160)(129,150)(130,151)(131,152)(132,145)(133,146)(134,147)(135,148)(136,149), (1,92,132,50,113)(2,51,93,114,133)(3,115,52,134,94)(4,135,116,95,53)(5,96,136,54,117)(6,55,89,118,129)(7,119,56,130,90)(8,131,120,91,49)(9,26,126,58,103)(10,59,27,104,127)(11,97,60,128,28)(12,121,98,29,61)(13,30,122,62,99)(14,63,31,100,123)(15,101,64,124,32)(16,125,102,25,57)(17,36,112,83,146)(18,84,37,147,105)(19,148,85,106,38)(20,107,149,39,86)(21,40,108,87,150)(22,88,33,151,109)(23,152,81,110,34)(24,111,145,35,82)(41,71,73,143,157)(42,144,72,158,74)(43,159,137,75,65)(44,76,160,66,138)(45,67,77,139,153)(46,140,68,154,78)(47,155,141,79,69)(48,80,156,70,142), (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) );
G=PermutationGroup([[(1,141),(2,142),(3,143),(4,144),(5,137),(6,138),(7,139),(8,140),(9,19),(10,20),(11,21),(12,22),(13,23),(14,24),(15,17),(16,18),(25,147),(26,148),(27,149),(28,150),(29,151),(30,152),(31,145),(32,146),(33,98),(34,99),(35,100),(36,101),(37,102),(38,103),(39,104),(40,97),(41,52),(42,53),(43,54),(44,55),(45,56),(46,49),(47,50),(48,51),(57,105),(58,106),(59,107),(60,108),(61,109),(62,110),(63,111),(64,112),(65,136),(66,129),(67,130),(68,131),(69,132),(70,133),(71,134),(72,135),(73,94),(74,95),(75,96),(76,89),(77,90),(78,91),(79,92),(80,93),(81,122),(82,123),(83,124),(84,125),(85,126),(86,127),(87,128),(88,121),(113,155),(114,156),(115,157),(116,158),(117,159),(118,160),(119,153),(120,154)], [(1,7,5,3),(2,144,6,140),(4,138,8,142),(9,17,13,21),(10,12,14,16),(11,19,15,23),(18,20,22,24),(25,104,29,100),(26,36,30,40),(27,98,31,102),(28,38,32,34),(33,145,37,149),(35,147,39,151),(41,69,45,65),(42,129,46,133),(43,71,47,67),(44,131,48,135),(49,70,53,66),(50,130,54,134),(51,72,55,68),(52,132,56,136),(57,127,61,123),(58,83,62,87),(59,121,63,125),(60,85,64,81),(73,155,77,159),(74,118,78,114),(75,157,79,153),(76,120,80,116),(82,105,86,109),(84,107,88,111),(89,154,93,158),(90,117,94,113),(91,156,95,160),(92,119,96,115),(97,148,101,152),(99,150,103,146),(106,124,110,128),(108,126,112,122),(137,143,141,139)], [(1,24),(2,17),(3,18),(4,19),(5,20),(6,21),(7,22),(8,23),(9,144),(10,137),(11,138),(12,139),(13,140),(14,141),(15,142),(16,143),(25,71),(26,72),(27,65),(28,66),(29,67),(30,68),(31,69),(32,70),(33,56),(34,49),(35,50),(36,51),(37,52),(38,53),(39,54),(40,55),(41,102),(42,103),(43,104),(44,97),(45,98),(46,99),(47,100),(48,101),(57,73),(58,74),(59,75),(60,76),(61,77),(62,78),(63,79),(64,80),(81,120),(82,113),(83,114),(84,115),(85,116),(86,117),(87,118),(88,119),(89,108),(90,109),(91,110),(92,111),(93,112),(94,105),(95,106),(96,107),(121,153),(122,154),(123,155),(124,156),(125,157),(126,158),(127,159),(128,160),(129,150),(130,151),(131,152),(132,145),(133,146),(134,147),(135,148),(136,149)], [(1,92,132,50,113),(2,51,93,114,133),(3,115,52,134,94),(4,135,116,95,53),(5,96,136,54,117),(6,55,89,118,129),(7,119,56,130,90),(8,131,120,91,49),(9,26,126,58,103),(10,59,27,104,127),(11,97,60,128,28),(12,121,98,29,61),(13,30,122,62,99),(14,63,31,100,123),(15,101,64,124,32),(16,125,102,25,57),(17,36,112,83,146),(18,84,37,147,105),(19,148,85,106,38),(20,107,149,39,86),(21,40,108,87,150),(22,88,33,151,109),(23,152,81,110,34),(24,111,145,35,82),(41,71,73,143,157),(42,144,72,158,74),(43,159,137,75,65),(44,76,160,66,138),(45,67,77,139,153),(46,140,68,154,78),(47,155,141,79,69),(48,80,156,70,142)], [(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)]])
38 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 20A | 20B |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 20 | 4 | 5 | 5 | 5 | 5 | 10 | 10 | 20 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 |
38 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | D4 | C8○D4 | F5 | C2×F5 | C2×F5 | C22⋊F5 | D4.F5 |
| kernel | (C2×D4).7F5 | D10⋊C8 | C23.2F5 | C22×C5⋊C8 | C2×C22.F5 | C2×D4⋊2D5 | C2×Dic10 | C2×C5⋊D4 | D4×C10 | C2×Dic5 | C10 | C2×D4 | C2×C4 | C23 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 4 | 2 | 4 | 8 | 1 | 1 | 2 | 4 | 2 |
Matrix representation of (C2×D4).7F5 ►in GL6(𝔽41)
| 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 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 16 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 0 | 38 | 38 |
| 0 | 0 | 3 | 22 | 3 | 0 |
| 0 | 0 | 0 | 3 | 22 | 3 |
| 0 | 0 | 38 | 38 | 0 | 19 |
| 40 | 4 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 40 | 40 | 40 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 34 | 30 | 4 |
| 0 | 0 | 37 | 11 | 7 | 24 |
| 0 | 0 | 37 | 13 | 30 | 26 |
| 0 | 0 | 17 | 13 | 28 | 24 |
G:=sub<GL(6,GF(41))| [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],[32,16,0,0,0,0,0,9,0,0,0,0,0,0,19,3,0,38,0,0,0,22,3,38,0,0,38,3,22,0,0,0,38,0,3,19],[40,0,0,0,0,0,4,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,1,0,0,0,0,40,0,1,0,0,0,40,0,0,1,0,0,40,0,0,0],[3,0,0,0,0,0,0,3,0,0,0,0,0,0,17,37,37,17,0,0,34,11,13,13,0,0,30,7,30,28,0,0,4,24,26,24] >;
(C2×D4).7F5 in GAP, Magma, Sage, TeX
(C_2\times D_4)._7F_5
% in TeX
G:=Group("(C2xD4).7F5"); // GroupNames label
G:=SmallGroup(320,1113);
// by ID
G=gap.SmallGroup(320,1113);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,136,6278,1595]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^5=1,e^4=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,e*b*e^-1=a*b^-1,c*d=d*c,c*e=e*c,e*d*e^-1=d^3>;
// generators/relations