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G = C23×D29  order 464 = 24·29

Direct product of C23 and D29

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C23×D29, C29⋊C24, C58⋊C23, (C22×C58)⋊3C2, (C2×C58)⋊4C22, SmallGroup(464,50)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C29 — C23×D29
Chief series
C1 — C29 — D29 — D58 — C22×D29 — C23×D29
Lower central
C29 — C23×D29
Upper central
C1 — C23

Generators and relations for C23×D29
 G = < a,b,c,d,e | a2=b2=c2=d29=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >

Subgroups: 1562 in 134 conjugacy classes, 83 normal (5 characteristic)
C1, C2, C2, C22, C22, C23, C23, C24, C29, D29, C58, D58, C2×C58, C22×D29, C22×C58, C23×D29
Quotients: C1, C2, C22, C23, C24, D29, D58, C22×D29, C23×D29

Smallest permutation representation of C23×D29
►On 232 points
Generators in S232
(1 132)(2 133)(3 134)(4 135)(5 136)(6 137)(7 138)(8 139)(9 140)(10 141)(11 142)(12 143)(13 144)(14 145)(15 117)(16 118)(17 119)(18 120)(19 121)(20 122)(21 123)(22 124)(23 125)(24 126)(25 127)(26 128)(27 129)(28 130)(29 131)(30 168)(31 169)(32 170)(33 171)(34 172)(35 173)(36 174)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(43 152)(44 153)(45 154)(46 155)(47 156)(48 157)(49 158)(50 159)(51 160)(52 161)(53 162)(54 163)(55 164)(56 165)(57 166)(58 167)(59 175)(60 176)(61 177)(62 178)(63 179)(64 180)(65 181)(66 182)(67 183)(68 184)(69 185)(70 186)(71 187)(72 188)(73 189)(74 190)(75 191)(76 192)(77 193)(78 194)(79 195)(80 196)(81 197)(82 198)(83 199)(84 200)(85 201)(86 202)(87 203)(88 221)(89 222)(90 223)(91 224)(92 225)(93 226)(94 227)(95 228)(96 229)(97 230)(98 231)(99 232)(100 204)(101 205)(102 206)(103 207)(104 208)(105 209)(106 210)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 217)(114 218)(115 219)(116 220)

(1 95)(2 96)(3 97)(4 98)(5 99)(6 100)(7 101)(8 102)(9 103)(10 104)(11 105)(12 106)(13 107)(14 108)(15 109)(16 110)(17 111)(18 112)(19 113)(20 114)(21 115)(22 116)(23 88)(24 89)(25 90)(26 91)(27 92)(28 93)(29 94)(30 66)(31 67)(32 68)(33 69)(34 70)(35 71)(36 72)(37 73)(38 74)(39 75)(40 76)(41 77)(42 78)(43 79)(44 80)(45 81)(46 82)(47 83)(48 84)(49 85)(50 86)(51 87)(52 59)(53 60)(54 61)(55 62)(56 63)(57 64)(58 65)(117 213)(118 214)(119 215)(120 216)(121 217)(122 218)(123 219)(124 220)(125 221)(126 222)(127 223)(128 224)(129 225)(130 226)(131 227)(132 228)(133 229)(134 230)(135 231)(136 232)(137 204)(138 205)(139 206)(140 207)(141 208)(142 209)(143 210)(144 211)(145 212)(146 189)(147 190)(148 191)(149 192)(150 193)(151 194)(152 195)(153 196)(154 197)(155 198)(156 199)(157 200)(158 201)(159 202)(160 203)(161 175)(162 176)(163 177)(164 178)(165 179)(166 180)(167 181)(168 182)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)

(1 45)(2 46)(3 47)(4 48)(5 49)(6 50)(7 51)(8 52)(9 53)(10 54)(11 55)(12 56)(13 57)(14 58)(15 30)(16 31)(17 32)(18 33)(19 34)(20 35)(21 36)(22 37)(23 38)(24 39)(25 40)(26 41)(27 42)(28 43)(29 44)(59 102)(60 103)(61 104)(62 105)(63 106)(64 107)(65 108)(66 109)(67 110)(68 111)(69 112)(70 113)(71 114)(72 115)(73 116)(74 88)(75 89)(76 90)(77 91)(78 92)(79 93)(80 94)(81 95)(82 96)(83 97)(84 98)(85 99)(86 100)(87 101)(117 168)(118 169)(119 170)(120 171)(121 172)(122 173)(123 174)(124 146)(125 147)(126 148)(127 149)(128 150)(129 151)(130 152)(131 153)(132 154)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 161)(140 162)(141 163)(142 164)(143 165)(144 166)(145 167)(175 206)(176 207)(177 208)(178 209)(179 210)(180 211)(181 212)(182 213)(183 214)(184 215)(185 216)(186 217)(187 218)(188 219)(189 220)(190 221)(191 222)(192 223)(193 224)(194 225)(195 226)(196 227)(197 228)(198 229)(199 230)(200 231)(201 232)(202 204)(203 205)

(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)(175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)

(1 153)(2 152)(3 151)(4 150)(5 149)(6 148)(7 147)(8 146)(9 174)(10 173)(11 172)(12 171)(13 170)(14 169)(15 168)(16 167)(17 166)(18 165)(19 164)(20 163)(21 162)(22 161)(23 160)(24 159)(25 158)(26 157)(27 156)(28 155)(29 154)(30 117)(31 145)(32 144)(33 143)(34 142)(35 141)(36 140)(37 139)(38 138)(39 137)(40 136)(41 135)(42 134)(43 133)(44 132)(45 131)(46 130)(47 129)(48 128)(49 127)(50 126)(51 125)(52 124)(53 123)(54 122)(55 121)(56 120)(57 119)(58 118)(59 220)(60 219)(61 218)(62 217)(63 216)(64 215)(65 214)(66 213)(67 212)(68 211)(69 210)(70 209)(71 208)(72 207)(73 206)(74 205)(75 204)(76 232)(77 231)(78 230)(79 229)(80 228)(81 227)(82 226)(83 225)(84 224)(85 223)(86 222)(87 221)(88 203)(89 202)(90 201)(91 200)(92 199)(93 198)(94 197)(95 196)(96 195)(97 194)(98 193)(99 192)(100 191)(101 190)(102 189)(103 188)(104 187)(105 186)(106 185)(107 184)(108 183)(109 182)(110 181)(111 180)(112 179)(113 178)(114 177)(115 176)(116 175)
 
G:=sub<Sym(232)| (1,132)(2,133)(3,134)(4,135)(5,136)(6,137)(7,138)(8,139)(9,140)(10,141)(11,142)(12,143)(13,144)(14,145)(15,117)(16,118)(17,119)(18,120)(19,121)(20,122)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,131)(30,168)(31,169)(32,170)(33,171)(34,172)(35,173)(36,174)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,152)(44,153)(45,154)(46,155)(47,156)(48,157)(49,158)(50,159)(51,160)(52,161)(53,162)(54,163)(55,164)(56,165)(57,166)(58,167)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,183)(68,184)(69,185)(70,186)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,197)(82,198)(83,199)(84,200)(85,201)(86,202)(87,203)(88,221)(89,222)(90,223)(91,224)(92,225)(93,226)(94,227)(95,228)(96,229)(97,230)(98,231)(99,232)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,217)(114,218)(115,219)(116,220), (1,95)(2,96)(3,97)(4,98)(5,99)(6,100)(7,101)(8,102)(9,103)(10,104)(11,105)(12,106)(13,107)(14,108)(15,109)(16,110)(17,111)(18,112)(19,113)(20,114)(21,115)(22,116)(23,88)(24,89)(25,90)(26,91)(27,92)(28,93)(29,94)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84)(49,85)(50,86)(51,87)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(117,213)(118,214)(119,215)(120,216)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,204)(138,205)(139,206)(140,207)(141,208)(142,209)(143,210)(144,211)(145,212)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,197)(155,198)(156,199)(157,200)(158,201)(159,202)(160,203)(161,175)(162,176)(163,177)(164,178)(165,179)(166,180)(167,181)(168,182)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,51)(8,52)(9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(59,102)(60,103)(61,104)(62,105)(63,106)(64,107)(65,108)(66,109)(67,110)(68,111)(69,112)(70,113)(71,114)(72,115)(73,116)(74,88)(75,89)(76,90)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(175,206)(176,207)(177,208)(178,209)(179,210)(180,211)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,204)(203,205), (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)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,153)(2,152)(3,151)(4,150)(5,149)(6,148)(7,147)(8,146)(9,174)(10,173)(11,172)(12,171)(13,170)(14,169)(15,168)(16,167)(17,166)(18,165)(19,164)(20,163)(21,162)(22,161)(23,160)(24,159)(25,158)(26,157)(27,156)(28,155)(29,154)(30,117)(31,145)(32,144)(33,143)(34,142)(35,141)(36,140)(37,139)(38,138)(39,137)(40,136)(41,135)(42,134)(43,133)(44,132)(45,131)(46,130)(47,129)(48,128)(49,127)(50,126)(51,125)(52,124)(53,123)(54,122)(55,121)(56,120)(57,119)(58,118)(59,220)(60,219)(61,218)(62,217)(63,216)(64,215)(65,214)(66,213)(67,212)(68,211)(69,210)(70,209)(71,208)(72,207)(73,206)(74,205)(75,204)(76,232)(77,231)(78,230)(79,229)(80,228)(81,227)(82,226)(83,225)(84,224)(85,223)(86,222)(87,221)(88,203)(89,202)(90,201)(91,200)(92,199)(93,198)(94,197)(95,196)(96,195)(97,194)(98,193)(99,192)(100,191)(101,190)(102,189)(103,188)(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)(113,178)(114,177)(115,176)(116,175)>;
 
G:=Group( (1,132)(2,133)(3,134)(4,135)(5,136)(6,137)(7,138)(8,139)(9,140)(10,141)(11,142)(12,143)(13,144)(14,145)(15,117)(16,118)(17,119)(18,120)(19,121)(20,122)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,131)(30,168)(31,169)(32,170)(33,171)(34,172)(35,173)(36,174)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,152)(44,153)(45,154)(46,155)(47,156)(48,157)(49,158)(50,159)(51,160)(52,161)(53,162)(54,163)(55,164)(56,165)(57,166)(58,167)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,183)(68,184)(69,185)(70,186)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,197)(82,198)(83,199)(84,200)(85,201)(86,202)(87,203)(88,221)(89,222)(90,223)(91,224)(92,225)(93,226)(94,227)(95,228)(96,229)(97,230)(98,231)(99,232)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,217)(114,218)(115,219)(116,220), (1,95)(2,96)(3,97)(4,98)(5,99)(6,100)(7,101)(8,102)(9,103)(10,104)(11,105)(12,106)(13,107)(14,108)(15,109)(16,110)(17,111)(18,112)(19,113)(20,114)(21,115)(22,116)(23,88)(24,89)(25,90)(26,91)(27,92)(28,93)(29,94)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84)(49,85)(50,86)(51,87)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(117,213)(118,214)(119,215)(120,216)(121,217)(122,218)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,204)(138,205)(139,206)(140,207)(141,208)(142,209)(143,210)(144,211)(145,212)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,197)(155,198)(156,199)(157,200)(158,201)(159,202)(160,203)(161,175)(162,176)(163,177)(164,178)(165,179)(166,180)(167,181)(168,182)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,51)(8,52)(9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,30)(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(59,102)(60,103)(61,104)(62,105)(63,106)(64,107)(65,108)(66,109)(67,110)(68,111)(69,112)(70,113)(71,114)(72,115)(73,116)(74,88)(75,89)(76,90)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(175,206)(176,207)(177,208)(178,209)(179,210)(180,211)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,204)(203,205), (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)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,153)(2,152)(3,151)(4,150)(5,149)(6,148)(7,147)(8,146)(9,174)(10,173)(11,172)(12,171)(13,170)(14,169)(15,168)(16,167)(17,166)(18,165)(19,164)(20,163)(21,162)(22,161)(23,160)(24,159)(25,158)(26,157)(27,156)(28,155)(29,154)(30,117)(31,145)(32,144)(33,143)(34,142)(35,141)(36,140)(37,139)(38,138)(39,137)(40,136)(41,135)(42,134)(43,133)(44,132)(45,131)(46,130)(47,129)(48,128)(49,127)(50,126)(51,125)(52,124)(53,123)(54,122)(55,121)(56,120)(57,119)(58,118)(59,220)(60,219)(61,218)(62,217)(63,216)(64,215)(65,214)(66,213)(67,212)(68,211)(69,210)(70,209)(71,208)(72,207)(73,206)(74,205)(75,204)(76,232)(77,231)(78,230)(79,229)(80,228)(81,227)(82,226)(83,225)(84,224)(85,223)(86,222)(87,221)(88,203)(89,202)(90,201)(91,200)(92,199)(93,198)(94,197)(95,196)(96,195)(97,194)(98,193)(99,192)(100,191)(101,190)(102,189)(103,188)(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)(113,178)(114,177)(115,176)(116,175) );
 
G=PermutationGroup([[(1,132),(2,133),(3,134),(4,135),(5,136),(6,137),(7,138),(8,139),(9,140),(10,141),(11,142),(12,143),(13,144),(14,145),(15,117),(16,118),(17,119),(18,120),(19,121),(20,122),(21,123),(22,124),(23,125),(24,126),(25,127),(26,128),(27,129),(28,130),(29,131),(30,168),(31,169),(32,170),(33,171),(34,172),(35,173),(36,174),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(43,152),(44,153),(45,154),(46,155),(47,156),(48,157),(49,158),(50,159),(51,160),(52,161),(53,162),(54,163),(55,164),(56,165),(57,166),(58,167),(59,175),(60,176),(61,177),(62,178),(63,179),(64,180),(65,181),(66,182),(67,183),(68,184),(69,185),(70,186),(71,187),(72,188),(73,189),(74,190),(75,191),(76,192),(77,193),(78,194),(79,195),(80,196),(81,197),(82,198),(83,199),(84,200),(85,201),(86,202),(87,203),(88,221),(89,222),(90,223),(91,224),(92,225),(93,226),(94,227),(95,228),(96,229),(97,230),(98,231),(99,232),(100,204),(101,205),(102,206),(103,207),(104,208),(105,209),(106,210),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216),(113,217),(114,218),(115,219),(116,220)], [(1,95),(2,96),(3,97),(4,98),(5,99),(6,100),(7,101),(8,102),(9,103),(10,104),(11,105),(12,106),(13,107),(14,108),(15,109),(16,110),(17,111),(18,112),(19,113),(20,114),(21,115),(22,116),(23,88),(24,89),(25,90),(26,91),(27,92),(28,93),(29,94),(30,66),(31,67),(32,68),(33,69),(34,70),(35,71),(36,72),(37,73),(38,74),(39,75),(40,76),(41,77),(42,78),(43,79),(44,80),(45,81),(46,82),(47,83),(48,84),(49,85),(50,86),(51,87),(52,59),(53,60),(54,61),(55,62),(56,63),(57,64),(58,65),(117,213),(118,214),(119,215),(120,216),(121,217),(122,218),(123,219),(124,220),(125,221),(126,222),(127,223),(128,224),(129,225),(130,226),(131,227),(132,228),(133,229),(134,230),(135,231),(136,232),(137,204),(138,205),(139,206),(140,207),(141,208),(142,209),(143,210),(144,211),(145,212),(146,189),(147,190),(148,191),(149,192),(150,193),(151,194),(152,195),(153,196),(154,197),(155,198),(156,199),(157,200),(158,201),(159,202),(160,203),(161,175),(162,176),(163,177),(164,178),(165,179),(166,180),(167,181),(168,182),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188)], [(1,45),(2,46),(3,47),(4,48),(5,49),(6,50),(7,51),(8,52),(9,53),(10,54),(11,55),(12,56),(13,57),(14,58),(15,30),(16,31),(17,32),(18,33),(19,34),(20,35),(21,36),(22,37),(23,38),(24,39),(25,40),(26,41),(27,42),(28,43),(29,44),(59,102),(60,103),(61,104),(62,105),(63,106),(64,107),(65,108),(66,109),(67,110),(68,111),(69,112),(70,113),(71,114),(72,115),(73,116),(74,88),(75,89),(76,90),(77,91),(78,92),(79,93),(80,94),(81,95),(82,96),(83,97),(84,98),(85,99),(86,100),(87,101),(117,168),(118,169),(119,170),(120,171),(121,172),(122,173),(123,174),(124,146),(125,147),(126,148),(127,149),(128,150),(129,151),(130,152),(131,153),(132,154),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,161),(140,162),(141,163),(142,164),(143,165),(144,166),(145,167),(175,206),(176,207),(177,208),(178,209),(179,210),(180,211),(181,212),(182,213),(183,214),(184,215),(185,216),(186,217),(187,218),(188,219),(189,220),(190,221),(191,222),(192,223),(193,224),(194,225),(195,226),(196,227),(197,228),(198,229),(199,230),(200,231),(201,232),(202,204),(203,205)], [(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),(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)], [(1,153),(2,152),(3,151),(4,150),(5,149),(6,148),(7,147),(8,146),(9,174),(10,173),(11,172),(12,171),(13,170),(14,169),(15,168),(16,167),(17,166),(18,165),(19,164),(20,163),(21,162),(22,161),(23,160),(24,159),(25,158),(26,157),(27,156),(28,155),(29,154),(30,117),(31,145),(32,144),(33,143),(34,142),(35,141),(36,140),(37,139),(38,138),(39,137),(40,136),(41,135),(42,134),(43,133),(44,132),(45,131),(46,130),(47,129),(48,128),(49,127),(50,126),(51,125),(52,124),(53,123),(54,122),(55,121),(56,120),(57,119),(58,118),(59,220),(60,219),(61,218),(62,217),(63,216),(64,215),(65,214),(66,213),(67,212),(68,211),(69,210),(70,209),(71,208),(72,207),(73,206),(74,205),(75,204),(76,232),(77,231),(78,230),(79,229),(80,228),(81,227),(82,226),(83,225),(84,224),(85,223),(86,222),(87,221),(88,203),(89,202),(90,201),(91,200),(92,199),(93,198),(94,197),(95,196),(96,195),(97,194),(98,193),(99,192),(100,191),(101,190),(102,189),(103,188),(104,187),(105,186),(106,185),(107,184),(108,183),(109,182),(110,181),(111,180),(112,179),(113,178),(114,177),(115,176),(116,175)]])
 

128 conjugacy classes

class 1 2A···2G2H···2O29A···29N58A···58CT
order12···22···229···2958···58
size11···129···292···22···2

128 irreducible representations

dim11122
type+++++
imageC1C2C2D29D58
kernelC23×D29C22×D29C22×C58C23C22
# reps11411498

Matrix representation of C23×D29 ►in GL4(𝔽59) generated by

1000
05800
0010
0001
,
1000
0100
00580
00058
,
58000
05800
0010
0001
,
1000
0100
00361
002950
,
1000
05800
005058
00219
G:=sub<GL(4,GF(59))| [1,0,0,0,0,58,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,58,0,0,0,0,58],[58,0,0,0,0,58,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,36,29,0,0,1,50],[1,0,0,0,0,58,0,0,0,0,50,21,0,0,58,9] >;
 

C23×D29 in GAP, Magma, Sage, TeX 

C_2^3\times D_{29}
 
% in TeX
 
G:=Group("C2^3xD29");
 
// GroupNames label
 
G:=SmallGroup(464,50);
 
// by ID
 
G=gap.SmallGroup(464,50);
 
# by ID
 
G:=PCGroup([5,-2,-2,-2,-2,-29,11204]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^29=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,c*e=e*c,e*d*e=d^-1>;
 
// generators/relations
 

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