G = C10.792- 1+4 order 320 = 26·5
34th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.792- 1+4, C20⋊Q8⋊30C2, C4⋊C4.103D10, C22.42(D4×D5), D10⋊Q8⋊26C2, (C2×D4).158D10, (C2×C20).66C23, C22⋊C4.25D10, (C2×Dic5).87D4, Dic5.20(C2×D4), C22.D4⋊2D5, C10.80(C22×D4), (C2×C10).192C24, (C22×C4).254D10, Dic5.5D4⋊29C2, (C22×Dic10)⋊10C2, (D4×C10).130C22, C23.23D10⋊6C2, C22.D20⋊18C2, C4⋊Dic5.223C22, (C22×C10).28C23, (C22×C20).85C22, (C22×D5).83C23, C22.213(C23×D5), C23.198(C22×D5), Dic5.14D4⋊27C2, C23.D5.38C22, D10⋊C4.30C22, C23.18D10⋊13C2, C23.11D10⋊10C2, C5⋊3(C23.38C23), (C2×Dic5).252C23, (C4×Dic5).127C22, C10.D4.37C22, C2.40(D4.10D10), (C2×Dic10).257C22, (C22×Dic5).126C22, C2.53(C2×D4×D5), (C2×C10).56(C2×D4), (C2×C4×D5).117C22, (C2×D4⋊2D5).10C2, (C5×C4⋊C4).172C22, (C2×C4).188(C22×D5), (C5×C22.D4)⋊2C2, (C2×C5⋊D4).44C22, (C5×C22⋊C4).47C22, SmallGroup(320,1320)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.792- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=e2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=b-1, bd=db, ebe-1=a5b, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 926 in 270 conjugacy classes, 103 normal (39 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C10, C42, C22⋊C4, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C42⋊C2, C22⋊Q8, C22.D4, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic10, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C23.38C23, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C23.D5, C5×C22⋊C4, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×Dic10, C2×Dic10, C2×C4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, C23.11D10, Dic5.14D4, Dic5.5D4, C22.D20, C20⋊Q8, D10⋊Q8, C23.23D10, C23.18D10, C5×C22.D4, C22×Dic10, C2×D4⋊2D5, C10.792- 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C22×D4, 2- 1+4, C22×D5, C23.38C23, D4×D5, C23×D5, C2×D4×D5, D4.10D10, C10.792- 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)
(1 150 30 138)(2 141 21 139)(3 142 22 140)(4 143 23 131)(5 144 24 132)(6 145 25 133)(7 146 26 134)(8 147 27 135)(9 148 28 136)(10 149 29 137)(11 45 153 33)(12 46 154 34)(13 47 155 35)(14 48 156 36)(15 49 157 37)(16 50 158 38)(17 41 159 39)(18 42 160 40)(19 43 151 31)(20 44 152 32)(51 103 63 91)(52 104 64 92)(53 105 65 93)(54 106 66 94)(55 107 67 95)(56 108 68 96)(57 109 69 97)(58 110 70 98)(59 101 61 99)(60 102 62 100)(71 123 83 111)(72 124 84 112)(73 125 85 113)(74 126 86 114)(75 127 87 115)(76 128 88 116)(77 129 89 117)(78 130 90 118)(79 121 81 119)(80 122 82 120)
(1 98)(2 99)(3 100)(4 91)(5 92)(6 93)(7 94)(8 95)(9 96)(10 97)(11 85)(12 86)(13 87)(14 88)(15 89)(16 90)(17 81)(18 82)(19 83)(20 84)(21 101)(22 102)(23 103)(24 104)(25 105)(26 106)(27 107)(28 108)(29 109)(30 110)(31 111)(32 112)(33 113)(34 114)(35 115)(36 116)(37 117)(38 118)(39 119)(40 120)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(51 131)(52 132)(53 133)(54 134)(55 135)(56 136)(57 137)(58 138)(59 139)(60 140)(61 141)(62 142)(63 143)(64 144)(65 145)(66 146)(67 147)(68 148)(69 149)(70 150)(71 151)(72 152)(73 153)(74 154)(75 155)(76 156)(77 157)(78 158)(79 159)(80 160)
(1 138 30 150)(2 137 21 149)(3 136 22 148)(4 135 23 147)(5 134 24 146)(6 133 25 145)(7 132 26 144)(8 131 27 143)(9 140 28 142)(10 139 29 141)(11 50 153 38)(12 49 154 37)(13 48 155 36)(14 47 156 35)(15 46 157 34)(16 45 158 33)(17 44 159 32)(18 43 160 31)(19 42 151 40)(20 41 152 39)(51 107 63 95)(52 106 64 94)(53 105 65 93)(54 104 66 92)(55 103 67 91)(56 102 68 100)(57 101 69 99)(58 110 70 98)(59 109 61 97)(60 108 62 96)(71 120 83 122)(72 119 84 121)(73 118 85 130)(74 117 86 129)(75 116 87 128)(76 115 88 127)(77 114 89 126)(78 113 90 125)(79 112 81 124)(80 111 82 123)
(1 50 30 38)(2 41 21 39)(3 42 22 40)(4 43 23 31)(5 44 24 32)(6 45 25 33)(7 46 26 34)(8 47 27 35)(9 48 28 36)(10 49 29 37)(11 150 153 138)(12 141 154 139)(13 142 155 140)(14 143 156 131)(15 144 157 132)(16 145 158 133)(17 146 159 134)(18 147 160 135)(19 148 151 136)(20 149 152 137)(51 88 63 76)(52 89 64 77)(53 90 65 78)(54 81 66 79)(55 82 67 80)(56 83 68 71)(57 84 69 72)(58 85 70 73)(59 86 61 74)(60 87 62 75)(91 123 103 111)(92 124 104 112)(93 125 105 113)(94 126 106 114)(95 127 107 115)(96 128 108 116)(97 129 109 117)(98 130 110 118)(99 121 101 119)(100 122 102 120)
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), (1,150,30,138)(2,141,21,139)(3,142,22,140)(4,143,23,131)(5,144,24,132)(6,145,25,133)(7,146,26,134)(8,147,27,135)(9,148,28,136)(10,149,29,137)(11,45,153,33)(12,46,154,34)(13,47,155,35)(14,48,156,36)(15,49,157,37)(16,50,158,38)(17,41,159,39)(18,42,160,40)(19,43,151,31)(20,44,152,32)(51,103,63,91)(52,104,64,92)(53,105,65,93)(54,106,66,94)(55,107,67,95)(56,108,68,96)(57,109,69,97)(58,110,70,98)(59,101,61,99)(60,102,62,100)(71,123,83,111)(72,124,84,112)(73,125,85,113)(74,126,86,114)(75,127,87,115)(76,128,88,116)(77,129,89,117)(78,130,90,118)(79,121,81,119)(80,122,82,120), (1,98)(2,99)(3,100)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,97)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,81)(18,82)(19,83)(20,84)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,116)(37,117)(38,118)(39,119)(40,120)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,137)(58,138)(59,139)(60,140)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160), (1,138,30,150)(2,137,21,149)(3,136,22,148)(4,135,23,147)(5,134,24,146)(6,133,25,145)(7,132,26,144)(8,131,27,143)(9,140,28,142)(10,139,29,141)(11,50,153,38)(12,49,154,37)(13,48,155,36)(14,47,156,35)(15,46,157,34)(16,45,158,33)(17,44,159,32)(18,43,160,31)(19,42,151,40)(20,41,152,39)(51,107,63,95)(52,106,64,94)(53,105,65,93)(54,104,66,92)(55,103,67,91)(56,102,68,100)(57,101,69,99)(58,110,70,98)(59,109,61,97)(60,108,62,96)(71,120,83,122)(72,119,84,121)(73,118,85,130)(74,117,86,129)(75,116,87,128)(76,115,88,127)(77,114,89,126)(78,113,90,125)(79,112,81,124)(80,111,82,123), (1,50,30,38)(2,41,21,39)(3,42,22,40)(4,43,23,31)(5,44,24,32)(6,45,25,33)(7,46,26,34)(8,47,27,35)(9,48,28,36)(10,49,29,37)(11,150,153,138)(12,141,154,139)(13,142,155,140)(14,143,156,131)(15,144,157,132)(16,145,158,133)(17,146,159,134)(18,147,160,135)(19,148,151,136)(20,149,152,137)(51,88,63,76)(52,89,64,77)(53,90,65,78)(54,81,66,79)(55,82,67,80)(56,83,68,71)(57,84,69,72)(58,85,70,73)(59,86,61,74)(60,87,62,75)(91,123,103,111)(92,124,104,112)(93,125,105,113)(94,126,106,114)(95,127,107,115)(96,128,108,116)(97,129,109,117)(98,130,110,118)(99,121,101,119)(100,122,102,120)>;
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), (1,150,30,138)(2,141,21,139)(3,142,22,140)(4,143,23,131)(5,144,24,132)(6,145,25,133)(7,146,26,134)(8,147,27,135)(9,148,28,136)(10,149,29,137)(11,45,153,33)(12,46,154,34)(13,47,155,35)(14,48,156,36)(15,49,157,37)(16,50,158,38)(17,41,159,39)(18,42,160,40)(19,43,151,31)(20,44,152,32)(51,103,63,91)(52,104,64,92)(53,105,65,93)(54,106,66,94)(55,107,67,95)(56,108,68,96)(57,109,69,97)(58,110,70,98)(59,101,61,99)(60,102,62,100)(71,123,83,111)(72,124,84,112)(73,125,85,113)(74,126,86,114)(75,127,87,115)(76,128,88,116)(77,129,89,117)(78,130,90,118)(79,121,81,119)(80,122,82,120), (1,98)(2,99)(3,100)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,97)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,81)(18,82)(19,83)(20,84)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,116)(37,117)(38,118)(39,119)(40,120)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,137)(58,138)(59,139)(60,140)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160), (1,138,30,150)(2,137,21,149)(3,136,22,148)(4,135,23,147)(5,134,24,146)(6,133,25,145)(7,132,26,144)(8,131,27,143)(9,140,28,142)(10,139,29,141)(11,50,153,38)(12,49,154,37)(13,48,155,36)(14,47,156,35)(15,46,157,34)(16,45,158,33)(17,44,159,32)(18,43,160,31)(19,42,151,40)(20,41,152,39)(51,107,63,95)(52,106,64,94)(53,105,65,93)(54,104,66,92)(55,103,67,91)(56,102,68,100)(57,101,69,99)(58,110,70,98)(59,109,61,97)(60,108,62,96)(71,120,83,122)(72,119,84,121)(73,118,85,130)(74,117,86,129)(75,116,87,128)(76,115,88,127)(77,114,89,126)(78,113,90,125)(79,112,81,124)(80,111,82,123), (1,50,30,38)(2,41,21,39)(3,42,22,40)(4,43,23,31)(5,44,24,32)(6,45,25,33)(7,46,26,34)(8,47,27,35)(9,48,28,36)(10,49,29,37)(11,150,153,138)(12,141,154,139)(13,142,155,140)(14,143,156,131)(15,144,157,132)(16,145,158,133)(17,146,159,134)(18,147,160,135)(19,148,151,136)(20,149,152,137)(51,88,63,76)(52,89,64,77)(53,90,65,78)(54,81,66,79)(55,82,67,80)(56,83,68,71)(57,84,69,72)(58,85,70,73)(59,86,61,74)(60,87,62,75)(91,123,103,111)(92,124,104,112)(93,125,105,113)(94,126,106,114)(95,127,107,115)(96,128,108,116)(97,129,109,117)(98,130,110,118)(99,121,101,119)(100,122,102,120) );
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)], [(1,150,30,138),(2,141,21,139),(3,142,22,140),(4,143,23,131),(5,144,24,132),(6,145,25,133),(7,146,26,134),(8,147,27,135),(9,148,28,136),(10,149,29,137),(11,45,153,33),(12,46,154,34),(13,47,155,35),(14,48,156,36),(15,49,157,37),(16,50,158,38),(17,41,159,39),(18,42,160,40),(19,43,151,31),(20,44,152,32),(51,103,63,91),(52,104,64,92),(53,105,65,93),(54,106,66,94),(55,107,67,95),(56,108,68,96),(57,109,69,97),(58,110,70,98),(59,101,61,99),(60,102,62,100),(71,123,83,111),(72,124,84,112),(73,125,85,113),(74,126,86,114),(75,127,87,115),(76,128,88,116),(77,129,89,117),(78,130,90,118),(79,121,81,119),(80,122,82,120)], [(1,98),(2,99),(3,100),(4,91),(5,92),(6,93),(7,94),(8,95),(9,96),(10,97),(11,85),(12,86),(13,87),(14,88),(15,89),(16,90),(17,81),(18,82),(19,83),(20,84),(21,101),(22,102),(23,103),(24,104),(25,105),(26,106),(27,107),(28,108),(29,109),(30,110),(31,111),(32,112),(33,113),(34,114),(35,115),(36,116),(37,117),(38,118),(39,119),(40,120),(41,121),(42,122),(43,123),(44,124),(45,125),(46,126),(47,127),(48,128),(49,129),(50,130),(51,131),(52,132),(53,133),(54,134),(55,135),(56,136),(57,137),(58,138),(59,139),(60,140),(61,141),(62,142),(63,143),(64,144),(65,145),(66,146),(67,147),(68,148),(69,149),(70,150),(71,151),(72,152),(73,153),(74,154),(75,155),(76,156),(77,157),(78,158),(79,159),(80,160)], [(1,138,30,150),(2,137,21,149),(3,136,22,148),(4,135,23,147),(5,134,24,146),(6,133,25,145),(7,132,26,144),(8,131,27,143),(9,140,28,142),(10,139,29,141),(11,50,153,38),(12,49,154,37),(13,48,155,36),(14,47,156,35),(15,46,157,34),(16,45,158,33),(17,44,159,32),(18,43,160,31),(19,42,151,40),(20,41,152,39),(51,107,63,95),(52,106,64,94),(53,105,65,93),(54,104,66,92),(55,103,67,91),(56,102,68,100),(57,101,69,99),(58,110,70,98),(59,109,61,97),(60,108,62,96),(71,120,83,122),(72,119,84,121),(73,118,85,130),(74,117,86,129),(75,116,87,128),(76,115,88,127),(77,114,89,126),(78,113,90,125),(79,112,81,124),(80,111,82,123)], [(1,50,30,38),(2,41,21,39),(3,42,22,40),(4,43,23,31),(5,44,24,32),(6,45,25,33),(7,46,26,34),(8,47,27,35),(9,48,28,36),(10,49,29,37),(11,150,153,138),(12,141,154,139),(13,142,155,140),(14,143,156,131),(15,144,157,132),(16,145,158,133),(17,146,159,134),(18,147,160,135),(19,148,151,136),(20,149,152,137),(51,88,63,76),(52,89,64,77),(53,90,65,78),(54,81,66,79),(55,82,67,80),(56,83,68,71),(57,84,69,72),(58,85,70,73),(59,86,61,74),(60,87,62,75),(91,123,103,111),(92,124,104,112),(93,125,105,113),(94,126,106,114),(95,127,107,115),(96,128,108,116),(97,129,109,117),(98,130,110,118),(99,121,101,119),(100,122,102,120)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4E | 4F | 4G | 4H | 4I | 4J | ··· | 4N | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 20A | ··· | 20H | 20I | ··· | 20N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 20 | 4 | ··· | 4 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | D10 | D10 | D10 | D10 | 2- 1+4 | D4×D5 | D4.10D10 |
| kernel | C10.792- 1+4 | C23.11D10 | Dic5.14D4 | Dic5.5D4 | C22.D20 | C20⋊Q8 | D10⋊Q8 | C23.23D10 | C23.18D10 | C5×C22.D4 | C22×Dic10 | C2×D4⋊2D5 | C2×Dic5 | C22.D4 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C22 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 2 | 6 | 4 | 2 | 2 | 2 | 4 | 8 |
Matrix representation of C10.792- 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 34 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 34 |
| 0 | 0 | 0 | 0 | 7 | 1 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 15 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 39 |
| 0 | 0 | 0 | 17 | 2 | 2 |
| 0 | 0 | 19 | 19 | 24 | 0 |
| 0 | 0 | 22 | 0 | 0 | 24 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 39 | 9 | 35 | 20 |
| 0 | 0 | 4 | 2 | 26 | 15 |
| 0 | 0 | 6 | 33 | 30 | 32 |
| 0 | 0 | 6 | 14 | 9 | 11 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 4 | 27 | 39 |
| 0 | 0 | 3 | 20 | 12 | 2 |
| 0 | 0 | 22 | 22 | 17 | 0 |
| 0 | 0 | 32 | 10 | 4 | 24 |
| 24 | 36 | 0 | 0 | 0 | 0 |
| 33 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 28 |
| 0 | 0 | 0 | 1 | 13 | 13 |
| 0 | 0 | 3 | 3 | 40 | 0 |
| 0 | 0 | 38 | 0 | 0 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,35,6,0,0,0,0,34,0,0,0,0,0,0,0,34,7,0,0,0,0,34,1],[40,15,0,0,0,0,0,1,0,0,0,0,0,0,17,0,19,22,0,0,0,17,19,0,0,0,0,2,24,0,0,0,39,2,0,24],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,39,4,6,6,0,0,9,2,33,14,0,0,35,26,30,9,0,0,20,15,32,11],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,21,3,22,32,0,0,4,20,22,10,0,0,27,12,17,4,0,0,39,2,0,24],[24,33,0,0,0,0,36,17,0,0,0,0,0,0,1,0,3,38,0,0,0,1,3,0,0,0,0,13,40,0,0,0,28,13,0,40] >;
C10.792- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{79}2_-^{1+4} % in TeX
G:=Group("C10.79ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1320);
// by ID
G=gap.SmallGroup(320,1320);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,387,1123,185,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=e^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c=b^-1,b*d=d*b,e*b*e^-1=a^5*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations