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G = C24×C14order 224 = 25·7

Abelian group of type [2,2,2,2,14]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C14, SmallGroup(224,197)

Series: Derived Chief Lower central Upper central

C1 — C24×C14
C1C7C14C2×C14C22×C14C23×C14 — C24×C14
C1 — C24×C14
C1 — C24×C14

Generators and relations for C24×C14
 G = < a,b,c,d,e | a2=b2=c2=d2=e14=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 748, all normal (4 characteristic)
C1, C2 [×31], C22 [×155], C7, C23 [×155], C14 [×31], C24 [×31], C2×C14 [×155], C25, C22×C14 [×155], C23×C14 [×31], C24×C14
Quotients: C1, C2 [×31], C22 [×155], C7, C23 [×155], C14 [×31], C24 [×31], C2×C14 [×155], C25, C22×C14 [×155], C23×C14 [×31], C24×C14

Smallest permutation representation of C24×C14
Regular action on 224 points
Generators in S224
(1 125)(2 126)(3 113)(4 114)(5 115)(6 116)(7 117)(8 118)(9 119)(10 120)(11 121)(12 122)(13 123)(14 124)(15 139)(16 140)(17 127)(18 128)(19 129)(20 130)(21 131)(22 132)(23 133)(24 134)(25 135)(26 136)(27 137)(28 138)(29 151)(30 152)(31 153)(32 154)(33 141)(34 142)(35 143)(36 144)(37 145)(38 146)(39 147)(40 148)(41 149)(42 150)(43 165)(44 166)(45 167)(46 168)(47 155)(48 156)(49 157)(50 158)(51 159)(52 160)(53 161)(54 162)(55 163)(56 164)(57 171)(58 172)(59 173)(60 174)(61 175)(62 176)(63 177)(64 178)(65 179)(66 180)(67 181)(68 182)(69 169)(70 170)(71 185)(72 186)(73 187)(74 188)(75 189)(76 190)(77 191)(78 192)(79 193)(80 194)(81 195)(82 196)(83 183)(84 184)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 197)(98 198)(99 221)(100 222)(101 223)(102 224)(103 211)(104 212)(105 213)(106 214)(107 215)(108 216)(109 217)(110 218)(111 219)(112 220)
(1 66)(2 67)(3 68)(4 69)(5 70)(6 57)(7 58)(8 59)(9 60)(10 61)(11 62)(12 63)(13 64)(14 65)(15 80)(16 81)(17 82)(18 83)(19 84)(20 71)(21 72)(22 73)(23 74)(24 75)(25 76)(26 77)(27 78)(28 79)(29 98)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 100)(44 101)(45 102)(46 103)(47 104)(48 105)(49 106)(50 107)(51 108)(52 109)(53 110)(54 111)(55 112)(56 99)(113 182)(114 169)(115 170)(116 171)(117 172)(118 173)(119 174)(120 175)(121 176)(122 177)(123 178)(124 179)(125 180)(126 181)(127 196)(128 183)(129 184)(130 185)(131 186)(132 187)(133 188)(134 189)(135 190)(136 191)(137 192)(138 193)(139 194)(140 195)(141 202)(142 203)(143 204)(144 205)(145 206)(146 207)(147 208)(148 209)(149 210)(150 197)(151 198)(152 199)(153 200)(154 201)(155 212)(156 213)(157 214)(158 215)(159 216)(160 217)(161 218)(162 219)(163 220)(164 221)(165 222)(166 223)(167 224)(168 211)
(1 41)(2 42)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(57 87)(58 88)(59 89)(60 90)(61 91)(62 92)(63 93)(64 94)(65 95)(66 96)(67 97)(68 98)(69 85)(70 86)(71 105)(72 106)(73 107)(74 108)(75 109)(76 110)(77 111)(78 112)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(113 151)(114 152)(115 153)(116 154)(117 141)(118 142)(119 143)(120 144)(121 145)(122 146)(123 147)(124 148)(125 149)(126 150)(127 167)(128 168)(129 155)(130 156)(131 157)(132 158)(133 159)(134 160)(135 161)(136 162)(137 163)(138 164)(139 165)(140 166)(169 199)(170 200)(171 201)(172 202)(173 203)(174 204)(175 205)(176 206)(177 207)(178 208)(179 209)(180 210)(181 197)(182 198)(183 211)(184 212)(185 213)(186 214)(187 215)(188 216)(189 217)(190 218)(191 219)(192 220)(193 221)(194 222)(195 223)(196 224)
(1 28)(2 15)(3 16)(4 17)(5 18)(6 19)(7 20)(8 21)(9 22)(10 23)(11 24)(12 25)(13 26)(14 27)(29 44)(30 45)(31 46)(32 47)(33 48)(34 49)(35 50)(36 51)(37 52)(38 53)(39 54)(40 55)(41 56)(42 43)(57 84)(58 71)(59 72)(60 73)(61 74)(62 75)(63 76)(64 77)(65 78)(66 79)(67 80)(68 81)(69 82)(70 83)(85 102)(86 103)(87 104)(88 105)(89 106)(90 107)(91 108)(92 109)(93 110)(94 111)(95 112)(96 99)(97 100)(98 101)(113 140)(114 127)(115 128)(116 129)(117 130)(118 131)(119 132)(120 133)(121 134)(122 135)(123 136)(124 137)(125 138)(126 139)(141 156)(142 157)(143 158)(144 159)(145 160)(146 161)(147 162)(148 163)(149 164)(150 165)(151 166)(152 167)(153 168)(154 155)(169 196)(170 183)(171 184)(172 185)(173 186)(174 187)(175 188)(176 189)(177 190)(178 191)(179 192)(180 193)(181 194)(182 195)(197 222)(198 223)(199 224)(200 211)(201 212)(202 213)(203 214)(204 215)(205 216)(206 217)(207 218)(208 219)(209 220)(210 221)
(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)

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

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

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

C24×C14 is a maximal subgroup of   C25.D7

224 conjugacy classes

class 1 2A···2AE7A···7F14A···14GD
order12···27···714···14
size11···11···11···1

224 irreducible representations

dim1111
type++
imageC1C2C7C14
kernelC24×C14C23×C14C25C24
# reps1316186

Matrix representation of C24×C14 in GL5(𝔽29)

280000
01000
00100
00010
00001
,
10000
01000
00100
000280
00001
,
280000
028000
00100
00010
00001
,
10000
01000
002800
00010
00001
,
50000
05000
00700
00070
000028

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[5,0,0,0,0,0,5,0,0,0,0,0,7,0,0,0,0,0,7,0,0,0,0,0,28] >;

C24×C14 in GAP, Magma, Sage, TeX

C_2^4\times C_{14}
% in TeX

G:=Group("C2^4xC14");
// GroupNames label

G:=SmallGroup(224,197);
// by ID

G=gap.SmallGroup(224,197);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-7]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^14=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,d*e=e*d>;
// generators/relations

׿
×
𝔽