G = C10.672+ 1+4 order 320 = 26·5
67th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.672+ 1+4, C4⋊C4.201D10, (C2×D4).104D10, C20⋊D4.10C2, (C2×C20).75C23, C22⋊C4.31D10, (C22×C4).51D10, Dic5⋊3Q8⋊33C2, Dic5⋊4D4⋊25C2, (C2×C10).208C24, C22.D4⋊13D5, D10.13D4⋊31C2, C2.69(D4⋊6D10), C23.32(C22×D5), Dic5.64(C4○D4), Dic5.5D4⋊35C2, (C2×D20).165C22, (D4×C10).146C22, (C22×C10).40C23, (C22×D5).89C23, C22.229(C23×D5), C23.D5.46C22, C23.18D10⋊16C2, (C22×C20).370C22, C5⋊3(C22.53C24), (C4×Dic5).135C22, (C2×Dic5).258C23, D10⋊C4.133C22, (C2×Dic10).176C22, C10.D4.140C22, (C22×Dic5).134C22, (C4×C5⋊D4)⋊50C2, C2.70(D5×C4○D4), C10.182(C2×C4○D4), (C2×C4×D5).264C22, (C2×C4).70(C22×D5), (C5×C4⋊C4).181C22, (C2×C5⋊D4).52C22, (C5×C22.D4)⋊16C2, (C5×C22⋊C4).56C22, SmallGroup(320,1336)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.672+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=a5b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=b-1, bd=db, ebe=a5b, cd=dc, ce=ec, ede=a5b2d >
Subgroups: 854 in 236 conjugacy classes, 95 normal (27 characteristic)
C1, C2, C2, C2, C4, 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, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C4×D4, C4×Q8, C22.D4, C22.D4, C4.4D4, C4⋊1D4, Dic10, C4×D5, D20, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22.53C24, C4×Dic5, C4×Dic5, C10.D4, D10⋊C4, C23.D5, C23.D5, C5×C22⋊C4, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×D20, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, Dic5⋊4D4, Dic5.5D4, Dic5⋊3Q8, D10.13D4, C4×C5⋊D4, C23.18D10, C20⋊D4, C5×C22.D4, C10.672+ 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, C22×D5, C22.53C24, C23×D5, D4⋊6D10, D5×C4○D4, C10.672+ 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)
(1 138 13 128)(2 139 14 129)(3 140 15 130)(4 131 16 121)(5 132 17 122)(6 133 18 123)(7 134 19 124)(8 135 20 125)(9 136 11 126)(10 137 12 127)(21 156 31 146)(22 157 32 147)(23 158 33 148)(24 159 34 149)(25 160 35 150)(26 151 36 141)(27 152 37 142)(28 153 38 143)(29 154 39 144)(30 155 40 145)(41 91 51 81)(42 92 52 82)(43 93 53 83)(44 94 54 84)(45 95 55 85)(46 96 56 86)(47 97 57 87)(48 98 58 88)(49 99 59 89)(50 100 60 90)(61 111 71 101)(62 112 72 102)(63 113 73 103)(64 114 74 104)(65 115 75 105)(66 116 76 106)(67 117 77 107)(68 118 78 108)(69 119 79 109)(70 120 80 110)
(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 38 18 23)(2 37 19 22)(3 36 20 21)(4 35 11 30)(5 34 12 29)(6 33 13 28)(7 32 14 27)(8 31 15 26)(9 40 16 25)(10 39 17 24)(41 80 56 65)(42 79 57 64)(43 78 58 63)(44 77 59 62)(45 76 60 61)(46 75 51 70)(47 74 52 69)(48 73 53 68)(49 72 54 67)(50 71 55 66)(81 120 96 105)(82 119 97 104)(83 118 98 103)(84 117 99 102)(85 116 100 101)(86 115 91 110)(87 114 92 109)(88 113 93 108)(89 112 94 107)(90 111 95 106)(121 160 136 145)(122 159 137 144)(123 158 138 143)(124 157 139 142)(125 156 140 141)(126 155 131 150)(127 154 132 149)(128 153 133 148)(129 152 134 147)(130 151 135 146)
(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), (1,138,13,128)(2,139,14,129)(3,140,15,130)(4,131,16,121)(5,132,17,122)(6,133,18,123)(7,134,19,124)(8,135,20,125)(9,136,11,126)(10,137,12,127)(21,156,31,146)(22,157,32,147)(23,158,33,148)(24,159,34,149)(25,160,35,150)(26,151,36,141)(27,152,37,142)(28,153,38,143)(29,154,39,144)(30,155,40,145)(41,91,51,81)(42,92,52,82)(43,93,53,83)(44,94,54,84)(45,95,55,85)(46,96,56,86)(47,97,57,87)(48,98,58,88)(49,99,59,89)(50,100,60,90)(61,111,71,101)(62,112,72,102)(63,113,73,103)(64,114,74,104)(65,115,75,105)(66,116,76,106)(67,117,77,107)(68,118,78,108)(69,119,79,109)(70,120,80,110), (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), (1,38,18,23)(2,37,19,22)(3,36,20,21)(4,35,11,30)(5,34,12,29)(6,33,13,28)(7,32,14,27)(8,31,15,26)(9,40,16,25)(10,39,17,24)(41,80,56,65)(42,79,57,64)(43,78,58,63)(44,77,59,62)(45,76,60,61)(46,75,51,70)(47,74,52,69)(48,73,53,68)(49,72,54,67)(50,71,55,66)(81,120,96,105)(82,119,97,104)(83,118,98,103)(84,117,99,102)(85,116,100,101)(86,115,91,110)(87,114,92,109)(88,113,93,108)(89,112,94,107)(90,111,95,106)(121,160,136,145)(122,159,137,144)(123,158,138,143)(124,157,139,142)(125,156,140,141)(126,155,131,150)(127,154,132,149)(128,153,133,148)(129,152,134,147)(130,151,135,146), (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), (1,138,13,128)(2,139,14,129)(3,140,15,130)(4,131,16,121)(5,132,17,122)(6,133,18,123)(7,134,19,124)(8,135,20,125)(9,136,11,126)(10,137,12,127)(21,156,31,146)(22,157,32,147)(23,158,33,148)(24,159,34,149)(25,160,35,150)(26,151,36,141)(27,152,37,142)(28,153,38,143)(29,154,39,144)(30,155,40,145)(41,91,51,81)(42,92,52,82)(43,93,53,83)(44,94,54,84)(45,95,55,85)(46,96,56,86)(47,97,57,87)(48,98,58,88)(49,99,59,89)(50,100,60,90)(61,111,71,101)(62,112,72,102)(63,113,73,103)(64,114,74,104)(65,115,75,105)(66,116,76,106)(67,117,77,107)(68,118,78,108)(69,119,79,109)(70,120,80,110), (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), (1,38,18,23)(2,37,19,22)(3,36,20,21)(4,35,11,30)(5,34,12,29)(6,33,13,28)(7,32,14,27)(8,31,15,26)(9,40,16,25)(10,39,17,24)(41,80,56,65)(42,79,57,64)(43,78,58,63)(44,77,59,62)(45,76,60,61)(46,75,51,70)(47,74,52,69)(48,73,53,68)(49,72,54,67)(50,71,55,66)(81,120,96,105)(82,119,97,104)(83,118,98,103)(84,117,99,102)(85,116,100,101)(86,115,91,110)(87,114,92,109)(88,113,93,108)(89,112,94,107)(90,111,95,106)(121,160,136,145)(122,159,137,144)(123,158,138,143)(124,157,139,142)(125,156,140,141)(126,155,131,150)(127,154,132,149)(128,153,133,148)(129,152,134,147)(130,151,135,146), (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)], [(1,138,13,128),(2,139,14,129),(3,140,15,130),(4,131,16,121),(5,132,17,122),(6,133,18,123),(7,134,19,124),(8,135,20,125),(9,136,11,126),(10,137,12,127),(21,156,31,146),(22,157,32,147),(23,158,33,148),(24,159,34,149),(25,160,35,150),(26,151,36,141),(27,152,37,142),(28,153,38,143),(29,154,39,144),(30,155,40,145),(41,91,51,81),(42,92,52,82),(43,93,53,83),(44,94,54,84),(45,95,55,85),(46,96,56,86),(47,97,57,87),(48,98,58,88),(49,99,59,89),(50,100,60,90),(61,111,71,101),(62,112,72,102),(63,113,73,103),(64,114,74,104),(65,115,75,105),(66,116,76,106),(67,117,77,107),(68,118,78,108),(69,119,79,109),(70,120,80,110)], [(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)], [(1,38,18,23),(2,37,19,22),(3,36,20,21),(4,35,11,30),(5,34,12,29),(6,33,13,28),(7,32,14,27),(8,31,15,26),(9,40,16,25),(10,39,17,24),(41,80,56,65),(42,79,57,64),(43,78,58,63),(44,77,59,62),(45,76,60,61),(46,75,51,70),(47,74,52,69),(48,73,53,68),(49,72,54,67),(50,71,55,66),(81,120,96,105),(82,119,97,104),(83,118,98,103),(84,117,99,102),(85,116,100,101),(86,115,91,110),(87,114,92,109),(88,113,93,108),(89,112,94,107),(90,111,95,106),(121,160,136,145),(122,159,137,144),(123,158,138,143),(124,157,139,142),(125,156,140,141),(126,155,131,150),(127,154,132,149),(128,153,133,148),(129,152,134,147),(130,151,135,146)], [(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)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4O | 4P | 4Q | 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 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
53 irreducible representations
| dim | 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 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | D4⋊6D10 | D5×C4○D4 |
| kernel | C10.672+ 1+4 | Dic5⋊4D4 | Dic5.5D4 | Dic5⋊3Q8 | D10.13D4 | C4×C5⋊D4 | C23.18D10 | C20⋊D4 | C5×C22.D4 | C22.D4 | Dic5 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C2 | C2 |
| # reps | 1 | 2 | 4 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 8 | 6 | 4 | 2 | 2 | 1 | 4 | 8 |
Matrix representation of C10.672+ 1+4 ►in GL6(𝔽41)
| 0 | 35 | 0 | 0 | 0 | 0 |
| 7 | 34 | 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 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 23 | 0 | 0 |
| 0 | 0 | 9 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 18 |
| 0 | 0 | 0 | 0 | 0 | 32 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 0 | 9 | 9 |
| 34 | 1 | 0 | 0 | 0 | 0 |
| 34 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 2 | 0 | 0 |
| 0 | 0 | 40 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 39 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 40 | 40 |
G:=sub<GL(6,GF(41))| [0,7,0,0,0,0,35,34,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,32,9,0,0,0,0,23,9,0,0,0,0,0,0,9,0,0,0,0,0,18,32],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,32,9,0,0,0,0,0,9],[34,34,0,0,0,0,1,7,0,0,0,0,0,0,1,40,0,0,0,0,2,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,39,1,0,0,0,0,0,0,1,40,0,0,0,0,0,40] >;
C10.672+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{67}2_+^{1+4} % in TeX
G:=Group("C10.67ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1336);
// by ID
G=gap.SmallGroup(320,1336);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,184,1571,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=a^5*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,b*d=d*b,e*b*e=a^5*b,c*d=d*c,c*e=e*c,e*d*e=a^5*b^2*d>;
// generators/relations