G = C10.342+ 1+4 order 320 = 26·5
34th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.342+ 1+4, C4⋊D4⋊8D5, C4⋊C4.90D10, (D4×Dic5)⋊17C2, Dic5⋊4D4⋊7C2, (C2×D4).153D10, (C2×C20).36C23, C22⋊C4.48D10, Dic5⋊D4⋊29C2, (C2×C10).145C24, (C22×C4).220D10, D10.12D4⋊16C2, C2.36(D4⋊6D10), Dic5.38(C4○D4), Dic5.Q8⋊11C2, (D4×C10).119C22, C22.1(D4⋊2D5), C23.D10⋊15C2, C23.11D10⋊5C2, C4⋊Dic5.206C22, (C22×C10).16C23, (C2×Dic5).66C23, (C22×D5).63C23, C22.166(C23×D5), C23.179(C22×D5), C23.D5.22C22, D10⋊C4.13C22, C23.18D10⋊20C2, (C22×C20).378C22, C5⋊6(C22.47C24), (C4×Dic5).100C22, C10.D4.16C22, (C22×Dic5).106C22, (C5×C4⋊D4)⋊9C2, (C4×C5⋊D4)⋊53C2, C2.36(D5×C4○D4), C4⋊C4⋊D5⋊12C2, C10.81(C2×C4○D4), C2.33(C2×D4⋊2D5), (C2×C4×D5).259C22, (C2×C10).21(C4○D4), (C2×C10.D4)⋊40C2, (C5×C4⋊C4).141C22, (C2×C4).293(C22×D5), (C2×C5⋊D4).26C22, (C5×C22⋊C4).10C22, SmallGroup(320,1273)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.342+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, bab-1=cac-1=a-1, ad=da, ae=ea, cbc-1=b-1, dbd-1=ebe=a5b, cd=dc, ce=ec, ede=a5b2d >
Subgroups: 790 in 238 conjugacy classes, 97 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22.47C24, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×C4×D5, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, C23.11D10, C23.D10, Dic5⋊4D4, D10.12D4, Dic5.Q8, C4⋊C4⋊D5, C2×C10.D4, C4×C5⋊D4, D4×Dic5, C23.18D10, Dic5⋊D4, C5×C4⋊D4, C10.342+ 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, C22×D5, C22.47C24, D4⋊2D5, C23×D5, C2×D4⋊2D5, D4⋊6D10, D5×C4○D4, C10.342+ 1+4
►On 160 points
Generators in S160
(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)
(1 110 25 95)(2 109 26 94)(3 108 27 93)(4 107 28 92)(5 106 29 91)(6 105 30 100)(7 104 21 99)(8 103 22 98)(9 102 23 97)(10 101 24 96)(11 85 160 80)(12 84 151 79)(13 83 152 78)(14 82 153 77)(15 81 154 76)(16 90 155 75)(17 89 156 74)(18 88 157 73)(19 87 158 72)(20 86 159 71)(31 124 46 119)(32 123 47 118)(33 122 48 117)(34 121 49 116)(35 130 50 115)(36 129 41 114)(37 128 42 113)(38 127 43 112)(39 126 44 111)(40 125 45 120)(51 149 66 134)(52 148 67 133)(53 147 68 132)(54 146 69 131)(55 145 70 140)(56 144 61 139)(57 143 62 138)(58 142 63 137)(59 141 64 136)(60 150 65 135)
(1 65 6 70)(2 64 7 69)(3 63 8 68)(4 62 9 67)(5 61 10 66)(11 125 16 130)(12 124 17 129)(13 123 18 128)(14 122 19 127)(15 121 20 126)(21 54 26 59)(22 53 27 58)(23 52 28 57)(24 51 29 56)(25 60 30 55)(31 89 36 84)(32 88 37 83)(33 87 38 82)(34 86 39 81)(35 85 40 90)(41 79 46 74)(42 78 47 73)(43 77 48 72)(44 76 49 71)(45 75 50 80)(91 139 96 134)(92 138 97 133)(93 137 98 132)(94 136 99 131)(95 135 100 140)(101 149 106 144)(102 148 107 143)(103 147 108 142)(104 146 109 141)(105 145 110 150)(111 154 116 159)(112 153 117 158)(113 152 118 157)(114 151 119 156)(115 160 120 155)
(1 120 25 125)(2 111 26 126)(3 112 27 127)(4 113 28 128)(5 114 29 129)(6 115 30 130)(7 116 21 121)(8 117 22 122)(9 118 23 123)(10 119 24 124)(11 70 160 55)(12 61 151 56)(13 62 152 57)(14 63 153 58)(15 64 154 59)(16 65 155 60)(17 66 156 51)(18 67 157 52)(19 68 158 53)(20 69 159 54)(31 91 46 106)(32 92 47 107)(33 93 48 108)(34 94 49 109)(35 95 50 110)(36 96 41 101)(37 97 42 102)(38 98 43 103)(39 99 44 104)(40 100 45 105)(71 141 86 136)(72 142 87 137)(73 143 88 138)(74 144 89 139)(75 145 90 140)(76 146 81 131)(77 147 82 132)(78 148 83 133)(79 149 84 134)(80 150 85 135)
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 156)(22 157)(23 158)(24 159)(25 160)(26 151)(27 152)(28 153)(29 154)(30 155)(31 146)(32 147)(33 148)(34 149)(35 150)(36 141)(37 142)(38 143)(39 144)(40 145)(41 136)(42 137)(43 138)(44 139)(45 140)(46 131)(47 132)(48 133)(49 134)(50 135)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 121)(62 122)(63 123)(64 124)(65 125)(66 126)(67 127)(68 128)(69 129)(70 130)(71 91)(72 92)(73 93)(74 94)(75 95)(76 96)(77 97)(78 98)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)
G:=sub<Sym(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), (1,110,25,95)(2,109,26,94)(3,108,27,93)(4,107,28,92)(5,106,29,91)(6,105,30,100)(7,104,21,99)(8,103,22,98)(9,102,23,97)(10,101,24,96)(11,85,160,80)(12,84,151,79)(13,83,152,78)(14,82,153,77)(15,81,154,76)(16,90,155,75)(17,89,156,74)(18,88,157,73)(19,87,158,72)(20,86,159,71)(31,124,46,119)(32,123,47,118)(33,122,48,117)(34,121,49,116)(35,130,50,115)(36,129,41,114)(37,128,42,113)(38,127,43,112)(39,126,44,111)(40,125,45,120)(51,149,66,134)(52,148,67,133)(53,147,68,132)(54,146,69,131)(55,145,70,140)(56,144,61,139)(57,143,62,138)(58,142,63,137)(59,141,64,136)(60,150,65,135), (1,65,6,70)(2,64,7,69)(3,63,8,68)(4,62,9,67)(5,61,10,66)(11,125,16,130)(12,124,17,129)(13,123,18,128)(14,122,19,127)(15,121,20,126)(21,54,26,59)(22,53,27,58)(23,52,28,57)(24,51,29,56)(25,60,30,55)(31,89,36,84)(32,88,37,83)(33,87,38,82)(34,86,39,81)(35,85,40,90)(41,79,46,74)(42,78,47,73)(43,77,48,72)(44,76,49,71)(45,75,50,80)(91,139,96,134)(92,138,97,133)(93,137,98,132)(94,136,99,131)(95,135,100,140)(101,149,106,144)(102,148,107,143)(103,147,108,142)(104,146,109,141)(105,145,110,150)(111,154,116,159)(112,153,117,158)(113,152,118,157)(114,151,119,156)(115,160,120,155), (1,120,25,125)(2,111,26,126)(3,112,27,127)(4,113,28,128)(5,114,29,129)(6,115,30,130)(7,116,21,121)(8,117,22,122)(9,118,23,123)(10,119,24,124)(11,70,160,55)(12,61,151,56)(13,62,152,57)(14,63,153,58)(15,64,154,59)(16,65,155,60)(17,66,156,51)(18,67,157,52)(19,68,158,53)(20,69,159,54)(31,91,46,106)(32,92,47,107)(33,93,48,108)(34,94,49,109)(35,95,50,110)(36,96,41,101)(37,97,42,102)(38,98,43,103)(39,99,44,104)(40,100,45,105)(71,141,86,136)(72,142,87,137)(73,143,88,138)(74,144,89,139)(75,145,90,140)(76,146,81,131)(77,147,82,132)(78,148,83,133)(79,149,84,134)(80,150,85,135), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,156)(22,157)(23,158)(24,159)(25,160)(26,151)(27,152)(28,153)(29,154)(30,155)(31,146)(32,147)(33,148)(34,149)(35,150)(36,141)(37,142)(38,143)(39,144)(40,145)(41,136)(42,137)(43,138)(44,139)(45,140)(46,131)(47,132)(48,133)(49,134)(50,135)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,121)(62,122)(63,123)(64,124)(65,125)(66,126)(67,127)(68,128)(69,129)(70,130)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)>;
G:=Group( (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), (1,110,25,95)(2,109,26,94)(3,108,27,93)(4,107,28,92)(5,106,29,91)(6,105,30,100)(7,104,21,99)(8,103,22,98)(9,102,23,97)(10,101,24,96)(11,85,160,80)(12,84,151,79)(13,83,152,78)(14,82,153,77)(15,81,154,76)(16,90,155,75)(17,89,156,74)(18,88,157,73)(19,87,158,72)(20,86,159,71)(31,124,46,119)(32,123,47,118)(33,122,48,117)(34,121,49,116)(35,130,50,115)(36,129,41,114)(37,128,42,113)(38,127,43,112)(39,126,44,111)(40,125,45,120)(51,149,66,134)(52,148,67,133)(53,147,68,132)(54,146,69,131)(55,145,70,140)(56,144,61,139)(57,143,62,138)(58,142,63,137)(59,141,64,136)(60,150,65,135), (1,65,6,70)(2,64,7,69)(3,63,8,68)(4,62,9,67)(5,61,10,66)(11,125,16,130)(12,124,17,129)(13,123,18,128)(14,122,19,127)(15,121,20,126)(21,54,26,59)(22,53,27,58)(23,52,28,57)(24,51,29,56)(25,60,30,55)(31,89,36,84)(32,88,37,83)(33,87,38,82)(34,86,39,81)(35,85,40,90)(41,79,46,74)(42,78,47,73)(43,77,48,72)(44,76,49,71)(45,75,50,80)(91,139,96,134)(92,138,97,133)(93,137,98,132)(94,136,99,131)(95,135,100,140)(101,149,106,144)(102,148,107,143)(103,147,108,142)(104,146,109,141)(105,145,110,150)(111,154,116,159)(112,153,117,158)(113,152,118,157)(114,151,119,156)(115,160,120,155), (1,120,25,125)(2,111,26,126)(3,112,27,127)(4,113,28,128)(5,114,29,129)(6,115,30,130)(7,116,21,121)(8,117,22,122)(9,118,23,123)(10,119,24,124)(11,70,160,55)(12,61,151,56)(13,62,152,57)(14,63,153,58)(15,64,154,59)(16,65,155,60)(17,66,156,51)(18,67,157,52)(19,68,158,53)(20,69,159,54)(31,91,46,106)(32,92,47,107)(33,93,48,108)(34,94,49,109)(35,95,50,110)(36,96,41,101)(37,97,42,102)(38,98,43,103)(39,99,44,104)(40,100,45,105)(71,141,86,136)(72,142,87,137)(73,143,88,138)(74,144,89,139)(75,145,90,140)(76,146,81,131)(77,147,82,132)(78,148,83,133)(79,149,84,134)(80,150,85,135), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,156)(22,157)(23,158)(24,159)(25,160)(26,151)(27,152)(28,153)(29,154)(30,155)(31,146)(32,147)(33,148)(34,149)(35,150)(36,141)(37,142)(38,143)(39,144)(40,145)(41,136)(42,137)(43,138)(44,139)(45,140)(46,131)(47,132)(48,133)(49,134)(50,135)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,121)(62,122)(63,123)(64,124)(65,125)(66,126)(67,127)(68,128)(69,129)(70,130)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110) );
G=PermutationGroup([[(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)], [(1,110,25,95),(2,109,26,94),(3,108,27,93),(4,107,28,92),(5,106,29,91),(6,105,30,100),(7,104,21,99),(8,103,22,98),(9,102,23,97),(10,101,24,96),(11,85,160,80),(12,84,151,79),(13,83,152,78),(14,82,153,77),(15,81,154,76),(16,90,155,75),(17,89,156,74),(18,88,157,73),(19,87,158,72),(20,86,159,71),(31,124,46,119),(32,123,47,118),(33,122,48,117),(34,121,49,116),(35,130,50,115),(36,129,41,114),(37,128,42,113),(38,127,43,112),(39,126,44,111),(40,125,45,120),(51,149,66,134),(52,148,67,133),(53,147,68,132),(54,146,69,131),(55,145,70,140),(56,144,61,139),(57,143,62,138),(58,142,63,137),(59,141,64,136),(60,150,65,135)], [(1,65,6,70),(2,64,7,69),(3,63,8,68),(4,62,9,67),(5,61,10,66),(11,125,16,130),(12,124,17,129),(13,123,18,128),(14,122,19,127),(15,121,20,126),(21,54,26,59),(22,53,27,58),(23,52,28,57),(24,51,29,56),(25,60,30,55),(31,89,36,84),(32,88,37,83),(33,87,38,82),(34,86,39,81),(35,85,40,90),(41,79,46,74),(42,78,47,73),(43,77,48,72),(44,76,49,71),(45,75,50,80),(91,139,96,134),(92,138,97,133),(93,137,98,132),(94,136,99,131),(95,135,100,140),(101,149,106,144),(102,148,107,143),(103,147,108,142),(104,146,109,141),(105,145,110,150),(111,154,116,159),(112,153,117,158),(113,152,118,157),(114,151,119,156),(115,160,120,155)], [(1,120,25,125),(2,111,26,126),(3,112,27,127),(4,113,28,128),(5,114,29,129),(6,115,30,130),(7,116,21,121),(8,117,22,122),(9,118,23,123),(10,119,24,124),(11,70,160,55),(12,61,151,56),(13,62,152,57),(14,63,153,58),(15,64,154,59),(16,65,155,60),(17,66,156,51),(18,67,157,52),(19,68,158,53),(20,69,159,54),(31,91,46,106),(32,92,47,107),(33,93,48,108),(34,94,49,109),(35,95,50,110),(36,96,41,101),(37,97,42,102),(38,98,43,103),(39,99,44,104),(40,100,45,105),(71,141,86,136),(72,142,87,137),(73,143,88,138),(74,144,89,139),(75,145,90,140),(76,146,81,131),(77,147,82,132),(78,148,83,133),(79,149,84,134),(80,150,85,135)], [(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(21,156),(22,157),(23,158),(24,159),(25,160),(26,151),(27,152),(28,153),(29,154),(30,155),(31,146),(32,147),(33,148),(34,149),(35,150),(36,141),(37,142),(38,143),(39,144),(40,145),(41,136),(42,137),(43,138),(44,139),(45,140),(46,131),(47,132),(48,133),(49,134),(50,135),(51,111),(52,112),(53,113),(54,114),(55,115),(56,116),(57,117),(58,118),(59,119),(60,120),(61,121),(62,122),(63,123),(64,124),(65,125),(66,126),(67,127),(68,128),(69,129),(70,130),(71,91),(72,92),(73,93),(74,94),(75,95),(76,96),(77,97),(78,98),(79,99),(80,100),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 4P | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 20A | ··· | 20H | 20I | 20J | 20K | 20L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 20 | 2 | 2 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
53 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | D4⋊2D5 | D4⋊6D10 | D5×C4○D4 |
| kernel | C10.342+ 1+4 | C23.11D10 | C23.D10 | Dic5⋊4D4 | D10.12D4 | Dic5.Q8 | C4⋊C4⋊D5 | C2×C10.D4 | C4×C5⋊D4 | D4×Dic5 | C23.18D10 | Dic5⋊D4 | C5×C4⋊D4 | C4⋊D4 | Dic5 | C2×C10 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 3 | 1 | 2 | 4 | 4 | 4 | 2 | 2 | 6 | 1 | 4 | 4 | 4 |
Matrix representation of C10.342+ 1+4 ►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 | 35 |
| 0 | 0 | 0 | 0 | 6 | 35 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 35 | 6 |
| 0 | 0 | 0 | 0 | 1 | 6 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 0 | 35 | 6 |
| 0 | 0 | 0 | 0 | 1 | 6 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,6,0,0,0,0,35,35],[0,9,0,0,0,0,9,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,35,1,0,0,0,0,6,6],[9,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,35,1,0,0,0,0,6,6],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,0,40,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,32,0,0,0,0,9,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C10.342+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{34}2_+^{1+4} % in TeX
G:=Group("C10.34ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1273);
// by ID
G=gap.SmallGroup(320,1273);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,758,100,794,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=b^2,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,d*b*d^-1=e*b*e=a^5*b,c*d=d*c,c*e=e*c,e*d*e=a^5*b^2*d>;
// generators/relations