G = C10.632+ 1+4 order 320 = 26·5
63rd non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.632+ 1+4, C10.832- 1+4, C4⋊C4.107D10, D10⋊Q8⋊31C2, (C2×D4).100D10, C20⋊2D4.12C2, C22⋊C4.28D10, C4.Dic10⋊29C2, C22.D4⋊9D5, D10.13(C4○D4), Dic5⋊4D4⋊22C2, C20.48D4⋊22C2, (C2×C20).180C23, (C2×C10).204C24, (C22×C4).259D10, D10.12D4⋊33C2, C2.65(D4⋊6D10), C23.28(C22×D5), Dic5.Q8⋊27C2, (D4×C10).142C22, C23.D10⋊32C2, C4⋊Dic5.228C22, (C22×C10).36C23, C22.225(C23×D5), Dic5.14D4⋊33C2, C23.D5.44C22, C23.18D10⋊15C2, (C22×C20).115C22, C5⋊6(C22.33C24), (C2×Dic5).106C23, (C4×Dic5).132C22, (C2×Dic10).39C22, C10.D4.42C22, (C22×D5).220C23, C2.44(D4.10D10), D10⋊C4.108C22, (C22×Dic5).130C22, (D5×C4⋊C4)⋊33C2, (C4×C5⋊D4)⋊7C2, C2.66(D5×C4○D4), C10.178(C2×C4○D4), (C2×C4×D5).122C22, (C2×C4).66(C22×D5), (C5×C4⋊C4).177C22, (C2×C5⋊D4).48C22, (C5×C22.D4)⋊12C2, (C5×C22⋊C4).52C22, SmallGroup(320,1332)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.632+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=b-1, dbd-1=ebe=a5b, cd=dc, ce=ec, ede=b2d >
Subgroups: 734 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, 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×D4, C2×Q8, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C22.D4, C42.C2, C42⋊2C2, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22.33C24, 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, D4×C10, Dic5.14D4, C23.D10, Dic5⋊4D4, D10.12D4, Dic5.Q8, C4.Dic10, D5×C4⋊C4, D10⋊Q8, C20.48D4, C4×C5⋊D4, C23.18D10, C20⋊2D4, C5×C22.D4, C10.632+ 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5, C22.33C24, C23×D5, D4⋊6D10, D5×C4○D4, D4.10D10, C10.632+ 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)
(1 133 13 123)(2 134 14 124)(3 135 15 125)(4 136 16 126)(5 137 17 127)(6 138 18 128)(7 139 19 129)(8 140 20 130)(9 131 11 121)(10 132 12 122)(21 151 31 141)(22 152 32 142)(23 153 33 143)(24 154 34 144)(25 155 35 145)(26 156 36 146)(27 157 37 147)(28 158 38 148)(29 159 39 149)(30 160 40 150)(41 96 51 86)(42 97 52 87)(43 98 53 88)(44 99 54 89)(45 100 55 90)(46 91 56 81)(47 92 57 82)(48 93 58 83)(49 94 59 84)(50 95 60 85)(61 116 71 106)(62 117 72 107)(63 118 73 108)(64 119 74 109)(65 120 75 110)(66 111 76 101)(67 112 77 102)(68 113 78 103)(69 114 79 104)(70 115 80 105)
(1 88 6 83)(2 89 7 84)(3 90 8 85)(4 81 9 86)(5 82 10 87)(11 96 16 91)(12 97 17 92)(13 98 18 93)(14 99 19 94)(15 100 20 95)(21 106 26 101)(22 107 27 102)(23 108 28 103)(24 109 29 104)(25 110 30 105)(31 116 36 111)(32 117 37 112)(33 118 38 113)(34 119 39 114)(35 120 40 115)(41 126 46 121)(42 127 47 122)(43 128 48 123)(44 129 49 124)(45 130 50 125)(51 136 56 131)(52 137 57 132)(53 138 58 133)(54 139 59 134)(55 140 60 135)(61 146 66 141)(62 147 67 142)(63 148 68 143)(64 149 69 144)(65 150 70 145)(71 156 76 151)(72 157 77 152)(73 158 78 153)(74 159 79 154)(75 160 80 155)
(1 33 13 23)(2 32 14 22)(3 31 15 21)(4 40 16 30)(5 39 17 29)(6 38 18 28)(7 37 19 27)(8 36 20 26)(9 35 11 25)(10 34 12 24)(41 80 51 70)(42 79 52 69)(43 78 53 68)(44 77 54 67)(45 76 55 66)(46 75 56 65)(47 74 57 64)(48 73 58 63)(49 72 59 62)(50 71 60 61)(81 115 91 105)(82 114 92 104)(83 113 93 103)(84 112 94 102)(85 111 95 101)(86 120 96 110)(87 119 97 109)(88 118 98 108)(89 117 99 107)(90 116 100 106)(121 160 131 150)(122 159 132 149)(123 158 133 148)(124 157 134 147)(125 156 135 146)(126 155 136 145)(127 154 137 144)(128 153 138 143)(129 152 139 142)(130 151 140 141)
(1 23)(2 24)(3 25)(4 26)(5 27)(6 28)(7 29)(8 30)(9 21)(10 22)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(41 66)(42 67)(43 68)(44 69)(45 70)(46 61)(47 62)(48 63)(49 64)(50 65)(51 76)(52 77)(53 78)(54 79)(55 80)(56 71)(57 72)(58 73)(59 74)(60 75)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(121 146)(122 147)(123 148)(124 149)(125 150)(126 141)(127 142)(128 143)(129 144)(130 145)(131 156)(132 157)(133 158)(134 159)(135 160)(136 151)(137 152)(138 153)(139 154)(140 155)
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), (1,133,13,123)(2,134,14,124)(3,135,15,125)(4,136,16,126)(5,137,17,127)(6,138,18,128)(7,139,19,129)(8,140,20,130)(9,131,11,121)(10,132,12,122)(21,151,31,141)(22,152,32,142)(23,153,33,143)(24,154,34,144)(25,155,35,145)(26,156,36,146)(27,157,37,147)(28,158,38,148)(29,159,39,149)(30,160,40,150)(41,96,51,86)(42,97,52,87)(43,98,53,88)(44,99,54,89)(45,100,55,90)(46,91,56,81)(47,92,57,82)(48,93,58,83)(49,94,59,84)(50,95,60,85)(61,116,71,106)(62,117,72,107)(63,118,73,108)(64,119,74,109)(65,120,75,110)(66,111,76,101)(67,112,77,102)(68,113,78,103)(69,114,79,104)(70,115,80,105), (1,88,6,83)(2,89,7,84)(3,90,8,85)(4,81,9,86)(5,82,10,87)(11,96,16,91)(12,97,17,92)(13,98,18,93)(14,99,19,94)(15,100,20,95)(21,106,26,101)(22,107,27,102)(23,108,28,103)(24,109,29,104)(25,110,30,105)(31,116,36,111)(32,117,37,112)(33,118,38,113)(34,119,39,114)(35,120,40,115)(41,126,46,121)(42,127,47,122)(43,128,48,123)(44,129,49,124)(45,130,50,125)(51,136,56,131)(52,137,57,132)(53,138,58,133)(54,139,59,134)(55,140,60,135)(61,146,66,141)(62,147,67,142)(63,148,68,143)(64,149,69,144)(65,150,70,145)(71,156,76,151)(72,157,77,152)(73,158,78,153)(74,159,79,154)(75,160,80,155), (1,33,13,23)(2,32,14,22)(3,31,15,21)(4,40,16,30)(5,39,17,29)(6,38,18,28)(7,37,19,27)(8,36,20,26)(9,35,11,25)(10,34,12,24)(41,80,51,70)(42,79,52,69)(43,78,53,68)(44,77,54,67)(45,76,55,66)(46,75,56,65)(47,74,57,64)(48,73,58,63)(49,72,59,62)(50,71,60,61)(81,115,91,105)(82,114,92,104)(83,113,93,103)(84,112,94,102)(85,111,95,101)(86,120,96,110)(87,119,97,109)(88,118,98,108)(89,117,99,107)(90,116,100,106)(121,160,131,150)(122,159,132,149)(123,158,133,148)(124,157,134,147)(125,156,135,146)(126,155,136,145)(127,154,137,144)(128,153,138,143)(129,152,139,142)(130,151,140,141), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,21)(10,22)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,66)(42,67)(43,68)(44,69)(45,70)(46,61)(47,62)(48,63)(49,64)(50,65)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,146)(122,147)(123,148)(124,149)(125,150)(126,141)(127,142)(128,143)(129,144)(130,145)(131,156)(132,157)(133,158)(134,159)(135,160)(136,151)(137,152)(138,153)(139,154)(140,155)>;
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), (1,133,13,123)(2,134,14,124)(3,135,15,125)(4,136,16,126)(5,137,17,127)(6,138,18,128)(7,139,19,129)(8,140,20,130)(9,131,11,121)(10,132,12,122)(21,151,31,141)(22,152,32,142)(23,153,33,143)(24,154,34,144)(25,155,35,145)(26,156,36,146)(27,157,37,147)(28,158,38,148)(29,159,39,149)(30,160,40,150)(41,96,51,86)(42,97,52,87)(43,98,53,88)(44,99,54,89)(45,100,55,90)(46,91,56,81)(47,92,57,82)(48,93,58,83)(49,94,59,84)(50,95,60,85)(61,116,71,106)(62,117,72,107)(63,118,73,108)(64,119,74,109)(65,120,75,110)(66,111,76,101)(67,112,77,102)(68,113,78,103)(69,114,79,104)(70,115,80,105), (1,88,6,83)(2,89,7,84)(3,90,8,85)(4,81,9,86)(5,82,10,87)(11,96,16,91)(12,97,17,92)(13,98,18,93)(14,99,19,94)(15,100,20,95)(21,106,26,101)(22,107,27,102)(23,108,28,103)(24,109,29,104)(25,110,30,105)(31,116,36,111)(32,117,37,112)(33,118,38,113)(34,119,39,114)(35,120,40,115)(41,126,46,121)(42,127,47,122)(43,128,48,123)(44,129,49,124)(45,130,50,125)(51,136,56,131)(52,137,57,132)(53,138,58,133)(54,139,59,134)(55,140,60,135)(61,146,66,141)(62,147,67,142)(63,148,68,143)(64,149,69,144)(65,150,70,145)(71,156,76,151)(72,157,77,152)(73,158,78,153)(74,159,79,154)(75,160,80,155), (1,33,13,23)(2,32,14,22)(3,31,15,21)(4,40,16,30)(5,39,17,29)(6,38,18,28)(7,37,19,27)(8,36,20,26)(9,35,11,25)(10,34,12,24)(41,80,51,70)(42,79,52,69)(43,78,53,68)(44,77,54,67)(45,76,55,66)(46,75,56,65)(47,74,57,64)(48,73,58,63)(49,72,59,62)(50,71,60,61)(81,115,91,105)(82,114,92,104)(83,113,93,103)(84,112,94,102)(85,111,95,101)(86,120,96,110)(87,119,97,109)(88,118,98,108)(89,117,99,107)(90,116,100,106)(121,160,131,150)(122,159,132,149)(123,158,133,148)(124,157,134,147)(125,156,135,146)(126,155,136,145)(127,154,137,144)(128,153,138,143)(129,152,139,142)(130,151,140,141), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,21)(10,22)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,66)(42,67)(43,68)(44,69)(45,70)(46,61)(47,62)(48,63)(49,64)(50,65)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,146)(122,147)(123,148)(124,149)(125,150)(126,141)(127,142)(128,143)(129,144)(130,145)(131,156)(132,157)(133,158)(134,159)(135,160)(136,151)(137,152)(138,153)(139,154)(140,155) );
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)], [(1,133,13,123),(2,134,14,124),(3,135,15,125),(4,136,16,126),(5,137,17,127),(6,138,18,128),(7,139,19,129),(8,140,20,130),(9,131,11,121),(10,132,12,122),(21,151,31,141),(22,152,32,142),(23,153,33,143),(24,154,34,144),(25,155,35,145),(26,156,36,146),(27,157,37,147),(28,158,38,148),(29,159,39,149),(30,160,40,150),(41,96,51,86),(42,97,52,87),(43,98,53,88),(44,99,54,89),(45,100,55,90),(46,91,56,81),(47,92,57,82),(48,93,58,83),(49,94,59,84),(50,95,60,85),(61,116,71,106),(62,117,72,107),(63,118,73,108),(64,119,74,109),(65,120,75,110),(66,111,76,101),(67,112,77,102),(68,113,78,103),(69,114,79,104),(70,115,80,105)], [(1,88,6,83),(2,89,7,84),(3,90,8,85),(4,81,9,86),(5,82,10,87),(11,96,16,91),(12,97,17,92),(13,98,18,93),(14,99,19,94),(15,100,20,95),(21,106,26,101),(22,107,27,102),(23,108,28,103),(24,109,29,104),(25,110,30,105),(31,116,36,111),(32,117,37,112),(33,118,38,113),(34,119,39,114),(35,120,40,115),(41,126,46,121),(42,127,47,122),(43,128,48,123),(44,129,49,124),(45,130,50,125),(51,136,56,131),(52,137,57,132),(53,138,58,133),(54,139,59,134),(55,140,60,135),(61,146,66,141),(62,147,67,142),(63,148,68,143),(64,149,69,144),(65,150,70,145),(71,156,76,151),(72,157,77,152),(73,158,78,153),(74,159,79,154),(75,160,80,155)], [(1,33,13,23),(2,32,14,22),(3,31,15,21),(4,40,16,30),(5,39,17,29),(6,38,18,28),(7,37,19,27),(8,36,20,26),(9,35,11,25),(10,34,12,24),(41,80,51,70),(42,79,52,69),(43,78,53,68),(44,77,54,67),(45,76,55,66),(46,75,56,65),(47,74,57,64),(48,73,58,63),(49,72,59,62),(50,71,60,61),(81,115,91,105),(82,114,92,104),(83,113,93,103),(84,112,94,102),(85,111,95,101),(86,120,96,110),(87,119,97,109),(88,118,98,108),(89,117,99,107),(90,116,100,106),(121,160,131,150),(122,159,132,149),(123,158,133,148),(124,157,134,147),(125,156,135,146),(126,155,136,145),(127,154,137,144),(128,153,138,143),(129,152,139,142),(130,151,140,141)], [(1,23),(2,24),(3,25),(4,26),(5,27),(6,28),(7,29),(8,30),(9,21),(10,22),(11,31),(12,32),(13,33),(14,34),(15,35),(16,36),(17,37),(18,38),(19,39),(20,40),(41,66),(42,67),(43,68),(44,69),(45,70),(46,61),(47,62),(48,63),(49,64),(50,65),(51,76),(52,77),(53,78),(54,79),(55,80),(56,71),(57,72),(58,73),(59,74),(60,75),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(99,119),(100,120),(121,146),(122,147),(123,148),(124,149),(125,150),(126,141),(127,142),(128,143),(129,144),(130,145),(131,156),(132,157),(133,158),(134,159),(135,160),(136,151),(137,152),(138,153),(139,154),(140,155)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 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 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 10 | 10 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4⋊6D10 | D5×C4○D4 | D4.10D10 |
| kernel | C10.632+ 1+4 | Dic5.14D4 | C23.D10 | Dic5⋊4D4 | D10.12D4 | Dic5.Q8 | C4.Dic10 | D5×C4⋊C4 | D10⋊Q8 | C20.48D4 | C4×C5⋊D4 | C23.18D10 | C20⋊2D4 | C5×C22.D4 | C22.D4 | D10 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C10 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 6 | 4 | 2 | 2 | 1 | 1 | 4 | 4 | 4 |
Matrix representation of C10.632+ 1+4 ►in GL8(𝔽41)
| 34 | 34 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 34 | 35 |
| 0 | 0 | 0 | 0 | 0 | 0 | 7 | 0 |
| 32 | 0 | 27 | 27 | 0 | 0 | 0 | 0 |
| 0 | 32 | 14 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 9 | 0 | 0 | 0 | 0 | 0 |
| 35 | 35 | 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 38 | 0 | 25 | 0 |
| 0 | 0 | 0 | 0 | 0 | 38 | 0 | 25 |
| 0 | 0 | 0 | 0 | 16 | 0 | 3 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 3 |
| 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 0 | 3 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 | 0 | 3 |
| 0 | 0 | 0 | 0 | 38 | 0 | 25 | 0 |
| 0 | 0 | 0 | 0 | 0 | 38 | 0 | 25 |
| 40 | 0 | 3 | 3 | 0 | 0 | 0 | 0 |
| 7 | 1 | 23 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 38 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 3 | 21 |
| 0 | 0 | 0 | 0 | 0 | 0 | 21 | 38 |
| 40 | 0 | 3 | 3 | 0 | 0 | 0 | 0 |
| 0 | 40 | 38 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 17 | 35 |
| 0 | 0 | 0 | 0 | 0 | 0 | 7 | 24 |
G:=sub<GL(8,GF(41))| [34,7,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,35,6,0,0,0,0,0,0,34,0,0,0,0,0,0,0,0,0,34,7,0,0,0,0,0,0,35,0,0,0,0,0,0,0,0,0,34,7,0,0,0,0,0,0,35,0],[32,0,0,35,0,0,0,0,0,32,6,35,0,0,0,0,27,14,9,0,0,0,0,0,27,0,0,9,0,0,0,0,0,0,0,0,38,0,16,0,0,0,0,0,0,38,0,16,0,0,0,0,25,0,3,0,0,0,0,0,0,25,0,3],[32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,16,0,38,0,0,0,0,0,0,16,0,38,0,0,0,0,3,0,25,0,0,0,0,0,0,3,0,25],[40,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,23,6,36,0,0,0,0,3,20,7,35,0,0,0,0,0,0,0,0,3,21,0,0,0,0,0,0,21,38,0,0,0,0,0,0,0,0,3,21,0,0,0,0,0,0,21,38],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,3,38,1,0,0,0,0,0,3,0,0,1,0,0,0,0,0,0,0,0,17,7,0,0,0,0,0,0,35,24,0,0,0,0,0,0,0,0,17,7,0,0,0,0,0,0,35,24] >;
C10.632+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{63}2_+^{1+4} % in TeX
G:=Group("C10.63ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1332);
// by ID
G=gap.SmallGroup(320,1332);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,219,184,675,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,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=b^2*d>;
// generators/relations