metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.5D14, C56⋊C4⋊16C2, D4⋊C4⋊15D7, C14.D8⋊3C2, (C2×D4).19D14, C28.3(C4○D4), (C2×C8).166D14, C28⋊D4.4C2, D4⋊Dic7⋊2C2, C28.3Q8⋊2C2, C2.D56⋊16C2, C4.21(C4○D28), C2.8(D56⋊C2), (C2×Dic7).15D4, C22.166(D4×D7), C4.47(D4⋊2D7), C2.11(D8⋊D7), C14.53(C8⋊C22), (C2×C56).179C22, (C2×C28).204C23, (D4×C14).25C22, (C2×D28).46C22, C4⋊Dic7.63C22, (C4×Dic7).8C22, C14.23(C4.4D4), C7⋊2(C42.29C22), C2.13(Dic7.D4), (C7×C4⋊C4).9C22, (C2×C7⋊C8).10C22, (C7×D4⋊C4)⋊17C2, (C2×C14).217(C2×D4), (C2×C4).311(C22×D7), SmallGroup(448,298)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.D14
G = < a,b,c,d | a4=b4=c14=d2=1, bab-1=cac-1=dad=a-1, cbc-1=a-1b-1, dbd=ab, dcd=b2c-1 >
Subgroups: 692 in 110 conjugacy classes, 37 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C14, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C8⋊C4, D4⋊C4, D4⋊C4, C42.C2, C4⋊1D4, C7⋊C8, C56, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C42.29C22, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C7×C4⋊C4, C2×C56, C2×D28, C2×C7⋊D4, D4×C14, C14.D8, C56⋊C4, C2.D56, D4⋊Dic7, C7×D4⋊C4, C28.3Q8, C28⋊D4, C4⋊C4.D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C22×D7, C42.29C22, C4○D28, D4×D7, D4⋊2D7, Dic7.D4, D8⋊D7, D56⋊C2, C4⋊C4.D14
►On 224 points
Generators in S224
(1 196 12 189)(2 190 13 183)(3 184 14 191)(4 192 8 185)(5 186 9 193)(6 194 10 187)(7 188 11 195)(15 36 27 29)(16 30 28 37)(17 38 22 31)(18 32 23 39)(19 40 24 33)(20 34 25 41)(21 42 26 35)(43 150 90 171)(44 172 91 151)(45 152 92 173)(46 174 93 153)(47 154 94 175)(48 176 95 141)(49 142 96 177)(50 178 97 143)(51 144 98 179)(52 180 85 145)(53 146 86 181)(54 182 87 147)(55 148 88 169)(56 170 89 149)(57 199 162 215)(58 216 163 200)(59 201 164 217)(60 218 165 202)(61 203 166 219)(62 220 167 204)(63 205 168 221)(64 222 155 206)(65 207 156 223)(66 224 157 208)(67 209 158 211)(68 212 159 210)(69 197 160 213)(70 214 161 198)(71 78 121 114)(72 115 122 79)(73 80 123 116)(74 117 124 81)(75 82 125 118)(76 119 126 83)(77 84 113 120)(99 129 136 106)(100 107 137 130)(101 131 138 108)(102 109 139 132)(103 133 140 110)(104 111 127 134)(105 135 128 112)
(1 179 19 44)(2 173 20 52)(3 181 21 46)(4 175 15 54)(5 169 16 48)(6 177 17 56)(7 171 18 50)(8 154 27 87)(9 148 28 95)(10 142 22 89)(11 150 23 97)(12 144 24 91)(13 152 25 85)(14 146 26 93)(29 182 185 47)(30 141 186 88)(31 170 187 49)(32 143 188 90)(33 172 189 51)(34 145 190 92)(35 174 191 53)(36 147 192 94)(37 176 193 55)(38 149 194 96)(39 178 195 43)(40 151 196 98)(41 180 183 45)(42 153 184 86)(57 119 64 133)(58 127 65 113)(59 121 66 135)(60 129 67 115)(61 123 68 137)(62 131 69 117)(63 125 70 139)(71 157 112 164)(72 218 99 209)(73 159 100 166)(74 220 101 197)(75 161 102 168)(76 222 103 199)(77 163 104 156)(78 224 105 201)(79 165 106 158)(80 212 107 203)(81 167 108 160)(82 214 109 205)(83 155 110 162)(84 216 111 207)(114 208 128 217)(116 210 130 219)(118 198 132 221)(120 200 134 223)(122 202 136 211)(124 204 138 213)(126 206 140 215)
(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)
(1 155)(2 161)(3 167)(4 159)(5 165)(6 157)(7 163)(8 68)(9 60)(10 66)(11 58)(12 64)(13 70)(14 62)(15 166)(16 158)(17 164)(18 156)(19 162)(20 168)(21 160)(22 59)(23 65)(24 57)(25 63)(26 69)(27 61)(28 67)(29 219)(30 209)(31 217)(32 207)(33 215)(34 205)(35 213)(36 203)(37 211)(38 201)(39 223)(40 199)(41 221)(42 197)(43 127)(44 126)(45 139)(46 124)(47 137)(48 122)(49 135)(50 120)(51 133)(52 118)(53 131)(54 116)(55 129)(56 114)(71 149)(72 95)(73 147)(74 93)(75 145)(76 91)(77 143)(78 89)(79 141)(80 87)(81 153)(82 85)(83 151)(84 97)(86 108)(88 106)(90 104)(92 102)(94 100)(96 112)(98 110)(99 148)(101 146)(103 144)(105 142)(107 154)(109 152)(111 150)(113 178)(115 176)(117 174)(119 172)(121 170)(123 182)(125 180)(128 177)(130 175)(132 173)(134 171)(136 169)(138 181)(140 179)(183 198)(184 220)(185 210)(186 218)(187 208)(188 216)(189 206)(190 214)(191 204)(192 212)(193 202)(194 224)(195 200)(196 222)
G:=sub<Sym(224)| (1,196,12,189)(2,190,13,183)(3,184,14,191)(4,192,8,185)(5,186,9,193)(6,194,10,187)(7,188,11,195)(15,36,27,29)(16,30,28,37)(17,38,22,31)(18,32,23,39)(19,40,24,33)(20,34,25,41)(21,42,26,35)(43,150,90,171)(44,172,91,151)(45,152,92,173)(46,174,93,153)(47,154,94,175)(48,176,95,141)(49,142,96,177)(50,178,97,143)(51,144,98,179)(52,180,85,145)(53,146,86,181)(54,182,87,147)(55,148,88,169)(56,170,89,149)(57,199,162,215)(58,216,163,200)(59,201,164,217)(60,218,165,202)(61,203,166,219)(62,220,167,204)(63,205,168,221)(64,222,155,206)(65,207,156,223)(66,224,157,208)(67,209,158,211)(68,212,159,210)(69,197,160,213)(70,214,161,198)(71,78,121,114)(72,115,122,79)(73,80,123,116)(74,117,124,81)(75,82,125,118)(76,119,126,83)(77,84,113,120)(99,129,136,106)(100,107,137,130)(101,131,138,108)(102,109,139,132)(103,133,140,110)(104,111,127,134)(105,135,128,112), (1,179,19,44)(2,173,20,52)(3,181,21,46)(4,175,15,54)(5,169,16,48)(6,177,17,56)(7,171,18,50)(8,154,27,87)(9,148,28,95)(10,142,22,89)(11,150,23,97)(12,144,24,91)(13,152,25,85)(14,146,26,93)(29,182,185,47)(30,141,186,88)(31,170,187,49)(32,143,188,90)(33,172,189,51)(34,145,190,92)(35,174,191,53)(36,147,192,94)(37,176,193,55)(38,149,194,96)(39,178,195,43)(40,151,196,98)(41,180,183,45)(42,153,184,86)(57,119,64,133)(58,127,65,113)(59,121,66,135)(60,129,67,115)(61,123,68,137)(62,131,69,117)(63,125,70,139)(71,157,112,164)(72,218,99,209)(73,159,100,166)(74,220,101,197)(75,161,102,168)(76,222,103,199)(77,163,104,156)(78,224,105,201)(79,165,106,158)(80,212,107,203)(81,167,108,160)(82,214,109,205)(83,155,110,162)(84,216,111,207)(114,208,128,217)(116,210,130,219)(118,198,132,221)(120,200,134,223)(122,202,136,211)(124,204,138,213)(126,206,140,215), (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), (1,155)(2,161)(3,167)(4,159)(5,165)(6,157)(7,163)(8,68)(9,60)(10,66)(11,58)(12,64)(13,70)(14,62)(15,166)(16,158)(17,164)(18,156)(19,162)(20,168)(21,160)(22,59)(23,65)(24,57)(25,63)(26,69)(27,61)(28,67)(29,219)(30,209)(31,217)(32,207)(33,215)(34,205)(35,213)(36,203)(37,211)(38,201)(39,223)(40,199)(41,221)(42,197)(43,127)(44,126)(45,139)(46,124)(47,137)(48,122)(49,135)(50,120)(51,133)(52,118)(53,131)(54,116)(55,129)(56,114)(71,149)(72,95)(73,147)(74,93)(75,145)(76,91)(77,143)(78,89)(79,141)(80,87)(81,153)(82,85)(83,151)(84,97)(86,108)(88,106)(90,104)(92,102)(94,100)(96,112)(98,110)(99,148)(101,146)(103,144)(105,142)(107,154)(109,152)(111,150)(113,178)(115,176)(117,174)(119,172)(121,170)(123,182)(125,180)(128,177)(130,175)(132,173)(134,171)(136,169)(138,181)(140,179)(183,198)(184,220)(185,210)(186,218)(187,208)(188,216)(189,206)(190,214)(191,204)(192,212)(193,202)(194,224)(195,200)(196,222)>;
G:=Group( (1,196,12,189)(2,190,13,183)(3,184,14,191)(4,192,8,185)(5,186,9,193)(6,194,10,187)(7,188,11,195)(15,36,27,29)(16,30,28,37)(17,38,22,31)(18,32,23,39)(19,40,24,33)(20,34,25,41)(21,42,26,35)(43,150,90,171)(44,172,91,151)(45,152,92,173)(46,174,93,153)(47,154,94,175)(48,176,95,141)(49,142,96,177)(50,178,97,143)(51,144,98,179)(52,180,85,145)(53,146,86,181)(54,182,87,147)(55,148,88,169)(56,170,89,149)(57,199,162,215)(58,216,163,200)(59,201,164,217)(60,218,165,202)(61,203,166,219)(62,220,167,204)(63,205,168,221)(64,222,155,206)(65,207,156,223)(66,224,157,208)(67,209,158,211)(68,212,159,210)(69,197,160,213)(70,214,161,198)(71,78,121,114)(72,115,122,79)(73,80,123,116)(74,117,124,81)(75,82,125,118)(76,119,126,83)(77,84,113,120)(99,129,136,106)(100,107,137,130)(101,131,138,108)(102,109,139,132)(103,133,140,110)(104,111,127,134)(105,135,128,112), (1,179,19,44)(2,173,20,52)(3,181,21,46)(4,175,15,54)(5,169,16,48)(6,177,17,56)(7,171,18,50)(8,154,27,87)(9,148,28,95)(10,142,22,89)(11,150,23,97)(12,144,24,91)(13,152,25,85)(14,146,26,93)(29,182,185,47)(30,141,186,88)(31,170,187,49)(32,143,188,90)(33,172,189,51)(34,145,190,92)(35,174,191,53)(36,147,192,94)(37,176,193,55)(38,149,194,96)(39,178,195,43)(40,151,196,98)(41,180,183,45)(42,153,184,86)(57,119,64,133)(58,127,65,113)(59,121,66,135)(60,129,67,115)(61,123,68,137)(62,131,69,117)(63,125,70,139)(71,157,112,164)(72,218,99,209)(73,159,100,166)(74,220,101,197)(75,161,102,168)(76,222,103,199)(77,163,104,156)(78,224,105,201)(79,165,106,158)(80,212,107,203)(81,167,108,160)(82,214,109,205)(83,155,110,162)(84,216,111,207)(114,208,128,217)(116,210,130,219)(118,198,132,221)(120,200,134,223)(122,202,136,211)(124,204,138,213)(126,206,140,215), (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), (1,155)(2,161)(3,167)(4,159)(5,165)(6,157)(7,163)(8,68)(9,60)(10,66)(11,58)(12,64)(13,70)(14,62)(15,166)(16,158)(17,164)(18,156)(19,162)(20,168)(21,160)(22,59)(23,65)(24,57)(25,63)(26,69)(27,61)(28,67)(29,219)(30,209)(31,217)(32,207)(33,215)(34,205)(35,213)(36,203)(37,211)(38,201)(39,223)(40,199)(41,221)(42,197)(43,127)(44,126)(45,139)(46,124)(47,137)(48,122)(49,135)(50,120)(51,133)(52,118)(53,131)(54,116)(55,129)(56,114)(71,149)(72,95)(73,147)(74,93)(75,145)(76,91)(77,143)(78,89)(79,141)(80,87)(81,153)(82,85)(83,151)(84,97)(86,108)(88,106)(90,104)(92,102)(94,100)(96,112)(98,110)(99,148)(101,146)(103,144)(105,142)(107,154)(109,152)(111,150)(113,178)(115,176)(117,174)(119,172)(121,170)(123,182)(125,180)(128,177)(130,175)(132,173)(134,171)(136,169)(138,181)(140,179)(183,198)(184,220)(185,210)(186,218)(187,208)(188,216)(189,206)(190,214)(191,204)(192,212)(193,202)(194,224)(195,200)(196,222) );
G=PermutationGroup([[(1,196,12,189),(2,190,13,183),(3,184,14,191),(4,192,8,185),(5,186,9,193),(6,194,10,187),(7,188,11,195),(15,36,27,29),(16,30,28,37),(17,38,22,31),(18,32,23,39),(19,40,24,33),(20,34,25,41),(21,42,26,35),(43,150,90,171),(44,172,91,151),(45,152,92,173),(46,174,93,153),(47,154,94,175),(48,176,95,141),(49,142,96,177),(50,178,97,143),(51,144,98,179),(52,180,85,145),(53,146,86,181),(54,182,87,147),(55,148,88,169),(56,170,89,149),(57,199,162,215),(58,216,163,200),(59,201,164,217),(60,218,165,202),(61,203,166,219),(62,220,167,204),(63,205,168,221),(64,222,155,206),(65,207,156,223),(66,224,157,208),(67,209,158,211),(68,212,159,210),(69,197,160,213),(70,214,161,198),(71,78,121,114),(72,115,122,79),(73,80,123,116),(74,117,124,81),(75,82,125,118),(76,119,126,83),(77,84,113,120),(99,129,136,106),(100,107,137,130),(101,131,138,108),(102,109,139,132),(103,133,140,110),(104,111,127,134),(105,135,128,112)], [(1,179,19,44),(2,173,20,52),(3,181,21,46),(4,175,15,54),(5,169,16,48),(6,177,17,56),(7,171,18,50),(8,154,27,87),(9,148,28,95),(10,142,22,89),(11,150,23,97),(12,144,24,91),(13,152,25,85),(14,146,26,93),(29,182,185,47),(30,141,186,88),(31,170,187,49),(32,143,188,90),(33,172,189,51),(34,145,190,92),(35,174,191,53),(36,147,192,94),(37,176,193,55),(38,149,194,96),(39,178,195,43),(40,151,196,98),(41,180,183,45),(42,153,184,86),(57,119,64,133),(58,127,65,113),(59,121,66,135),(60,129,67,115),(61,123,68,137),(62,131,69,117),(63,125,70,139),(71,157,112,164),(72,218,99,209),(73,159,100,166),(74,220,101,197),(75,161,102,168),(76,222,103,199),(77,163,104,156),(78,224,105,201),(79,165,106,158),(80,212,107,203),(81,167,108,160),(82,214,109,205),(83,155,110,162),(84,216,111,207),(114,208,128,217),(116,210,130,219),(118,198,132,221),(120,200,134,223),(122,202,136,211),(124,204,138,213),(126,206,140,215)], [(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)], [(1,155),(2,161),(3,167),(4,159),(5,165),(6,157),(7,163),(8,68),(9,60),(10,66),(11,58),(12,64),(13,70),(14,62),(15,166),(16,158),(17,164),(18,156),(19,162),(20,168),(21,160),(22,59),(23,65),(24,57),(25,63),(26,69),(27,61),(28,67),(29,219),(30,209),(31,217),(32,207),(33,215),(34,205),(35,213),(36,203),(37,211),(38,201),(39,223),(40,199),(41,221),(42,197),(43,127),(44,126),(45,139),(46,124),(47,137),(48,122),(49,135),(50,120),(51,133),(52,118),(53,131),(54,116),(55,129),(56,114),(71,149),(72,95),(73,147),(74,93),(75,145),(76,91),(77,143),(78,89),(79,141),(80,87),(81,153),(82,85),(83,151),(84,97),(86,108),(88,106),(90,104),(92,102),(94,100),(96,112),(98,110),(99,148),(101,146),(103,144),(105,142),(107,154),(109,152),(111,150),(113,178),(115,176),(117,174),(119,172),(121,170),(123,182),(125,180),(128,177),(130,175),(132,173),(134,171),(136,169),(138,181),(140,179),(183,198),(184,220),(185,210),(186,218),(187,208),(188,216),(189,206),(190,214),(191,204),(192,212),(193,202),(194,224),(195,200),(196,222)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 56 | 2 | 2 | 8 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | C8⋊C22 | D4⋊2D7 | D4×D7 | D8⋊D7 | D56⋊C2 |
| kernel | C4⋊C4.D14 | C14.D8 | C56⋊C4 | C2.D56 | D4⋊Dic7 | C7×D4⋊C4 | C28.3Q8 | C28⋊D4 | C2×Dic7 | D4⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×D4 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 3 | 3 | 3 | 12 | 2 | 3 | 3 | 6 | 6 |
Matrix representation of C4⋊C4.D14 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 55 |
| 0 | 0 | 0 | 112 | 58 | 15 |
| 0 | 0 | 62 | 74 | 1 | 0 |
| 0 | 0 | 39 | 0 | 0 | 1 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 2 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 23 |
| 0 | 0 | 0 | 0 | 56 | 4 |
| 0 | 0 | 9 | 33 | 0 | 0 |
| 0 | 0 | 100 | 18 | 0 | 0 |
| 1 | 15 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 103 | 25 | 19 | 62 |
| 0 | 0 | 99 | 1 | 55 | 77 |
| 0 | 0 | 0 | 0 | 88 | 88 |
| 0 | 0 | 0 | 0 | 25 | 34 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 30 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 52 | 29 | 0 | 0 |
| 0 | 0 | 12 | 61 | 0 | 0 |
| 0 | 0 | 69 | 16 | 101 | 73 |
| 0 | 0 | 6 | 112 | 29 | 12 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,62,39,0,0,0,112,74,0,0,0,0,58,1,0,0,0,55,15,0,1],[98,2,0,0,0,0,0,15,0,0,0,0,0,0,0,0,9,100,0,0,0,0,33,18,0,0,8,56,0,0,0,0,23,4,0,0],[1,0,0,0,0,0,15,112,0,0,0,0,0,0,103,99,0,0,0,0,25,1,0,0,0,0,19,55,88,25,0,0,62,77,88,34],[1,30,0,0,0,0,0,112,0,0,0,0,0,0,52,12,69,6,0,0,29,61,16,112,0,0,0,0,101,29,0,0,0,0,73,12] >;
C4⋊C4.D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4.D_{14} % in TeX
G:=Group("C4:C4.D14"); // GroupNames label
G:=SmallGroup(448,298);
// by ID
G=gap.SmallGroup(448,298);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,253,1094,135,100,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=d^2=1,b*a*b^-1=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=a^-1*b^-1,d*b*d=a*b,d*c*d=b^2*c^-1>;
// generators/relations