G = C10.522+ 1+4 order 320 = 26·5
52nd non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.522+ 1+4, C5⋊D4⋊3Q8, C4⋊C4.97D10, C5⋊6(D4⋊3Q8), C22⋊Q8⋊13D5, C22.2(Q8×D5), D10.22(C2×Q8), (C2×Q8).75D10, D10⋊3Q8⋊18C2, D10⋊Q8⋊22C2, (C2×C20).59C23, C22⋊C4.61D10, Dic5.24(C2×Q8), Dic5⋊Q8⋊16C2, Dic5⋊3Q8⋊27C2, C10.38(C22×Q8), (C2×C10).180C24, Dic5⋊4D4.3C2, (C22×C4).242D10, C2.54(D4⋊6D10), Dic5.40(C4○D4), Dic5.Q8⋊19C2, C4⋊Dic5.217C22, (Q8×C10).111C22, (C2×Dic5).91C23, C22.201(C23×D5), C23.193(C22×D5), Dic5.14D4⋊26C2, D10⋊C4.25C22, (C22×C10).208C23, (C22×C20).380C22, (C4×Dic5).117C22, C10.D4.30C22, (C22×D5).212C23, C23.D5.120C22, (C2×Dic10).167C22, (C22×Dic5).121C22, (D5×C4⋊C4)⋊28C2, C2.21(C2×Q8×D5), C2.51(D5×C4○D4), (C2×C10).9(C2×Q8), (C4×C5⋊D4).18C2, (C5×C22⋊Q8)⋊16C2, C10.163(C2×C4○D4), (C2×C4×D5).109C22, (C2×C4).50(C22×D5), (C2×C10.D4)⋊41C2, (C5×C4⋊C4).162C22, (C2×C5⋊D4).135C22, (C5×C22⋊C4).35C22, SmallGroup(320,1308)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.522+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, ab=ba, ac=ca, dad-1=eae=a-1, cbc-1=b-1, dbd-1=a5b, be=eb, cd=dc, ce=ec, ede=a5b2d >
Subgroups: 742 in 228 conjugacy classes, 105 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic5, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, D4⋊3Q8, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C22×Dic5, C2×C5⋊D4, C22×C20, Q8×C10, Dic5.14D4, Dic5⋊4D4, Dic5⋊3Q8, Dic5.Q8, D5×C4⋊C4, D10⋊Q8, C2×C10.D4, C4×C5⋊D4, Dic5⋊Q8, D10⋊3Q8, C5×C22⋊Q8, C10.522+ 1+4
Quotients: C1, C2, C22, Q8, C23, D5, C2×Q8, C4○D4, C24, D10, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D5, D4⋊3Q8, Q8×D5, C23×D5, D4⋊6D10, C2×Q8×D5, D5×C4○D4, C10.522+ 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 90 25 73)(2 81 26 74)(3 82 27 75)(4 83 28 76)(5 84 29 77)(6 85 30 78)(7 86 21 79)(8 87 22 80)(9 88 23 71)(10 89 24 72)(11 98 158 105)(12 99 159 106)(13 100 160 107)(14 91 151 108)(15 92 152 109)(16 93 153 110)(17 94 154 101)(18 95 155 102)(19 96 156 103)(20 97 157 104)(31 68 48 51)(32 69 49 52)(33 70 50 53)(34 61 41 54)(35 62 42 55)(36 63 43 56)(37 64 44 57)(38 65 45 58)(39 66 46 59)(40 67 47 60)(111 136 128 143)(112 137 129 144)(113 138 130 145)(114 139 121 146)(115 140 122 147)(116 131 123 148)(117 132 124 149)(118 133 125 150)(119 134 126 141)(120 135 127 142)
(1 53 6 58)(2 54 7 59)(3 55 8 60)(4 56 9 51)(5 57 10 52)(11 125 16 130)(12 126 17 121)(13 127 18 122)(14 128 19 123)(15 129 20 124)(21 66 26 61)(22 67 27 62)(23 68 28 63)(24 69 29 64)(25 70 30 65)(31 76 36 71)(32 77 37 72)(33 78 38 73)(34 79 39 74)(35 80 40 75)(41 86 46 81)(42 87 47 82)(43 88 48 83)(44 89 49 84)(45 90 50 85)(91 136 96 131)(92 137 97 132)(93 138 98 133)(94 139 99 134)(95 140 100 135)(101 146 106 141)(102 147 107 142)(103 148 108 143)(104 149 109 144)(105 150 110 145)(111 156 116 151)(112 157 117 152)(113 158 118 153)(114 159 119 154)(115 160 120 155)
(1 133 25 150)(2 132 26 149)(3 131 27 148)(4 140 28 147)(5 139 29 146)(6 138 30 145)(7 137 21 144)(8 136 22 143)(9 135 23 142)(10 134 24 141)(11 33 158 50)(12 32 159 49)(13 31 160 48)(14 40 151 47)(15 39 152 46)(16 38 153 45)(17 37 154 44)(18 36 155 43)(19 35 156 42)(20 34 157 41)(51 95 68 102)(52 94 69 101)(53 93 70 110)(54 92 61 109)(55 91 62 108)(56 100 63 107)(57 99 64 106)(58 98 65 105)(59 97 66 104)(60 96 67 103)(71 115 88 122)(72 114 89 121)(73 113 90 130)(74 112 81 129)(75 111 82 128)(76 120 83 127)(77 119 84 126)(78 118 85 125)(79 117 86 124)(80 116 87 123)
(2 10)(3 9)(4 8)(5 7)(11 153)(12 152)(13 151)(14 160)(15 159)(16 158)(17 157)(18 156)(19 155)(20 154)(21 29)(22 28)(23 27)(24 26)(31 35)(32 34)(36 40)(37 39)(41 49)(42 48)(43 47)(44 46)(51 55)(52 54)(56 60)(57 59)(61 69)(62 68)(63 67)(64 66)(71 75)(72 74)(76 80)(77 79)(81 89)(82 88)(83 87)(84 86)(91 107)(92 106)(93 105)(94 104)(95 103)(96 102)(97 101)(98 110)(99 109)(100 108)(111 127)(112 126)(113 125)(114 124)(115 123)(116 122)(117 121)(118 130)(119 129)(120 128)(131 147)(132 146)(133 145)(134 144)(135 143)(136 142)(137 141)(138 150)(139 149)(140 148)
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), (1,90,25,73)(2,81,26,74)(3,82,27,75)(4,83,28,76)(5,84,29,77)(6,85,30,78)(7,86,21,79)(8,87,22,80)(9,88,23,71)(10,89,24,72)(11,98,158,105)(12,99,159,106)(13,100,160,107)(14,91,151,108)(15,92,152,109)(16,93,153,110)(17,94,154,101)(18,95,155,102)(19,96,156,103)(20,97,157,104)(31,68,48,51)(32,69,49,52)(33,70,50,53)(34,61,41,54)(35,62,42,55)(36,63,43,56)(37,64,44,57)(38,65,45,58)(39,66,46,59)(40,67,47,60)(111,136,128,143)(112,137,129,144)(113,138,130,145)(114,139,121,146)(115,140,122,147)(116,131,123,148)(117,132,124,149)(118,133,125,150)(119,134,126,141)(120,135,127,142), (1,53,6,58)(2,54,7,59)(3,55,8,60)(4,56,9,51)(5,57,10,52)(11,125,16,130)(12,126,17,121)(13,127,18,122)(14,128,19,123)(15,129,20,124)(21,66,26,61)(22,67,27,62)(23,68,28,63)(24,69,29,64)(25,70,30,65)(31,76,36,71)(32,77,37,72)(33,78,38,73)(34,79,39,74)(35,80,40,75)(41,86,46,81)(42,87,47,82)(43,88,48,83)(44,89,49,84)(45,90,50,85)(91,136,96,131)(92,137,97,132)(93,138,98,133)(94,139,99,134)(95,140,100,135)(101,146,106,141)(102,147,107,142)(103,148,108,143)(104,149,109,144)(105,150,110,145)(111,156,116,151)(112,157,117,152)(113,158,118,153)(114,159,119,154)(115,160,120,155), (1,133,25,150)(2,132,26,149)(3,131,27,148)(4,140,28,147)(5,139,29,146)(6,138,30,145)(7,137,21,144)(8,136,22,143)(9,135,23,142)(10,134,24,141)(11,33,158,50)(12,32,159,49)(13,31,160,48)(14,40,151,47)(15,39,152,46)(16,38,153,45)(17,37,154,44)(18,36,155,43)(19,35,156,42)(20,34,157,41)(51,95,68,102)(52,94,69,101)(53,93,70,110)(54,92,61,109)(55,91,62,108)(56,100,63,107)(57,99,64,106)(58,98,65,105)(59,97,66,104)(60,96,67,103)(71,115,88,122)(72,114,89,121)(73,113,90,130)(74,112,81,129)(75,111,82,128)(76,120,83,127)(77,119,84,126)(78,118,85,125)(79,117,86,124)(80,116,87,123), (2,10)(3,9)(4,8)(5,7)(11,153)(12,152)(13,151)(14,160)(15,159)(16,158)(17,157)(18,156)(19,155)(20,154)(21,29)(22,28)(23,27)(24,26)(31,35)(32,34)(36,40)(37,39)(41,49)(42,48)(43,47)(44,46)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,75)(72,74)(76,80)(77,79)(81,89)(82,88)(83,87)(84,86)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,110)(99,109)(100,108)(111,127)(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(118,130)(119,129)(120,128)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,150)(139,149)(140,148)>;
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), (1,90,25,73)(2,81,26,74)(3,82,27,75)(4,83,28,76)(5,84,29,77)(6,85,30,78)(7,86,21,79)(8,87,22,80)(9,88,23,71)(10,89,24,72)(11,98,158,105)(12,99,159,106)(13,100,160,107)(14,91,151,108)(15,92,152,109)(16,93,153,110)(17,94,154,101)(18,95,155,102)(19,96,156,103)(20,97,157,104)(31,68,48,51)(32,69,49,52)(33,70,50,53)(34,61,41,54)(35,62,42,55)(36,63,43,56)(37,64,44,57)(38,65,45,58)(39,66,46,59)(40,67,47,60)(111,136,128,143)(112,137,129,144)(113,138,130,145)(114,139,121,146)(115,140,122,147)(116,131,123,148)(117,132,124,149)(118,133,125,150)(119,134,126,141)(120,135,127,142), (1,53,6,58)(2,54,7,59)(3,55,8,60)(4,56,9,51)(5,57,10,52)(11,125,16,130)(12,126,17,121)(13,127,18,122)(14,128,19,123)(15,129,20,124)(21,66,26,61)(22,67,27,62)(23,68,28,63)(24,69,29,64)(25,70,30,65)(31,76,36,71)(32,77,37,72)(33,78,38,73)(34,79,39,74)(35,80,40,75)(41,86,46,81)(42,87,47,82)(43,88,48,83)(44,89,49,84)(45,90,50,85)(91,136,96,131)(92,137,97,132)(93,138,98,133)(94,139,99,134)(95,140,100,135)(101,146,106,141)(102,147,107,142)(103,148,108,143)(104,149,109,144)(105,150,110,145)(111,156,116,151)(112,157,117,152)(113,158,118,153)(114,159,119,154)(115,160,120,155), (1,133,25,150)(2,132,26,149)(3,131,27,148)(4,140,28,147)(5,139,29,146)(6,138,30,145)(7,137,21,144)(8,136,22,143)(9,135,23,142)(10,134,24,141)(11,33,158,50)(12,32,159,49)(13,31,160,48)(14,40,151,47)(15,39,152,46)(16,38,153,45)(17,37,154,44)(18,36,155,43)(19,35,156,42)(20,34,157,41)(51,95,68,102)(52,94,69,101)(53,93,70,110)(54,92,61,109)(55,91,62,108)(56,100,63,107)(57,99,64,106)(58,98,65,105)(59,97,66,104)(60,96,67,103)(71,115,88,122)(72,114,89,121)(73,113,90,130)(74,112,81,129)(75,111,82,128)(76,120,83,127)(77,119,84,126)(78,118,85,125)(79,117,86,124)(80,116,87,123), (2,10)(3,9)(4,8)(5,7)(11,153)(12,152)(13,151)(14,160)(15,159)(16,158)(17,157)(18,156)(19,155)(20,154)(21,29)(22,28)(23,27)(24,26)(31,35)(32,34)(36,40)(37,39)(41,49)(42,48)(43,47)(44,46)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,75)(72,74)(76,80)(77,79)(81,89)(82,88)(83,87)(84,86)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,110)(99,109)(100,108)(111,127)(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(118,130)(119,129)(120,128)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,150)(139,149)(140,148) );
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)], [(1,90,25,73),(2,81,26,74),(3,82,27,75),(4,83,28,76),(5,84,29,77),(6,85,30,78),(7,86,21,79),(8,87,22,80),(9,88,23,71),(10,89,24,72),(11,98,158,105),(12,99,159,106),(13,100,160,107),(14,91,151,108),(15,92,152,109),(16,93,153,110),(17,94,154,101),(18,95,155,102),(19,96,156,103),(20,97,157,104),(31,68,48,51),(32,69,49,52),(33,70,50,53),(34,61,41,54),(35,62,42,55),(36,63,43,56),(37,64,44,57),(38,65,45,58),(39,66,46,59),(40,67,47,60),(111,136,128,143),(112,137,129,144),(113,138,130,145),(114,139,121,146),(115,140,122,147),(116,131,123,148),(117,132,124,149),(118,133,125,150),(119,134,126,141),(120,135,127,142)], [(1,53,6,58),(2,54,7,59),(3,55,8,60),(4,56,9,51),(5,57,10,52),(11,125,16,130),(12,126,17,121),(13,127,18,122),(14,128,19,123),(15,129,20,124),(21,66,26,61),(22,67,27,62),(23,68,28,63),(24,69,29,64),(25,70,30,65),(31,76,36,71),(32,77,37,72),(33,78,38,73),(34,79,39,74),(35,80,40,75),(41,86,46,81),(42,87,47,82),(43,88,48,83),(44,89,49,84),(45,90,50,85),(91,136,96,131),(92,137,97,132),(93,138,98,133),(94,139,99,134),(95,140,100,135),(101,146,106,141),(102,147,107,142),(103,148,108,143),(104,149,109,144),(105,150,110,145),(111,156,116,151),(112,157,117,152),(113,158,118,153),(114,159,119,154),(115,160,120,155)], [(1,133,25,150),(2,132,26,149),(3,131,27,148),(4,140,28,147),(5,139,29,146),(6,138,30,145),(7,137,21,144),(8,136,22,143),(9,135,23,142),(10,134,24,141),(11,33,158,50),(12,32,159,49),(13,31,160,48),(14,40,151,47),(15,39,152,46),(16,38,153,45),(17,37,154,44),(18,36,155,43),(19,35,156,42),(20,34,157,41),(51,95,68,102),(52,94,69,101),(53,93,70,110),(54,92,61,109),(55,91,62,108),(56,100,63,107),(57,99,64,106),(58,98,65,105),(59,97,66,104),(60,96,67,103),(71,115,88,122),(72,114,89,121),(73,113,90,130),(74,112,81,129),(75,111,82,128),(76,120,83,127),(77,119,84,126),(78,118,85,125),(79,117,86,124),(80,116,87,123)], [(2,10),(3,9),(4,8),(5,7),(11,153),(12,152),(13,151),(14,160),(15,159),(16,158),(17,157),(18,156),(19,155),(20,154),(21,29),(22,28),(23,27),(24,26),(31,35),(32,34),(36,40),(37,39),(41,49),(42,48),(43,47),(44,46),(51,55),(52,54),(56,60),(57,59),(61,69),(62,68),(63,67),(64,66),(71,75),(72,74),(76,80),(77,79),(81,89),(82,88),(83,87),(84,86),(91,107),(92,106),(93,105),(94,104),(95,103),(96,102),(97,101),(98,110),(99,109),(100,108),(111,127),(112,126),(113,125),(114,124),(115,123),(116,122),(117,121),(118,130),(119,129),(120,128),(131,147),(132,146),(133,145),(134,144),(135,143),(136,142),(137,141),(138,150),(139,149),(140,148)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 4Q | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | ··· | 20P |
| order | 1 | 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 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 10 | 10 | 2 | 2 | 4 | ··· | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
53 irreducible representations
| dim | 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 | Q8 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | Q8×D5 | D4⋊6D10 | D5×C4○D4 |
| kernel | C10.522+ 1+4 | Dic5.14D4 | Dic5⋊4D4 | Dic5⋊3Q8 | Dic5.Q8 | D5×C4⋊C4 | D10⋊Q8 | C2×C10.D4 | C4×C5⋊D4 | Dic5⋊Q8 | D10⋊3Q8 | C5×C22⋊Q8 | C5⋊D4 | C22⋊Q8 | Dic5 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C22 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 2 | 4 | 4 | 6 | 2 | 2 | 1 | 4 | 4 | 4 |
Matrix representation of C10.522+ 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 7 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 35 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 6 |
| 0 | 0 | 0 | 0 | 19 | 7 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 38 |
| 0 | 0 | 0 | 0 | 38 | 20 |
| 6 | 39 | 0 | 0 | 0 | 0 |
| 38 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 7 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 3 |
| 0 | 0 | 0 | 0 | 3 | 21 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 6 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,7,34,0,0,0,0,7,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,35,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,34,19,0,0,0,0,6,7],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,21,38,0,0,0,0,38,20],[6,38,0,0,0,0,39,35,0,0,0,0,0,0,40,7,0,0,0,0,0,1,0,0,0,0,0,0,20,3,0,0,0,0,3,21],[1,6,0,0,0,0,0,40,0,0,0,0,0,0,1,34,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C10.522+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{52}2_+^{1+4} % in TeX
G:=Group("C10.52ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1308);
// by ID
G=gap.SmallGroup(320,1308);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,100,570,409,80,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=e*a*e=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^5*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=a^5*b^2*d>;
// generators/relations