G = C10.1072- 1+4 order 320 = 26·5
62nd non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.1072- 1+4, (C5×Q8)⋊18D4, Q8⋊9(C5⋊D4), C5⋊7(Q8⋊5D4), C20⋊2D4⋊42C2, (Q8×Dic5)⋊29C2, C20.267(C2×D4), D10⋊16(C4○D4), (C2×D4).236D10, (C2×Q8).210D10, C20.48D4⋊40C2, C20.17D4⋊31C2, (C2×C20).561C23, (C2×C10).317C24, C10.167(C22×D4), (C22×C4).287D10, (D4×C10).276C22, C4⋊Dic5.260C22, (Q8×C10).243C22, C22.326(C23×D5), C23.138(C22×D5), C23.D5.76C22, (C22×C20).296C22, (C22×C10).243C23, (C2×Dic5).164C23, (C4×Dic5).184C22, (C22×D5).254C23, C2.70(D4.10D10), D10⋊C4.164C22, (C2×Dic10).210C22, C10.D4.101C22, (C2×Q8×D5)⋊19C2, (C2×C4○D4)⋊9D5, (C10×C4○D4)⋊9C2, (C4×C5⋊D4)⋊30C2, C4.73(C2×C5⋊D4), C2.105(D5×C4○D4), C10.217(C2×C4○D4), (C2×C4×D5).178C22, C2.40(C22×C5⋊D4), (C2×C4).640(C22×D5), (C2×C5⋊D4).149C22, SmallGroup(320,1503)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.1072- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=e2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, dbd-1=a5b, be=eb, dcd-1=a5c, ce=ec, ede-1=a5b2d >
Subgroups: 902 in 290 conjugacy classes, 113 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, D5, C10, C10, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C5×Q8, C22×D5, C22×C10, Q8⋊5D4, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C2×Dic10, C2×C4×D5, Q8×D5, C2×C5⋊D4, C22×C20, D4×C10, Q8×C10, C5×C4○D4, C20.48D4, C4×C5⋊D4, C20.17D4, C20⋊2D4, Q8×Dic5, C2×Q8×D5, C10×C4○D4, C10.1072- 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C22×D4, C2×C4○D4, 2- 1+4, C5⋊D4, C22×D5, Q8⋊5D4, C2×C5⋊D4, C23×D5, D5×C4○D4, D4.10D10, C22×C5⋊D4, C10.1072- 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)
(1 125 28 113)(2 124 29 112)(3 123 30 111)(4 122 21 120)(5 121 22 119)(6 130 23 118)(7 129 24 117)(8 128 25 116)(9 127 26 115)(10 126 27 114)(11 53 153 65)(12 52 154 64)(13 51 155 63)(14 60 156 62)(15 59 157 61)(16 58 158 70)(17 57 159 69)(18 56 160 68)(19 55 151 67)(20 54 152 66)(31 100 43 102)(32 99 44 101)(33 98 45 110)(34 97 46 109)(35 96 47 108)(36 95 48 107)(37 94 49 106)(38 93 50 105)(39 92 41 104)(40 91 42 103)(71 140 83 142)(72 139 84 141)(73 138 85 150)(74 137 86 149)(75 136 87 148)(76 135 88 147)(77 134 89 146)(78 133 90 145)(79 132 81 144)(80 131 82 143)
(1 118)(2 119)(3 120)(4 111)(5 112)(6 113)(7 114)(8 115)(9 116)(10 117)(11 58)(12 59)(13 60)(14 51)(15 52)(16 53)(17 54)(18 55)(19 56)(20 57)(21 123)(22 124)(23 125)(24 126)(25 127)(26 128)(27 129)(28 130)(29 121)(30 122)(31 91)(32 92)(33 93)(34 94)(35 95)(36 96)(37 97)(38 98)(39 99)(40 100)(41 101)(42 102)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(61 154)(62 155)(63 156)(64 157)(65 158)(66 159)(67 160)(68 151)(69 152)(70 153)(71 131)(72 132)(73 133)(74 134)(75 135)(76 136)(77 137)(78 138)(79 139)(80 140)(81 141)(82 142)(83 143)(84 144)(85 145)(86 146)(87 147)(88 148)(89 149)(90 150)
(1 65 23 58)(2 64 24 57)(3 63 25 56)(4 62 26 55)(5 61 27 54)(6 70 28 53)(7 69 29 52)(8 68 30 51)(9 67 21 60)(10 66 22 59)(11 113 158 130)(12 112 159 129)(13 111 160 128)(14 120 151 127)(15 119 152 126)(16 118 153 125)(17 117 154 124)(18 116 155 123)(19 115 156 122)(20 114 157 121)(31 87 48 80)(32 86 49 79)(33 85 50 78)(34 84 41 77)(35 83 42 76)(36 82 43 75)(37 81 44 74)(38 90 45 73)(39 89 46 72)(40 88 47 71)(91 142 108 135)(92 141 109 134)(93 150 110 133)(94 149 101 132)(95 148 102 131)(96 147 103 140)(97 146 104 139)(98 145 105 138)(99 144 106 137)(100 143 107 136)
(1 98 23 105)(2 99 24 106)(3 100 25 107)(4 91 26 108)(5 92 27 109)(6 93 28 110)(7 94 29 101)(8 95 30 102)(9 96 21 103)(10 97 22 104)(11 85 158 78)(12 86 159 79)(13 87 160 80)(14 88 151 71)(15 89 152 72)(16 90 153 73)(17 81 154 74)(18 82 155 75)(19 83 156 76)(20 84 157 77)(31 128 48 111)(32 129 49 112)(33 130 50 113)(34 121 41 114)(35 122 42 115)(36 123 43 116)(37 124 44 117)(38 125 45 118)(39 126 46 119)(40 127 47 120)(51 148 68 131)(52 149 69 132)(53 150 70 133)(54 141 61 134)(55 142 62 135)(56 143 63 136)(57 144 64 137)(58 145 65 138)(59 146 66 139)(60 147 67 140)
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), (1,125,28,113)(2,124,29,112)(3,123,30,111)(4,122,21,120)(5,121,22,119)(6,130,23,118)(7,129,24,117)(8,128,25,116)(9,127,26,115)(10,126,27,114)(11,53,153,65)(12,52,154,64)(13,51,155,63)(14,60,156,62)(15,59,157,61)(16,58,158,70)(17,57,159,69)(18,56,160,68)(19,55,151,67)(20,54,152,66)(31,100,43,102)(32,99,44,101)(33,98,45,110)(34,97,46,109)(35,96,47,108)(36,95,48,107)(37,94,49,106)(38,93,50,105)(39,92,41,104)(40,91,42,103)(71,140,83,142)(72,139,84,141)(73,138,85,150)(74,137,86,149)(75,136,87,148)(76,135,88,147)(77,134,89,146)(78,133,90,145)(79,132,81,144)(80,131,82,143), (1,118)(2,119)(3,120)(4,111)(5,112)(6,113)(7,114)(8,115)(9,116)(10,117)(11,58)(12,59)(13,60)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,121)(30,122)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,99)(40,100)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(61,154)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,151)(69,152)(70,153)(71,131)(72,132)(73,133)(74,134)(75,135)(76,136)(77,137)(78,138)(79,139)(80,140)(81,141)(82,142)(83,143)(84,144)(85,145)(86,146)(87,147)(88,148)(89,149)(90,150), (1,65,23,58)(2,64,24,57)(3,63,25,56)(4,62,26,55)(5,61,27,54)(6,70,28,53)(7,69,29,52)(8,68,30,51)(9,67,21,60)(10,66,22,59)(11,113,158,130)(12,112,159,129)(13,111,160,128)(14,120,151,127)(15,119,152,126)(16,118,153,125)(17,117,154,124)(18,116,155,123)(19,115,156,122)(20,114,157,121)(31,87,48,80)(32,86,49,79)(33,85,50,78)(34,84,41,77)(35,83,42,76)(36,82,43,75)(37,81,44,74)(38,90,45,73)(39,89,46,72)(40,88,47,71)(91,142,108,135)(92,141,109,134)(93,150,110,133)(94,149,101,132)(95,148,102,131)(96,147,103,140)(97,146,104,139)(98,145,105,138)(99,144,106,137)(100,143,107,136), (1,98,23,105)(2,99,24,106)(3,100,25,107)(4,91,26,108)(5,92,27,109)(6,93,28,110)(7,94,29,101)(8,95,30,102)(9,96,21,103)(10,97,22,104)(11,85,158,78)(12,86,159,79)(13,87,160,80)(14,88,151,71)(15,89,152,72)(16,90,153,73)(17,81,154,74)(18,82,155,75)(19,83,156,76)(20,84,157,77)(31,128,48,111)(32,129,49,112)(33,130,50,113)(34,121,41,114)(35,122,42,115)(36,123,43,116)(37,124,44,117)(38,125,45,118)(39,126,46,119)(40,127,47,120)(51,148,68,131)(52,149,69,132)(53,150,70,133)(54,141,61,134)(55,142,62,135)(56,143,63,136)(57,144,64,137)(58,145,65,138)(59,146,66,139)(60,147,67,140)>;
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), (1,125,28,113)(2,124,29,112)(3,123,30,111)(4,122,21,120)(5,121,22,119)(6,130,23,118)(7,129,24,117)(8,128,25,116)(9,127,26,115)(10,126,27,114)(11,53,153,65)(12,52,154,64)(13,51,155,63)(14,60,156,62)(15,59,157,61)(16,58,158,70)(17,57,159,69)(18,56,160,68)(19,55,151,67)(20,54,152,66)(31,100,43,102)(32,99,44,101)(33,98,45,110)(34,97,46,109)(35,96,47,108)(36,95,48,107)(37,94,49,106)(38,93,50,105)(39,92,41,104)(40,91,42,103)(71,140,83,142)(72,139,84,141)(73,138,85,150)(74,137,86,149)(75,136,87,148)(76,135,88,147)(77,134,89,146)(78,133,90,145)(79,132,81,144)(80,131,82,143), (1,118)(2,119)(3,120)(4,111)(5,112)(6,113)(7,114)(8,115)(9,116)(10,117)(11,58)(12,59)(13,60)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,121)(30,122)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,99)(40,100)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(61,154)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,151)(69,152)(70,153)(71,131)(72,132)(73,133)(74,134)(75,135)(76,136)(77,137)(78,138)(79,139)(80,140)(81,141)(82,142)(83,143)(84,144)(85,145)(86,146)(87,147)(88,148)(89,149)(90,150), (1,65,23,58)(2,64,24,57)(3,63,25,56)(4,62,26,55)(5,61,27,54)(6,70,28,53)(7,69,29,52)(8,68,30,51)(9,67,21,60)(10,66,22,59)(11,113,158,130)(12,112,159,129)(13,111,160,128)(14,120,151,127)(15,119,152,126)(16,118,153,125)(17,117,154,124)(18,116,155,123)(19,115,156,122)(20,114,157,121)(31,87,48,80)(32,86,49,79)(33,85,50,78)(34,84,41,77)(35,83,42,76)(36,82,43,75)(37,81,44,74)(38,90,45,73)(39,89,46,72)(40,88,47,71)(91,142,108,135)(92,141,109,134)(93,150,110,133)(94,149,101,132)(95,148,102,131)(96,147,103,140)(97,146,104,139)(98,145,105,138)(99,144,106,137)(100,143,107,136), (1,98,23,105)(2,99,24,106)(3,100,25,107)(4,91,26,108)(5,92,27,109)(6,93,28,110)(7,94,29,101)(8,95,30,102)(9,96,21,103)(10,97,22,104)(11,85,158,78)(12,86,159,79)(13,87,160,80)(14,88,151,71)(15,89,152,72)(16,90,153,73)(17,81,154,74)(18,82,155,75)(19,83,156,76)(20,84,157,77)(31,128,48,111)(32,129,49,112)(33,130,50,113)(34,121,41,114)(35,122,42,115)(36,123,43,116)(37,124,44,117)(38,125,45,118)(39,126,46,119)(40,127,47,120)(51,148,68,131)(52,149,69,132)(53,150,70,133)(54,141,61,134)(55,142,62,135)(56,143,63,136)(57,144,64,137)(58,145,65,138)(59,146,66,139)(60,147,67,140) );
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)], [(1,125,28,113),(2,124,29,112),(3,123,30,111),(4,122,21,120),(5,121,22,119),(6,130,23,118),(7,129,24,117),(8,128,25,116),(9,127,26,115),(10,126,27,114),(11,53,153,65),(12,52,154,64),(13,51,155,63),(14,60,156,62),(15,59,157,61),(16,58,158,70),(17,57,159,69),(18,56,160,68),(19,55,151,67),(20,54,152,66),(31,100,43,102),(32,99,44,101),(33,98,45,110),(34,97,46,109),(35,96,47,108),(36,95,48,107),(37,94,49,106),(38,93,50,105),(39,92,41,104),(40,91,42,103),(71,140,83,142),(72,139,84,141),(73,138,85,150),(74,137,86,149),(75,136,87,148),(76,135,88,147),(77,134,89,146),(78,133,90,145),(79,132,81,144),(80,131,82,143)], [(1,118),(2,119),(3,120),(4,111),(5,112),(6,113),(7,114),(8,115),(9,116),(10,117),(11,58),(12,59),(13,60),(14,51),(15,52),(16,53),(17,54),(18,55),(19,56),(20,57),(21,123),(22,124),(23,125),(24,126),(25,127),(26,128),(27,129),(28,130),(29,121),(30,122),(31,91),(32,92),(33,93),(34,94),(35,95),(36,96),(37,97),(38,98),(39,99),(40,100),(41,101),(42,102),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(61,154),(62,155),(63,156),(64,157),(65,158),(66,159),(67,160),(68,151),(69,152),(70,153),(71,131),(72,132),(73,133),(74,134),(75,135),(76,136),(77,137),(78,138),(79,139),(80,140),(81,141),(82,142),(83,143),(84,144),(85,145),(86,146),(87,147),(88,148),(89,149),(90,150)], [(1,65,23,58),(2,64,24,57),(3,63,25,56),(4,62,26,55),(5,61,27,54),(6,70,28,53),(7,69,29,52),(8,68,30,51),(9,67,21,60),(10,66,22,59),(11,113,158,130),(12,112,159,129),(13,111,160,128),(14,120,151,127),(15,119,152,126),(16,118,153,125),(17,117,154,124),(18,116,155,123),(19,115,156,122),(20,114,157,121),(31,87,48,80),(32,86,49,79),(33,85,50,78),(34,84,41,77),(35,83,42,76),(36,82,43,75),(37,81,44,74),(38,90,45,73),(39,89,46,72),(40,88,47,71),(91,142,108,135),(92,141,109,134),(93,150,110,133),(94,149,101,132),(95,148,102,131),(96,147,103,140),(97,146,104,139),(98,145,105,138),(99,144,106,137),(100,143,107,136)], [(1,98,23,105),(2,99,24,106),(3,100,25,107),(4,91,26,108),(5,92,27,109),(6,93,28,110),(7,94,29,101),(8,95,30,102),(9,96,21,103),(10,97,22,104),(11,85,158,78),(12,86,159,79),(13,87,160,80),(14,88,151,71),(15,89,152,72),(16,90,153,73),(17,81,154,74),(18,82,155,75),(19,83,156,76),(20,84,157,77),(31,128,48,111),(32,129,49,112),(33,130,50,113),(34,121,41,114),(35,122,42,115),(36,123,43,116),(37,124,44,117),(38,125,45,118),(39,126,46,119),(40,127,47,120),(51,148,68,131),(52,149,69,132),(53,150,70,133),(54,141,61,134),(55,142,62,135),(56,143,63,136),(57,144,64,137),(58,145,65,138),(59,146,66,139),(60,147,67,140)]])
65 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4H | 4I | 4J | 4K | ··· | 4P | 5A | 5B | 10A | ··· | 10F | 10G | ··· | 10R | 20A | ··· | 20H | 20I | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 10 | 10 | 2 | ··· | 2 | 10 | 10 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
65 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C5⋊D4 | 2- 1+4 | D5×C4○D4 | D4.10D10 |
| kernel | C10.1072- 1+4 | C20.48D4 | C4×C5⋊D4 | C20.17D4 | C20⋊2D4 | Q8×Dic5 | C2×Q8×D5 | C10×C4○D4 | C5×Q8 | C2×C4○D4 | D10 | C22×C4 | C2×D4 | C2×Q8 | Q8 | C10 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 4 | 2 | 4 | 6 | 6 | 2 | 16 | 1 | 4 | 4 |
Matrix representation of C10.1072- 1+4 ►in GL6(𝔽41)
| 35 | 35 | 0 | 0 | 0 | 0 |
| 6 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 6 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 23 | 0 | 0 |
| 0 | 0 | 24 | 29 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 15 |
| 0 | 0 | 0 | 0 | 38 | 13 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 18 | 0 | 0 |
| 0 | 0 | 8 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 26 |
| 0 | 0 | 0 | 0 | 3 | 28 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 35 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 15 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 4 |
| 0 | 0 | 0 | 0 | 0 | 32 |
| 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 | 35 | 29 |
| 0 | 0 | 0 | 0 | 27 | 6 |
G:=sub<GL(6,GF(41))| [35,6,0,0,0,0,35,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,6,0,0,0,0,0,40,0,0,0,0,0,0,12,24,0,0,0,0,23,29,0,0,0,0,0,0,28,38,0,0,0,0,15,13],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,29,8,0,0,0,0,18,12,0,0,0,0,0,0,13,3,0,0,0,0,26,28],[40,35,0,0,0,0,0,1,0,0,0,0,0,0,1,15,0,0,0,0,0,40,0,0,0,0,0,0,9,0,0,0,0,0,4,32],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,35,27,0,0,0,0,29,6] >;
C10.1072- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{107}2_-^{1+4} % in TeX
G:=Group("C10.107ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1503);
// by ID
G=gap.SmallGroup(320,1503);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,387,184,675,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=e^2=a^5*b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,a*e=e*a,c*b*c=b^-1,d*b*d^-1=a^5*b,b*e=e*b,d*c*d^-1=a^5*c,c*e=e*c,e*d*e^-1=a^5*b^2*d>;
// generators/relations