direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C11×C22.D4, C4⋊C4⋊4C22, C2.7(D4×C22), C22⋊C4⋊4C22, (C22×C4)⋊3C22, (C22×C44)⋊5C2, (C2×D4).4C22, C22.70(C2×D4), (C2×C22).23D4, (D4×C22).11C2, C22.4(D4×C11), C22.43(C4○D4), (C2×C44).65C22, C23.10(C2×C22), (C2×C22).78C23, (C22×C22).29C22, C22.13(C22×C22), (C11×C4⋊C4)⋊13C2, (C2×C4).5(C2×C22), C2.6(C11×C4○D4), (C11×C22⋊C4)⋊12C2, SmallGroup(352,158)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C11×C22.D4
G = < a,b,c,d,e | a11=b2=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=ebe=bc=cb, cd=dc, ce=ec, ede=cd-1 >
Subgroups: 116 in 78 conjugacy classes, 44 normal (20 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, C2×C4, D4, C23, C11, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C22, C22, C22, C22.D4, C44, C2×C22, C2×C22, C2×C22, C2×C44, C2×C44, C2×C44, D4×C11, C22×C22, C11×C22⋊C4, C11×C22⋊C4, C11×C4⋊C4, C22×C44, D4×C22, C11×C22.D4
Quotients: C1, C2, C22, D4, C23, C11, C2×D4, C4○D4, C22, C22.D4, C2×C22, D4×C11, C22×C22, D4×C22, C11×C4○D4, C11×C22.D4
►On 176 points
Generators in S176
(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)(155 156 157 158 159 160 161 162 163 164 165)(166 167 168 169 170 171 172 173 174 175 176)
(1 134)(2 135)(3 136)(4 137)(5 138)(6 139)(7 140)(8 141)(9 142)(10 143)(11 133)(12 102)(13 103)(14 104)(15 105)(16 106)(17 107)(18 108)(19 109)(20 110)(21 100)(22 101)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 89)(30 90)(31 91)(32 92)(33 93)(34 84)(35 85)(36 86)(37 87)(38 88)(39 78)(40 79)(41 80)(42 81)(43 82)(44 83)(45 163)(46 164)(47 165)(48 155)(49 156)(50 157)(51 158)(52 159)(53 160)(54 161)(55 162)(56 154)(57 144)(58 145)(59 146)(60 147)(61 148)(62 149)(63 150)(64 151)(65 152)(66 153)(67 126)(68 127)(69 128)(70 129)(71 130)(72 131)(73 132)(74 122)(75 123)(76 124)(77 125)(111 170)(112 171)(113 172)(114 173)(115 174)(116 175)(117 176)(118 166)(119 167)(120 168)(121 169)
(1 45)(2 46)(3 47)(4 48)(5 49)(6 50)(7 51)(8 52)(9 53)(10 54)(11 55)(12 37)(13 38)(14 39)(15 40)(16 41)(17 42)(18 43)(19 44)(20 34)(21 35)(22 36)(23 171)(24 172)(25 173)(26 174)(27 175)(28 176)(29 166)(30 167)(31 168)(32 169)(33 170)(56 69)(57 70)(58 71)(59 72)(60 73)(61 74)(62 75)(63 76)(64 77)(65 67)(66 68)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)(85 100)(86 101)(87 102)(88 103)(89 118)(90 119)(91 120)(92 121)(93 111)(94 112)(95 113)(96 114)(97 115)(98 116)(99 117)(122 148)(123 149)(124 150)(125 151)(126 152)(127 153)(128 154)(129 144)(130 145)(131 146)(132 147)(133 162)(134 163)(135 164)(136 165)(137 155)(138 156)(139 157)(140 158)(141 159)(142 160)(143 161)
(1 79 75 90)(2 80 76 91)(3 81 77 92)(4 82 67 93)(5 83 68 94)(6 84 69 95)(7 85 70 96)(8 86 71 97)(9 87 72 98)(10 88 73 99)(11 78 74 89)(12 131 175 142)(13 132 176 143)(14 122 166 133)(15 123 167 134)(16 124 168 135)(17 125 169 136)(18 126 170 137)(19 127 171 138)(20 128 172 139)(21 129 173 140)(22 130 174 141)(23 156 44 153)(24 157 34 154)(25 158 35 144)(26 159 36 145)(27 160 37 146)(28 161 38 147)(29 162 39 148)(30 163 40 149)(31 164 41 150)(32 165 42 151)(33 155 43 152)(45 105 62 119)(46 106 63 120)(47 107 64 121)(48 108 65 111)(49 109 66 112)(50 110 56 113)(51 100 57 114)(52 101 58 115)(53 102 59 116)(54 103 60 117)(55 104 61 118)
(12 175)(13 176)(14 166)(15 167)(16 168)(17 169)(18 170)(19 171)(20 172)(21 173)(22 174)(23 44)(24 34)(25 35)(26 36)(27 37)(28 38)(29 39)(30 40)(31 41)(32 42)(33 43)(78 118)(79 119)(80 120)(81 121)(82 111)(83 112)(84 113)(85 114)(86 115)(87 116)(88 117)(89 104)(90 105)(91 106)(92 107)(93 108)(94 109)(95 110)(96 100)(97 101)(98 102)(99 103)(122 148)(123 149)(124 150)(125 151)(126 152)(127 153)(128 154)(129 144)(130 145)(131 146)(132 147)(133 162)(134 163)(135 164)(136 165)(137 155)(138 156)(139 157)(140 158)(141 159)(142 160)(143 161)
G:=sub<Sym(176)| (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)(155,156,157,158,159,160,161,162,163,164,165)(166,167,168,169,170,171,172,173,174,175,176), (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,141)(9,142)(10,143)(11,133)(12,102)(13,103)(14,104)(15,105)(16,106)(17,107)(18,108)(19,109)(20,110)(21,100)(22,101)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,89)(30,90)(31,91)(32,92)(33,93)(34,84)(35,85)(36,86)(37,87)(38,88)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,163)(46,164)(47,165)(48,155)(49,156)(50,157)(51,158)(52,159)(53,160)(54,161)(55,162)(56,154)(57,144)(58,145)(59,146)(60,147)(61,148)(62,149)(63,150)(64,151)(65,152)(66,153)(67,126)(68,127)(69,128)(70,129)(71,130)(72,131)(73,132)(74,122)(75,123)(76,124)(77,125)(111,170)(112,171)(113,172)(114,173)(115,174)(116,175)(117,176)(118,166)(119,167)(120,168)(121,169), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,51)(8,52)(9,53)(10,54)(11,55)(12,37)(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,34)(21,35)(22,36)(23,171)(24,172)(25,173)(26,174)(27,175)(28,176)(29,166)(30,167)(31,168)(32,169)(33,170)(56,69)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,67)(66,68)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(85,100)(86,101)(87,102)(88,103)(89,118)(90,119)(91,120)(92,121)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,144)(130,145)(131,146)(132,147)(133,162)(134,163)(135,164)(136,165)(137,155)(138,156)(139,157)(140,158)(141,159)(142,160)(143,161), (1,79,75,90)(2,80,76,91)(3,81,77,92)(4,82,67,93)(5,83,68,94)(6,84,69,95)(7,85,70,96)(8,86,71,97)(9,87,72,98)(10,88,73,99)(11,78,74,89)(12,131,175,142)(13,132,176,143)(14,122,166,133)(15,123,167,134)(16,124,168,135)(17,125,169,136)(18,126,170,137)(19,127,171,138)(20,128,172,139)(21,129,173,140)(22,130,174,141)(23,156,44,153)(24,157,34,154)(25,158,35,144)(26,159,36,145)(27,160,37,146)(28,161,38,147)(29,162,39,148)(30,163,40,149)(31,164,41,150)(32,165,42,151)(33,155,43,152)(45,105,62,119)(46,106,63,120)(47,107,64,121)(48,108,65,111)(49,109,66,112)(50,110,56,113)(51,100,57,114)(52,101,58,115)(53,102,59,116)(54,103,60,117)(55,104,61,118), (12,175)(13,176)(14,166)(15,167)(16,168)(17,169)(18,170)(19,171)(20,172)(21,173)(22,174)(23,44)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(33,43)(78,118)(79,119)(80,120)(81,121)(82,111)(83,112)(84,113)(85,114)(86,115)(87,116)(88,117)(89,104)(90,105)(91,106)(92,107)(93,108)(94,109)(95,110)(96,100)(97,101)(98,102)(99,103)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,144)(130,145)(131,146)(132,147)(133,162)(134,163)(135,164)(136,165)(137,155)(138,156)(139,157)(140,158)(141,159)(142,160)(143,161)>;
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)(155,156,157,158,159,160,161,162,163,164,165)(166,167,168,169,170,171,172,173,174,175,176), (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,141)(9,142)(10,143)(11,133)(12,102)(13,103)(14,104)(15,105)(16,106)(17,107)(18,108)(19,109)(20,110)(21,100)(22,101)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,89)(30,90)(31,91)(32,92)(33,93)(34,84)(35,85)(36,86)(37,87)(38,88)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,163)(46,164)(47,165)(48,155)(49,156)(50,157)(51,158)(52,159)(53,160)(54,161)(55,162)(56,154)(57,144)(58,145)(59,146)(60,147)(61,148)(62,149)(63,150)(64,151)(65,152)(66,153)(67,126)(68,127)(69,128)(70,129)(71,130)(72,131)(73,132)(74,122)(75,123)(76,124)(77,125)(111,170)(112,171)(113,172)(114,173)(115,174)(116,175)(117,176)(118,166)(119,167)(120,168)(121,169), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,51)(8,52)(9,53)(10,54)(11,55)(12,37)(13,38)(14,39)(15,40)(16,41)(17,42)(18,43)(19,44)(20,34)(21,35)(22,36)(23,171)(24,172)(25,173)(26,174)(27,175)(28,176)(29,166)(30,167)(31,168)(32,169)(33,170)(56,69)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,67)(66,68)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(85,100)(86,101)(87,102)(88,103)(89,118)(90,119)(91,120)(92,121)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,144)(130,145)(131,146)(132,147)(133,162)(134,163)(135,164)(136,165)(137,155)(138,156)(139,157)(140,158)(141,159)(142,160)(143,161), (1,79,75,90)(2,80,76,91)(3,81,77,92)(4,82,67,93)(5,83,68,94)(6,84,69,95)(7,85,70,96)(8,86,71,97)(9,87,72,98)(10,88,73,99)(11,78,74,89)(12,131,175,142)(13,132,176,143)(14,122,166,133)(15,123,167,134)(16,124,168,135)(17,125,169,136)(18,126,170,137)(19,127,171,138)(20,128,172,139)(21,129,173,140)(22,130,174,141)(23,156,44,153)(24,157,34,154)(25,158,35,144)(26,159,36,145)(27,160,37,146)(28,161,38,147)(29,162,39,148)(30,163,40,149)(31,164,41,150)(32,165,42,151)(33,155,43,152)(45,105,62,119)(46,106,63,120)(47,107,64,121)(48,108,65,111)(49,109,66,112)(50,110,56,113)(51,100,57,114)(52,101,58,115)(53,102,59,116)(54,103,60,117)(55,104,61,118), (12,175)(13,176)(14,166)(15,167)(16,168)(17,169)(18,170)(19,171)(20,172)(21,173)(22,174)(23,44)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(33,43)(78,118)(79,119)(80,120)(81,121)(82,111)(83,112)(84,113)(85,114)(86,115)(87,116)(88,117)(89,104)(90,105)(91,106)(92,107)(93,108)(94,109)(95,110)(96,100)(97,101)(98,102)(99,103)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,144)(130,145)(131,146)(132,147)(133,162)(134,163)(135,164)(136,165)(137,155)(138,156)(139,157)(140,158)(141,159)(142,160)(143,161) );
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),(155,156,157,158,159,160,161,162,163,164,165),(166,167,168,169,170,171,172,173,174,175,176)], [(1,134),(2,135),(3,136),(4,137),(5,138),(6,139),(7,140),(8,141),(9,142),(10,143),(11,133),(12,102),(13,103),(14,104),(15,105),(16,106),(17,107),(18,108),(19,109),(20,110),(21,100),(22,101),(23,94),(24,95),(25,96),(26,97),(27,98),(28,99),(29,89),(30,90),(31,91),(32,92),(33,93),(34,84),(35,85),(36,86),(37,87),(38,88),(39,78),(40,79),(41,80),(42,81),(43,82),(44,83),(45,163),(46,164),(47,165),(48,155),(49,156),(50,157),(51,158),(52,159),(53,160),(54,161),(55,162),(56,154),(57,144),(58,145),(59,146),(60,147),(61,148),(62,149),(63,150),(64,151),(65,152),(66,153),(67,126),(68,127),(69,128),(70,129),(71,130),(72,131),(73,132),(74,122),(75,123),(76,124),(77,125),(111,170),(112,171),(113,172),(114,173),(115,174),(116,175),(117,176),(118,166),(119,167),(120,168),(121,169)], [(1,45),(2,46),(3,47),(4,48),(5,49),(6,50),(7,51),(8,52),(9,53),(10,54),(11,55),(12,37),(13,38),(14,39),(15,40),(16,41),(17,42),(18,43),(19,44),(20,34),(21,35),(22,36),(23,171),(24,172),(25,173),(26,174),(27,175),(28,176),(29,166),(30,167),(31,168),(32,169),(33,170),(56,69),(57,70),(58,71),(59,72),(60,73),(61,74),(62,75),(63,76),(64,77),(65,67),(66,68),(78,104),(79,105),(80,106),(81,107),(82,108),(83,109),(84,110),(85,100),(86,101),(87,102),(88,103),(89,118),(90,119),(91,120),(92,121),(93,111),(94,112),(95,113),(96,114),(97,115),(98,116),(99,117),(122,148),(123,149),(124,150),(125,151),(126,152),(127,153),(128,154),(129,144),(130,145),(131,146),(132,147),(133,162),(134,163),(135,164),(136,165),(137,155),(138,156),(139,157),(140,158),(141,159),(142,160),(143,161)], [(1,79,75,90),(2,80,76,91),(3,81,77,92),(4,82,67,93),(5,83,68,94),(6,84,69,95),(7,85,70,96),(8,86,71,97),(9,87,72,98),(10,88,73,99),(11,78,74,89),(12,131,175,142),(13,132,176,143),(14,122,166,133),(15,123,167,134),(16,124,168,135),(17,125,169,136),(18,126,170,137),(19,127,171,138),(20,128,172,139),(21,129,173,140),(22,130,174,141),(23,156,44,153),(24,157,34,154),(25,158,35,144),(26,159,36,145),(27,160,37,146),(28,161,38,147),(29,162,39,148),(30,163,40,149),(31,164,41,150),(32,165,42,151),(33,155,43,152),(45,105,62,119),(46,106,63,120),(47,107,64,121),(48,108,65,111),(49,109,66,112),(50,110,56,113),(51,100,57,114),(52,101,58,115),(53,102,59,116),(54,103,60,117),(55,104,61,118)], [(12,175),(13,176),(14,166),(15,167),(16,168),(17,169),(18,170),(19,171),(20,172),(21,173),(22,174),(23,44),(24,34),(25,35),(26,36),(27,37),(28,38),(29,39),(30,40),(31,41),(32,42),(33,43),(78,118),(79,119),(80,120),(81,121),(82,111),(83,112),(84,113),(85,114),(86,115),(87,116),(88,117),(89,104),(90,105),(91,106),(92,107),(93,108),(94,109),(95,110),(96,100),(97,101),(98,102),(99,103),(122,148),(123,149),(124,150),(125,151),(126,152),(127,153),(128,154),(129,144),(130,145),(131,146),(132,147),(133,162),(134,163),(135,164),(136,165),(137,155),(138,156),(139,157),(140,158),(141,159),(142,160),(143,161)]])
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 11A | ··· | 11J | 22A | ··· | 22AD | 22AE | ··· | 22AX | 22AY | ··· | 22BH | 44A | ··· | 44AN | 44AO | ··· | 44BR |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 22 | ··· | 22 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C11 | C22 | C22 | C22 | C22 | D4 | C4○D4 | D4×C11 | C11×C4○D4 |
| kernel | C11×C22.D4 | C11×C22⋊C4 | C11×C4⋊C4 | C22×C44 | D4×C22 | C22.D4 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C2×C22 | C22 | C22 | C2 |
| # reps | 1 | 3 | 2 | 1 | 1 | 10 | 30 | 20 | 10 | 10 | 2 | 4 | 20 | 40 |
Matrix representation of C11×C22.D4 ►in GL4(𝔽89) generated by
| 4 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 |
| 0 | 0 | 67 | 0 |
| 0 | 0 | 0 | 67 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 24 | 2 |
| 0 | 0 | 24 | 65 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 0 | 88 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 55 | 0 |
| 0 | 0 | 15 | 34 |
| 1 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 65 | 88 |
G:=sub<GL(4,GF(89))| [4,0,0,0,0,4,0,0,0,0,67,0,0,0,0,67],[1,0,0,0,0,1,0,0,0,0,24,24,0,0,2,65],[1,0,0,0,0,1,0,0,0,0,88,0,0,0,0,88],[0,1,0,0,88,0,0,0,0,0,55,15,0,0,0,34],[1,0,0,0,0,88,0,0,0,0,1,65,0,0,0,88] >;
C11×C22.D4 in GAP, Magma, Sage, TeX
C_{11}\times C_2^2.D_4 % in TeX
G:=Group("C11xC2^2.D4"); // GroupNames label
G:=SmallGroup(352,158);
// by ID
G=gap.SmallGroup(352,158);
# by ID
G:=PCGroup([6,-2,-2,-2,-11,-2,-2,1081,3242,410]);
// Polycyclic
G:=Group<a,b,c,d,e|a^11=b^2=c^2=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=e*b*e=b*c=c*b,c*d=d*c,c*e=e*c,e*d*e=c*d^-1>;
// generators/relations