metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.D29, C58.11D4, C22⋊Dic29, C22.7D58, (C2×C58)⋊4C4, C29⋊3(C22⋊C4), C58.16(C2×C4), (C2×Dic29)⋊2C2, C2.3(C29⋊D4), (C22×C58).2C2, (C2×C58).7C22, C2.5(C2×Dic29), SmallGroup(464,19)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.D29
G = < a,b,c,d,e | a2=b2=c2=d29=1, e2=b, ab=ba, eae-1=ac=ca, ad=da, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Smallest permutation representation of C23.D29
►On 232 points
Generators in S232
(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 162)(134 163)(135 164)(136 165)(137 166)(138 167)(139 168)(140 169)(141 170)(142 171)(143 172)(144 173)(145 174)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(181 210)(182 211)(183 212)(184 213)(185 214)(186 215)(187 216)(188 217)(189 218)(190 219)(191 220)(192 221)(193 222)(194 223)(195 224)(196 225)(197 226)(198 227)(199 228)(200 229)(201 230)(202 231)(203 232)
(1 77)(2 78)(3 79)(4 80)(5 81)(6 82)(7 83)(8 84)(9 85)(10 86)(11 87)(12 59)(13 60)(14 61)(15 62)(16 63)(17 64)(18 65)(19 66)(20 67)(21 68)(22 69)(23 70)(24 71)(25 72)(26 73)(27 74)(28 75)(29 76)(30 109)(31 110)(32 111)(33 112)(34 113)(35 114)(36 115)(37 116)(38 88)(39 89)(40 90)(41 91)(42 92)(43 93)(44 94)(45 95)(46 96)(47 97)(48 98)(49 99)(50 100)(51 101)(52 102)(53 103)(54 104)(55 105)(56 106)(57 107)(58 108)(117 175)(118 176)(119 177)(120 178)(121 179)(122 180)(123 181)(124 182)(125 183)(126 184)(127 185)(128 186)(129 187)(130 188)(131 189)(132 190)(133 191)(134 192)(135 193)(136 194)(137 195)(138 196)(139 197)(140 198)(141 199)(142 200)(143 201)(144 202)(145 203)(146 204)(147 205)(148 206)(149 207)(150 208)(151 209)(152 210)(153 211)(154 212)(155 213)(156 214)(157 215)(158 216)(159 217)(160 218)(161 219)(162 220)(163 221)(164 222)(165 223)(166 224)(167 225)(168 226)(169 227)(170 228)(171 229)(172 230)(173 231)(174 232)
(1 47)(2 48)(3 49)(4 50)(5 51)(6 52)(7 53)(8 54)(9 55)(10 56)(11 57)(12 58)(13 30)(14 31)(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(21 38)(22 39)(23 40)(24 41)(25 42)(26 43)(27 44)(28 45)(29 46)(59 108)(60 109)(61 110)(62 111)(63 112)(64 113)(65 114)(66 115)(67 116)(68 88)(69 89)(70 90)(71 91)(72 92)(73 93)(74 94)(75 95)(76 96)(77 97)(78 98)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 162)(134 163)(135 164)(136 165)(137 166)(138 167)(139 168)(140 169)(141 170)(142 171)(143 172)(144 173)(145 174)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(181 210)(182 211)(183 212)(184 213)(185 214)(186 215)(187 216)(188 217)(189 218)(190 219)(191 220)(192 221)(193 222)(194 223)(195 224)(196 225)(197 226)(198 227)(199 228)(200 229)(201 230)(202 231)(203 232)
(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)
(1 203 77 145)(2 202 78 144)(3 201 79 143)(4 200 80 142)(5 199 81 141)(6 198 82 140)(7 197 83 139)(8 196 84 138)(9 195 85 137)(10 194 86 136)(11 193 87 135)(12 192 59 134)(13 191 60 133)(14 190 61 132)(15 189 62 131)(16 188 63 130)(17 187 64 129)(18 186 65 128)(19 185 66 127)(20 184 67 126)(21 183 68 125)(22 182 69 124)(23 181 70 123)(24 180 71 122)(25 179 72 121)(26 178 73 120)(27 177 74 119)(28 176 75 118)(29 175 76 117)(30 220 109 162)(31 219 110 161)(32 218 111 160)(33 217 112 159)(34 216 113 158)(35 215 114 157)(36 214 115 156)(37 213 116 155)(38 212 88 154)(39 211 89 153)(40 210 90 152)(41 209 91 151)(42 208 92 150)(43 207 93 149)(44 206 94 148)(45 205 95 147)(46 204 96 146)(47 232 97 174)(48 231 98 173)(49 230 99 172)(50 229 100 171)(51 228 101 170)(52 227 102 169)(53 226 103 168)(54 225 104 167)(55 224 105 166)(56 223 106 165)(57 222 107 164)(58 221 108 163)
G:=sub<Sym(232)| (117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)(144,173)(145,174)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232), (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,85)(10,86)(11,87)(12,59)(13,60)(14,61)(15,62)(16,63)(17,64)(18,65)(19,66)(20,67)(21,68)(22,69)(23,70)(24,71)(25,72)(26,73)(27,74)(28,75)(29,76)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,107)(58,108)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)(143,201)(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)(151,209)(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)(159,217)(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)(167,225)(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232), (1,47)(2,48)(3,49)(4,50)(5,51)(6,52)(7,53)(8,54)(9,55)(10,56)(11,57)(12,58)(13,30)(14,31)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,43)(27,44)(28,45)(29,46)(59,108)(60,109)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)(144,173)(145,174)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232), (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), (1,203,77,145)(2,202,78,144)(3,201,79,143)(4,200,80,142)(5,199,81,141)(6,198,82,140)(7,197,83,139)(8,196,84,138)(9,195,85,137)(10,194,86,136)(11,193,87,135)(12,192,59,134)(13,191,60,133)(14,190,61,132)(15,189,62,131)(16,188,63,130)(17,187,64,129)(18,186,65,128)(19,185,66,127)(20,184,67,126)(21,183,68,125)(22,182,69,124)(23,181,70,123)(24,180,71,122)(25,179,72,121)(26,178,73,120)(27,177,74,119)(28,176,75,118)(29,175,76,117)(30,220,109,162)(31,219,110,161)(32,218,111,160)(33,217,112,159)(34,216,113,158)(35,215,114,157)(36,214,115,156)(37,213,116,155)(38,212,88,154)(39,211,89,153)(40,210,90,152)(41,209,91,151)(42,208,92,150)(43,207,93,149)(44,206,94,148)(45,205,95,147)(46,204,96,146)(47,232,97,174)(48,231,98,173)(49,230,99,172)(50,229,100,171)(51,228,101,170)(52,227,102,169)(53,226,103,168)(54,225,104,167)(55,224,105,166)(56,223,106,165)(57,222,107,164)(58,221,108,163)>;
G:=Group( (117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)(144,173)(145,174)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232), (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,85)(10,86)(11,87)(12,59)(13,60)(14,61)(15,62)(16,63)(17,64)(18,65)(19,66)(20,67)(21,68)(22,69)(23,70)(24,71)(25,72)(26,73)(27,74)(28,75)(29,76)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,107)(58,108)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)(143,201)(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)(151,209)(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)(159,217)(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)(167,225)(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232), (1,47)(2,48)(3,49)(4,50)(5,51)(6,52)(7,53)(8,54)(9,55)(10,56)(11,57)(12,58)(13,30)(14,31)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,43)(27,44)(28,45)(29,46)(59,108)(60,109)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)(144,173)(145,174)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232), (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), (1,203,77,145)(2,202,78,144)(3,201,79,143)(4,200,80,142)(5,199,81,141)(6,198,82,140)(7,197,83,139)(8,196,84,138)(9,195,85,137)(10,194,86,136)(11,193,87,135)(12,192,59,134)(13,191,60,133)(14,190,61,132)(15,189,62,131)(16,188,63,130)(17,187,64,129)(18,186,65,128)(19,185,66,127)(20,184,67,126)(21,183,68,125)(22,182,69,124)(23,181,70,123)(24,180,71,122)(25,179,72,121)(26,178,73,120)(27,177,74,119)(28,176,75,118)(29,175,76,117)(30,220,109,162)(31,219,110,161)(32,218,111,160)(33,217,112,159)(34,216,113,158)(35,215,114,157)(36,214,115,156)(37,213,116,155)(38,212,88,154)(39,211,89,153)(40,210,90,152)(41,209,91,151)(42,208,92,150)(43,207,93,149)(44,206,94,148)(45,205,95,147)(46,204,96,146)(47,232,97,174)(48,231,98,173)(49,230,99,172)(50,229,100,171)(51,228,101,170)(52,227,102,169)(53,226,103,168)(54,225,104,167)(55,224,105,166)(56,223,106,165)(57,222,107,164)(58,221,108,163) );
G=PermutationGroup([[(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,162),(134,163),(135,164),(136,165),(137,166),(138,167),(139,168),(140,169),(141,170),(142,171),(143,172),(144,173),(145,174),(175,204),(176,205),(177,206),(178,207),(179,208),(180,209),(181,210),(182,211),(183,212),(184,213),(185,214),(186,215),(187,216),(188,217),(189,218),(190,219),(191,220),(192,221),(193,222),(194,223),(195,224),(196,225),(197,226),(198,227),(199,228),(200,229),(201,230),(202,231),(203,232)], [(1,77),(2,78),(3,79),(4,80),(5,81),(6,82),(7,83),(8,84),(9,85),(10,86),(11,87),(12,59),(13,60),(14,61),(15,62),(16,63),(17,64),(18,65),(19,66),(20,67),(21,68),(22,69),(23,70),(24,71),(25,72),(26,73),(27,74),(28,75),(29,76),(30,109),(31,110),(32,111),(33,112),(34,113),(35,114),(36,115),(37,116),(38,88),(39,89),(40,90),(41,91),(42,92),(43,93),(44,94),(45,95),(46,96),(47,97),(48,98),(49,99),(50,100),(51,101),(52,102),(53,103),(54,104),(55,105),(56,106),(57,107),(58,108),(117,175),(118,176),(119,177),(120,178),(121,179),(122,180),(123,181),(124,182),(125,183),(126,184),(127,185),(128,186),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,193),(136,194),(137,195),(138,196),(139,197),(140,198),(141,199),(142,200),(143,201),(144,202),(145,203),(146,204),(147,205),(148,206),(149,207),(150,208),(151,209),(152,210),(153,211),(154,212),(155,213),(156,214),(157,215),(158,216),(159,217),(160,218),(161,219),(162,220),(163,221),(164,222),(165,223),(166,224),(167,225),(168,226),(169,227),(170,228),(171,229),(172,230),(173,231),(174,232)], [(1,47),(2,48),(3,49),(4,50),(5,51),(6,52),(7,53),(8,54),(9,55),(10,56),(11,57),(12,58),(13,30),(14,31),(15,32),(16,33),(17,34),(18,35),(19,36),(20,37),(21,38),(22,39),(23,40),(24,41),(25,42),(26,43),(27,44),(28,45),(29,46),(59,108),(60,109),(61,110),(62,111),(63,112),(64,113),(65,114),(66,115),(67,116),(68,88),(69,89),(70,90),(71,91),(72,92),(73,93),(74,94),(75,95),(76,96),(77,97),(78,98),(79,99),(80,100),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,162),(134,163),(135,164),(136,165),(137,166),(138,167),(139,168),(140,169),(141,170),(142,171),(143,172),(144,173),(145,174),(175,204),(176,205),(177,206),(178,207),(179,208),(180,209),(181,210),(182,211),(183,212),(184,213),(185,214),(186,215),(187,216),(188,217),(189,218),(190,219),(191,220),(192,221),(193,222),(194,223),(195,224),(196,225),(197,226),(198,227),(199,228),(200,229),(201,230),(202,231),(203,232)], [(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)], [(1,203,77,145),(2,202,78,144),(3,201,79,143),(4,200,80,142),(5,199,81,141),(6,198,82,140),(7,197,83,139),(8,196,84,138),(9,195,85,137),(10,194,86,136),(11,193,87,135),(12,192,59,134),(13,191,60,133),(14,190,61,132),(15,189,62,131),(16,188,63,130),(17,187,64,129),(18,186,65,128),(19,185,66,127),(20,184,67,126),(21,183,68,125),(22,182,69,124),(23,181,70,123),(24,180,71,122),(25,179,72,121),(26,178,73,120),(27,177,74,119),(28,176,75,118),(29,175,76,117),(30,220,109,162),(31,219,110,161),(32,218,111,160),(33,217,112,159),(34,216,113,158),(35,215,114,157),(36,214,115,156),(37,213,116,155),(38,212,88,154),(39,211,89,153),(40,210,90,152),(41,209,91,151),(42,208,92,150),(43,207,93,149),(44,206,94,148),(45,205,95,147),(46,204,96,146),(47,232,97,174),(48,231,98,173),(49,230,99,172),(50,229,100,171),(51,228,101,170),(52,227,102,169),(53,226,103,168),(54,225,104,167),(55,224,105,166),(56,223,106,165),(57,222,107,164),(58,221,108,163)]])
122 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 29A | ··· | 29N | 58A | ··· | 58CT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 58 | 58 | 58 | 58 | 2 | ··· | 2 | 2 | ··· | 2 |
122 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C4 | D4 | D29 | Dic29 | D58 | C29⋊D4 |
| kernel | C23.D29 | C2×Dic29 | C22×C58 | C2×C58 | C58 | C23 | C22 | C22 | C2 |
| # reps | 1 | 2 | 1 | 4 | 2 | 14 | 28 | 14 | 56 |
Matrix representation of C23.D29 ►in GL4(𝔽233) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 89 | 232 |
| 232 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 |
| 0 | 0 | 232 | 0 |
| 0 | 0 | 0 | 232 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 232 | 0 |
| 0 | 0 | 0 | 232 |
| 232 | 1 | 0 | 0 |
| 9 | 223 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 191 | 89 | 0 | 0 |
| 43 | 42 | 0 | 0 |
| 0 | 0 | 89 | 231 |
| 0 | 0 | 0 | 144 |
G:=sub<GL(4,GF(233))| [1,0,0,0,0,1,0,0,0,0,1,89,0,0,0,232],[232,0,0,0,0,232,0,0,0,0,232,0,0,0,0,232],[1,0,0,0,0,1,0,0,0,0,232,0,0,0,0,232],[232,9,0,0,1,223,0,0,0,0,1,0,0,0,0,1],[191,43,0,0,89,42,0,0,0,0,89,0,0,0,231,144] >;
C23.D29 in GAP, Magma, Sage, TeX
C_2^3.D_{29} % in TeX
G:=Group("C2^3.D29"); // GroupNames label
G:=SmallGroup(464,19);
// by ID
G=gap.SmallGroup(464,19);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,20,101,11204]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^29=1,e^2=b,a*b=b*a,e*a*e^-1=a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations
Export