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## G = C3⋊S3×C2×C10order 360 = 23·32·5

### Direct product of C2×C10 and C3⋊S3

Aliases: C3⋊S3×C2×C10, C308D6, C625C10, C62(S3×C10), (C6×C30)⋊11C2, (C2×C30)⋊11S3, C159(C22×S3), (C3×C15)⋊11C23, (C3×C30)⋊10C22, C323(C22×C10), C32(S3×C2×C10), (C2×C6)⋊5(C5×S3), (C3×C6)⋊3(C2×C10), SmallGroup(360,160)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32 — C3⋊S3×C2×C10
 Chief series C1 — C3 — C32 — C3×C15 — C5×C3⋊S3 — C10×C3⋊S3 — C3⋊S3×C2×C10
 Lower central C32 — C3⋊S3×C2×C10
 Upper central C1 — C2×C10

Generators and relations for C3⋊S3×C2×C10
G = < a,b,c,d,e | a2=b10=c3=d3=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece=c-1, ede=d-1 >

Subgroups: 544 in 192 conjugacy classes, 82 normal (10 characteristic)
C1, C2, C2, C3, C22, C22, C5, S3, C6, C23, C32, C10, C10, D6, C2×C6, C15, C3⋊S3, C3×C6, C2×C10, C2×C10, C22×S3, C5×S3, C30, C2×C3⋊S3, C62, C22×C10, C3×C15, S3×C10, C2×C30, C22×C3⋊S3, C5×C3⋊S3, C3×C30, S3×C2×C10, C10×C3⋊S3, C6×C30, C3⋊S3×C2×C10
Quotients: C1, C2, C22, C5, S3, C23, C10, D6, C3⋊S3, C2×C10, C22×S3, C5×S3, C2×C3⋊S3, C22×C10, S3×C10, C22×C3⋊S3, C5×C3⋊S3, S3×C2×C10, C10×C3⋊S3, C3⋊S3×C2×C10

Smallest permutation representation of C3⋊S3×C2×C10
On 180 points
Generators in S180
(1 177)(2 178)(3 179)(4 180)(5 171)(6 172)(7 173)(8 174)(9 175)(10 176)(11 132)(12 133)(13 134)(14 135)(15 136)(16 137)(17 138)(18 139)(19 140)(20 131)(21 151)(22 152)(23 153)(24 154)(25 155)(26 156)(27 157)(28 158)(29 159)(30 160)(31 161)(32 162)(33 163)(34 164)(35 165)(36 166)(37 167)(38 168)(39 169)(40 170)(41 126)(42 127)(43 128)(44 129)(45 130)(46 121)(47 122)(48 123)(49 124)(50 125)(51 100)(52 91)(53 92)(54 93)(55 94)(56 95)(57 96)(58 97)(59 98)(60 99)(61 110)(62 101)(63 102)(64 103)(65 104)(66 105)(67 106)(68 107)(69 108)(70 109)(71 147)(72 148)(73 149)(74 150)(75 141)(76 142)(77 143)(78 144)(79 145)(80 146)(81 111)(82 112)(83 113)(84 114)(85 115)(86 116)(87 117)(88 118)(89 119)(90 120)
(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)(171 172 173 174 175 176 177 178 179 180)
(1 113 148)(2 114 149)(3 115 150)(4 116 141)(5 117 142)(6 118 143)(7 119 144)(8 120 145)(9 111 146)(10 112 147)(11 41 22)(12 42 23)(13 43 24)(14 44 25)(15 45 26)(16 46 27)(17 47 28)(18 48 29)(19 49 30)(20 50 21)(31 62 51)(32 63 52)(33 64 53)(34 65 54)(35 66 55)(36 67 56)(37 68 57)(38 69 58)(39 70 59)(40 61 60)(71 176 82)(72 177 83)(73 178 84)(74 179 85)(75 180 86)(76 171 87)(77 172 88)(78 173 89)(79 174 90)(80 175 81)(91 162 102)(92 163 103)(93 164 104)(94 165 105)(95 166 106)(96 167 107)(97 168 108)(98 169 109)(99 170 110)(100 161 101)(121 157 137)(122 158 138)(123 159 139)(124 160 140)(125 151 131)(126 152 132)(127 153 133)(128 154 134)(129 155 135)(130 156 136)
(1 124 161)(2 125 162)(3 126 163)(4 127 164)(5 128 165)(6 129 166)(7 130 167)(8 121 168)(9 122 169)(10 123 170)(11 53 74)(12 54 75)(13 55 76)(14 56 77)(15 57 78)(16 58 79)(17 59 80)(18 60 71)(19 51 72)(20 52 73)(21 63 84)(22 64 85)(23 65 86)(24 66 87)(25 67 88)(26 68 89)(27 69 90)(28 70 81)(29 61 82)(30 62 83)(31 177 49)(32 178 50)(33 179 41)(34 180 42)(35 171 43)(36 172 44)(37 173 45)(38 174 46)(39 175 47)(40 176 48)(91 149 131)(92 150 132)(93 141 133)(94 142 134)(95 143 135)(96 144 136)(97 145 137)(98 146 138)(99 147 139)(100 148 140)(101 113 160)(102 114 151)(103 115 152)(104 116 153)(105 117 154)(106 118 155)(107 119 156)(108 120 157)(109 111 158)(110 112 159)
(11 64)(12 65)(13 66)(14 67)(15 68)(16 69)(17 70)(18 61)(19 62)(20 63)(21 52)(22 53)(23 54)(24 55)(25 56)(26 57)(27 58)(28 59)(29 60)(30 51)(31 49)(32 50)(33 41)(34 42)(35 43)(36 44)(37 45)(38 46)(39 47)(40 48)(71 82)(72 83)(73 84)(74 85)(75 86)(76 87)(77 88)(78 89)(79 90)(80 81)(91 151)(92 152)(93 153)(94 154)(95 155)(96 156)(97 157)(98 158)(99 159)(100 160)(101 140)(102 131)(103 132)(104 133)(105 134)(106 135)(107 136)(108 137)(109 138)(110 139)(111 146)(112 147)(113 148)(114 149)(115 150)(116 141)(117 142)(118 143)(119 144)(120 145)(121 168)(122 169)(123 170)(124 161)(125 162)(126 163)(127 164)(128 165)(129 166)(130 167)

G:=sub<Sym(180)| (1,177)(2,178)(3,179)(4,180)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,132)(12,133)(13,134)(14,135)(15,136)(16,137)(17,138)(18,139)(19,140)(20,131)(21,151)(22,152)(23,153)(24,154)(25,155)(26,156)(27,157)(28,158)(29,159)(30,160)(31,161)(32,162)(33,163)(34,164)(35,165)(36,166)(37,167)(38,168)(39,169)(40,170)(41,126)(42,127)(43,128)(44,129)(45,130)(46,121)(47,122)(48,123)(49,124)(50,125)(51,100)(52,91)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,110)(62,101)(63,102)(64,103)(65,104)(66,105)(67,106)(68,107)(69,108)(70,109)(71,147)(72,148)(73,149)(74,150)(75,141)(76,142)(77,143)(78,144)(79,145)(80,146)(81,111)(82,112)(83,113)(84,114)(85,115)(86,116)(87,117)(88,118)(89,119)(90,120), (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)(171,172,173,174,175,176,177,178,179,180), (1,113,148)(2,114,149)(3,115,150)(4,116,141)(5,117,142)(6,118,143)(7,119,144)(8,120,145)(9,111,146)(10,112,147)(11,41,22)(12,42,23)(13,43,24)(14,44,25)(15,45,26)(16,46,27)(17,47,28)(18,48,29)(19,49,30)(20,50,21)(31,62,51)(32,63,52)(33,64,53)(34,65,54)(35,66,55)(36,67,56)(37,68,57)(38,69,58)(39,70,59)(40,61,60)(71,176,82)(72,177,83)(73,178,84)(74,179,85)(75,180,86)(76,171,87)(77,172,88)(78,173,89)(79,174,90)(80,175,81)(91,162,102)(92,163,103)(93,164,104)(94,165,105)(95,166,106)(96,167,107)(97,168,108)(98,169,109)(99,170,110)(100,161,101)(121,157,137)(122,158,138)(123,159,139)(124,160,140)(125,151,131)(126,152,132)(127,153,133)(128,154,134)(129,155,135)(130,156,136), (1,124,161)(2,125,162)(3,126,163)(4,127,164)(5,128,165)(6,129,166)(7,130,167)(8,121,168)(9,122,169)(10,123,170)(11,53,74)(12,54,75)(13,55,76)(14,56,77)(15,57,78)(16,58,79)(17,59,80)(18,60,71)(19,51,72)(20,52,73)(21,63,84)(22,64,85)(23,65,86)(24,66,87)(25,67,88)(26,68,89)(27,69,90)(28,70,81)(29,61,82)(30,62,83)(31,177,49)(32,178,50)(33,179,41)(34,180,42)(35,171,43)(36,172,44)(37,173,45)(38,174,46)(39,175,47)(40,176,48)(91,149,131)(92,150,132)(93,141,133)(94,142,134)(95,143,135)(96,144,136)(97,145,137)(98,146,138)(99,147,139)(100,148,140)(101,113,160)(102,114,151)(103,115,152)(104,116,153)(105,117,154)(106,118,155)(107,119,156)(108,120,157)(109,111,158)(110,112,159), (11,64)(12,65)(13,66)(14,67)(15,68)(16,69)(17,70)(18,61)(19,62)(20,63)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,51)(31,49)(32,50)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)(80,81)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,140)(102,131)(103,132)(104,133)(105,134)(106,135)(107,136)(108,137)(109,138)(110,139)(111,146)(112,147)(113,148)(114,149)(115,150)(116,141)(117,142)(118,143)(119,144)(120,145)(121,168)(122,169)(123,170)(124,161)(125,162)(126,163)(127,164)(128,165)(129,166)(130,167)>;

G:=Group( (1,177)(2,178)(3,179)(4,180)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,132)(12,133)(13,134)(14,135)(15,136)(16,137)(17,138)(18,139)(19,140)(20,131)(21,151)(22,152)(23,153)(24,154)(25,155)(26,156)(27,157)(28,158)(29,159)(30,160)(31,161)(32,162)(33,163)(34,164)(35,165)(36,166)(37,167)(38,168)(39,169)(40,170)(41,126)(42,127)(43,128)(44,129)(45,130)(46,121)(47,122)(48,123)(49,124)(50,125)(51,100)(52,91)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,110)(62,101)(63,102)(64,103)(65,104)(66,105)(67,106)(68,107)(69,108)(70,109)(71,147)(72,148)(73,149)(74,150)(75,141)(76,142)(77,143)(78,144)(79,145)(80,146)(81,111)(82,112)(83,113)(84,114)(85,115)(86,116)(87,117)(88,118)(89,119)(90,120), (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)(171,172,173,174,175,176,177,178,179,180), (1,113,148)(2,114,149)(3,115,150)(4,116,141)(5,117,142)(6,118,143)(7,119,144)(8,120,145)(9,111,146)(10,112,147)(11,41,22)(12,42,23)(13,43,24)(14,44,25)(15,45,26)(16,46,27)(17,47,28)(18,48,29)(19,49,30)(20,50,21)(31,62,51)(32,63,52)(33,64,53)(34,65,54)(35,66,55)(36,67,56)(37,68,57)(38,69,58)(39,70,59)(40,61,60)(71,176,82)(72,177,83)(73,178,84)(74,179,85)(75,180,86)(76,171,87)(77,172,88)(78,173,89)(79,174,90)(80,175,81)(91,162,102)(92,163,103)(93,164,104)(94,165,105)(95,166,106)(96,167,107)(97,168,108)(98,169,109)(99,170,110)(100,161,101)(121,157,137)(122,158,138)(123,159,139)(124,160,140)(125,151,131)(126,152,132)(127,153,133)(128,154,134)(129,155,135)(130,156,136), (1,124,161)(2,125,162)(3,126,163)(4,127,164)(5,128,165)(6,129,166)(7,130,167)(8,121,168)(9,122,169)(10,123,170)(11,53,74)(12,54,75)(13,55,76)(14,56,77)(15,57,78)(16,58,79)(17,59,80)(18,60,71)(19,51,72)(20,52,73)(21,63,84)(22,64,85)(23,65,86)(24,66,87)(25,67,88)(26,68,89)(27,69,90)(28,70,81)(29,61,82)(30,62,83)(31,177,49)(32,178,50)(33,179,41)(34,180,42)(35,171,43)(36,172,44)(37,173,45)(38,174,46)(39,175,47)(40,176,48)(91,149,131)(92,150,132)(93,141,133)(94,142,134)(95,143,135)(96,144,136)(97,145,137)(98,146,138)(99,147,139)(100,148,140)(101,113,160)(102,114,151)(103,115,152)(104,116,153)(105,117,154)(106,118,155)(107,119,156)(108,120,157)(109,111,158)(110,112,159), (11,64)(12,65)(13,66)(14,67)(15,68)(16,69)(17,70)(18,61)(19,62)(20,63)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,51)(31,49)(32,50)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)(80,81)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,140)(102,131)(103,132)(104,133)(105,134)(106,135)(107,136)(108,137)(109,138)(110,139)(111,146)(112,147)(113,148)(114,149)(115,150)(116,141)(117,142)(118,143)(119,144)(120,145)(121,168)(122,169)(123,170)(124,161)(125,162)(126,163)(127,164)(128,165)(129,166)(130,167) );

G=PermutationGroup([[(1,177),(2,178),(3,179),(4,180),(5,171),(6,172),(7,173),(8,174),(9,175),(10,176),(11,132),(12,133),(13,134),(14,135),(15,136),(16,137),(17,138),(18,139),(19,140),(20,131),(21,151),(22,152),(23,153),(24,154),(25,155),(26,156),(27,157),(28,158),(29,159),(30,160),(31,161),(32,162),(33,163),(34,164),(35,165),(36,166),(37,167),(38,168),(39,169),(40,170),(41,126),(42,127),(43,128),(44,129),(45,130),(46,121),(47,122),(48,123),(49,124),(50,125),(51,100),(52,91),(53,92),(54,93),(55,94),(56,95),(57,96),(58,97),(59,98),(60,99),(61,110),(62,101),(63,102),(64,103),(65,104),(66,105),(67,106),(68,107),(69,108),(70,109),(71,147),(72,148),(73,149),(74,150),(75,141),(76,142),(77,143),(78,144),(79,145),(80,146),(81,111),(82,112),(83,113),(84,114),(85,115),(86,116),(87,117),(88,118),(89,119),(90,120)], [(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),(171,172,173,174,175,176,177,178,179,180)], [(1,113,148),(2,114,149),(3,115,150),(4,116,141),(5,117,142),(6,118,143),(7,119,144),(8,120,145),(9,111,146),(10,112,147),(11,41,22),(12,42,23),(13,43,24),(14,44,25),(15,45,26),(16,46,27),(17,47,28),(18,48,29),(19,49,30),(20,50,21),(31,62,51),(32,63,52),(33,64,53),(34,65,54),(35,66,55),(36,67,56),(37,68,57),(38,69,58),(39,70,59),(40,61,60),(71,176,82),(72,177,83),(73,178,84),(74,179,85),(75,180,86),(76,171,87),(77,172,88),(78,173,89),(79,174,90),(80,175,81),(91,162,102),(92,163,103),(93,164,104),(94,165,105),(95,166,106),(96,167,107),(97,168,108),(98,169,109),(99,170,110),(100,161,101),(121,157,137),(122,158,138),(123,159,139),(124,160,140),(125,151,131),(126,152,132),(127,153,133),(128,154,134),(129,155,135),(130,156,136)], [(1,124,161),(2,125,162),(3,126,163),(4,127,164),(5,128,165),(6,129,166),(7,130,167),(8,121,168),(9,122,169),(10,123,170),(11,53,74),(12,54,75),(13,55,76),(14,56,77),(15,57,78),(16,58,79),(17,59,80),(18,60,71),(19,51,72),(20,52,73),(21,63,84),(22,64,85),(23,65,86),(24,66,87),(25,67,88),(26,68,89),(27,69,90),(28,70,81),(29,61,82),(30,62,83),(31,177,49),(32,178,50),(33,179,41),(34,180,42),(35,171,43),(36,172,44),(37,173,45),(38,174,46),(39,175,47),(40,176,48),(91,149,131),(92,150,132),(93,141,133),(94,142,134),(95,143,135),(96,144,136),(97,145,137),(98,146,138),(99,147,139),(100,148,140),(101,113,160),(102,114,151),(103,115,152),(104,116,153),(105,117,154),(106,118,155),(107,119,156),(108,120,157),(109,111,158),(110,112,159)], [(11,64),(12,65),(13,66),(14,67),(15,68),(16,69),(17,70),(18,61),(19,62),(20,63),(21,52),(22,53),(23,54),(24,55),(25,56),(26,57),(27,58),(28,59),(29,60),(30,51),(31,49),(32,50),(33,41),(34,42),(35,43),(36,44),(37,45),(38,46),(39,47),(40,48),(71,82),(72,83),(73,84),(74,85),(75,86),(76,87),(77,88),(78,89),(79,90),(80,81),(91,151),(92,152),(93,153),(94,154),(95,155),(96,156),(97,157),(98,158),(99,159),(100,160),(101,140),(102,131),(103,132),(104,133),(105,134),(106,135),(107,136),(108,137),(109,138),(110,139),(111,146),(112,147),(113,148),(114,149),(115,150),(116,141),(117,142),(118,143),(119,144),(120,145),(121,168),(122,169),(123,170),(124,161),(125,162),(126,163),(127,164),(128,165),(129,166),(130,167)]])

120 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 3A 3B 3C 3D 5A 5B 5C 5D 6A ··· 6L 10A ··· 10L 10M ··· 10AB 15A ··· 15P 30A ··· 30AV order 1 2 2 2 2 2 2 2 3 3 3 3 5 5 5 5 6 ··· 6 10 ··· 10 10 ··· 10 15 ··· 15 30 ··· 30 size 1 1 1 1 9 9 9 9 2 2 2 2 1 1 1 1 2 ··· 2 1 ··· 1 9 ··· 9 2 ··· 2 2 ··· 2

120 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 type + + + + + image C1 C2 C2 C5 C10 C10 S3 D6 C5×S3 S3×C10 kernel C3⋊S3×C2×C10 C10×C3⋊S3 C6×C30 C22×C3⋊S3 C2×C3⋊S3 C62 C2×C30 C30 C2×C6 C6 # reps 1 6 1 4 24 4 4 12 16 48

Matrix representation of C3⋊S3×C2×C10 in GL4(𝔽31) generated by

 30 0 0 0 0 30 0 0 0 0 30 0 0 0 0 30
,
 15 0 0 0 0 15 0 0 0 0 8 0 0 0 0 8
,
 1 0 0 0 0 1 0 0 0 0 30 1 0 0 30 0
,
 0 30 0 0 1 30 0 0 0 0 1 0 0 0 0 1
,
 1 30 0 0 0 30 0 0 0 0 30 1 0 0 0 1
G:=sub<GL(4,GF(31))| [30,0,0,0,0,30,0,0,0,0,30,0,0,0,0,30],[15,0,0,0,0,15,0,0,0,0,8,0,0,0,0,8],[1,0,0,0,0,1,0,0,0,0,30,30,0,0,1,0],[0,1,0,0,30,30,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,30,30,0,0,0,0,30,0,0,0,1,1] >;

C3⋊S3×C2×C10 in GAP, Magma, Sage, TeX

C_3\rtimes S_3\times C_2\times C_{10}
% in TeX

G:=Group("C3:S3xC2xC10");
// GroupNames label

G:=SmallGroup(360,160);
// by ID

G=gap.SmallGroup(360,160);
# by ID

G:=PCGroup([6,-2,-2,-2,-5,-3,-3,2404,8645]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^10=c^3=d^3=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations

׿
×
𝔽