metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C28.20(C4⋊C4), C28.88(C2×Q8), (C2×C28).25Q8, Dic7⋊C8⋊39C2, (C2×C28).165D4, C28.439(C2×D4), (C2×C8).186D14, C4⋊Dic7.20C4, C23.27(C4×D7), C14.30(C8○D4), C4.53(C2×Dic14), (C2×C4).35Dic14, C23.D7.10C4, C4.19(Dic7⋊C4), (C2×C56).316C22, C2.16(D28.C4), (C2×C28).864C23, (C22×C4).346D14, (C2×M4(2)).13D7, (C14×M4(2)).24C2, C7⋊4(C42.6C22), C22.11(Dic7⋊C4), (C22×C28).178C22, (C4×Dic7).188C22, C23.21D14.15C2, C14.49(C2×C4⋊C4), (C2×C4).82(C4×D7), (C2×C28).98(C2×C4), C4.129(C2×C7⋊D4), (C22×C7⋊C8).10C2, (C2×C14).15(C4⋊C4), C22.144(C2×C4×D7), (C2×C7⋊C8).322C22, C2.17(C2×Dic7⋊C4), (C2×C4).193(C7⋊D4), (C22×C14).64(C2×C4), (C2×Dic7).33(C2×C4), (C2×C4).806(C22×D7), (C2×C14).134(C22×C4), SmallGroup(448,653)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊Dic7.20C4
G = < a,b,c,d | a4=b14=1, c2=b7, d4=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, bd=db, dcd-1=b7c >
Subgroups: 356 in 114 conjugacy classes, 63 normal (23 characteristic)
C1, C2, C2 [×2], C2 [×2], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×2], C7, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×4], C23, C14, C14 [×2], C14 [×2], C42 [×2], C22⋊C4 [×2], C4⋊C4 [×2], C2×C8 [×2], C2×C8 [×4], M4(2) [×2], C22×C4, Dic7 [×4], C28 [×2], C28 [×2], C2×C14, C2×C14 [×2], C2×C14 [×2], C4⋊C8 [×4], C42⋊C2, C22×C8, C2×M4(2), C7⋊C8 [×2], C56 [×2], C2×Dic7 [×4], C2×C28 [×2], C2×C28 [×4], C22×C14, C42.6C22, C2×C7⋊C8 [×2], C2×C7⋊C8 [×2], C4×Dic7 [×2], C4⋊Dic7 [×2], C23.D7 [×2], C2×C56 [×2], C7×M4(2) [×2], C22×C28, Dic7⋊C8 [×4], C22×C7⋊C8, C23.21D14, C14×M4(2), C4⋊Dic7.20C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, D7, C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, D14 [×3], C2×C4⋊C4, C8○D4 [×2], Dic14 [×2], C4×D7 [×2], C7⋊D4 [×2], C22×D7, C42.6C22, Dic7⋊C4 [×4], C2×Dic14, C2×C4×D7, C2×C7⋊D4, D28.C4 [×2], C2×Dic7⋊C4, C4⋊Dic7.20C4
►On 224 points
Generators in S224
(1 52 206 190)(2 53 207 191)(3 54 208 192)(4 55 209 193)(5 56 210 194)(6 43 197 195)(7 44 198 196)(8 45 199 183)(9 46 200 184)(10 47 201 185)(11 48 202 186)(12 49 203 187)(13 50 204 188)(14 51 205 189)(15 57 72 139)(16 58 73 140)(17 59 74 127)(18 60 75 128)(19 61 76 129)(20 62 77 130)(21 63 78 131)(22 64 79 132)(23 65 80 133)(24 66 81 134)(25 67 82 135)(26 68 83 136)(27 69 84 137)(28 70 71 138)(29 85 125 144)(30 86 126 145)(31 87 113 146)(32 88 114 147)(33 89 115 148)(34 90 116 149)(35 91 117 150)(36 92 118 151)(37 93 119 152)(38 94 120 153)(39 95 121 154)(40 96 122 141)(41 97 123 142)(42 98 124 143)(99 178 219 155)(100 179 220 156)(101 180 221 157)(102 181 222 158)(103 182 223 159)(104 169 224 160)(105 170 211 161)(106 171 212 162)(107 172 213 163)(108 173 214 164)(109 174 215 165)(110 175 216 166)(111 176 217 167)(112 177 218 168)
(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)
(1 137 8 130)(2 136 9 129)(3 135 10 128)(4 134 11 127)(5 133 12 140)(6 132 13 139)(7 131 14 138)(15 195 22 188)(16 194 23 187)(17 193 24 186)(18 192 25 185)(19 191 26 184)(20 190 27 183)(21 189 28 196)(29 182 36 175)(30 181 37 174)(31 180 38 173)(32 179 39 172)(33 178 40 171)(34 177 41 170)(35 176 42 169)(43 79 50 72)(44 78 51 71)(45 77 52 84)(46 76 53 83)(47 75 54 82)(48 74 55 81)(49 73 56 80)(57 197 64 204)(58 210 65 203)(59 209 66 202)(60 208 67 201)(61 207 68 200)(62 206 69 199)(63 205 70 198)(85 103 92 110)(86 102 93 109)(87 101 94 108)(88 100 95 107)(89 99 96 106)(90 112 97 105)(91 111 98 104)(113 157 120 164)(114 156 121 163)(115 155 122 162)(116 168 123 161)(117 167 124 160)(118 166 125 159)(119 165 126 158)(141 212 148 219)(142 211 149 218)(143 224 150 217)(144 223 151 216)(145 222 152 215)(146 221 153 214)(147 220 154 213)
(1 169 52 104 206 160 190 224)(2 170 53 105 207 161 191 211)(3 171 54 106 208 162 192 212)(4 172 55 107 209 163 193 213)(5 173 56 108 210 164 194 214)(6 174 43 109 197 165 195 215)(7 175 44 110 198 166 196 216)(8 176 45 111 199 167 183 217)(9 177 46 112 200 168 184 218)(10 178 47 99 201 155 185 219)(11 179 48 100 202 156 186 220)(12 180 49 101 203 157 187 221)(13 181 50 102 204 158 188 222)(14 182 51 103 205 159 189 223)(15 145 139 30 72 86 57 126)(16 146 140 31 73 87 58 113)(17 147 127 32 74 88 59 114)(18 148 128 33 75 89 60 115)(19 149 129 34 76 90 61 116)(20 150 130 35 77 91 62 117)(21 151 131 36 78 92 63 118)(22 152 132 37 79 93 64 119)(23 153 133 38 80 94 65 120)(24 154 134 39 81 95 66 121)(25 141 135 40 82 96 67 122)(26 142 136 41 83 97 68 123)(27 143 137 42 84 98 69 124)(28 144 138 29 71 85 70 125)
G:=sub<Sym(224)| (1,52,206,190)(2,53,207,191)(3,54,208,192)(4,55,209,193)(5,56,210,194)(6,43,197,195)(7,44,198,196)(8,45,199,183)(9,46,200,184)(10,47,201,185)(11,48,202,186)(12,49,203,187)(13,50,204,188)(14,51,205,189)(15,57,72,139)(16,58,73,140)(17,59,74,127)(18,60,75,128)(19,61,76,129)(20,62,77,130)(21,63,78,131)(22,64,79,132)(23,65,80,133)(24,66,81,134)(25,67,82,135)(26,68,83,136)(27,69,84,137)(28,70,71,138)(29,85,125,144)(30,86,126,145)(31,87,113,146)(32,88,114,147)(33,89,115,148)(34,90,116,149)(35,91,117,150)(36,92,118,151)(37,93,119,152)(38,94,120,153)(39,95,121,154)(40,96,122,141)(41,97,123,142)(42,98,124,143)(99,178,219,155)(100,179,220,156)(101,180,221,157)(102,181,222,158)(103,182,223,159)(104,169,224,160)(105,170,211,161)(106,171,212,162)(107,172,213,163)(108,173,214,164)(109,174,215,165)(110,175,216,166)(111,176,217,167)(112,177,218,168), (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), (1,137,8,130)(2,136,9,129)(3,135,10,128)(4,134,11,127)(5,133,12,140)(6,132,13,139)(7,131,14,138)(15,195,22,188)(16,194,23,187)(17,193,24,186)(18,192,25,185)(19,191,26,184)(20,190,27,183)(21,189,28,196)(29,182,36,175)(30,181,37,174)(31,180,38,173)(32,179,39,172)(33,178,40,171)(34,177,41,170)(35,176,42,169)(43,79,50,72)(44,78,51,71)(45,77,52,84)(46,76,53,83)(47,75,54,82)(48,74,55,81)(49,73,56,80)(57,197,64,204)(58,210,65,203)(59,209,66,202)(60,208,67,201)(61,207,68,200)(62,206,69,199)(63,205,70,198)(85,103,92,110)(86,102,93,109)(87,101,94,108)(88,100,95,107)(89,99,96,106)(90,112,97,105)(91,111,98,104)(113,157,120,164)(114,156,121,163)(115,155,122,162)(116,168,123,161)(117,167,124,160)(118,166,125,159)(119,165,126,158)(141,212,148,219)(142,211,149,218)(143,224,150,217)(144,223,151,216)(145,222,152,215)(146,221,153,214)(147,220,154,213), (1,169,52,104,206,160,190,224)(2,170,53,105,207,161,191,211)(3,171,54,106,208,162,192,212)(4,172,55,107,209,163,193,213)(5,173,56,108,210,164,194,214)(6,174,43,109,197,165,195,215)(7,175,44,110,198,166,196,216)(8,176,45,111,199,167,183,217)(9,177,46,112,200,168,184,218)(10,178,47,99,201,155,185,219)(11,179,48,100,202,156,186,220)(12,180,49,101,203,157,187,221)(13,181,50,102,204,158,188,222)(14,182,51,103,205,159,189,223)(15,145,139,30,72,86,57,126)(16,146,140,31,73,87,58,113)(17,147,127,32,74,88,59,114)(18,148,128,33,75,89,60,115)(19,149,129,34,76,90,61,116)(20,150,130,35,77,91,62,117)(21,151,131,36,78,92,63,118)(22,152,132,37,79,93,64,119)(23,153,133,38,80,94,65,120)(24,154,134,39,81,95,66,121)(25,141,135,40,82,96,67,122)(26,142,136,41,83,97,68,123)(27,143,137,42,84,98,69,124)(28,144,138,29,71,85,70,125)>;
G:=Group( (1,52,206,190)(2,53,207,191)(3,54,208,192)(4,55,209,193)(5,56,210,194)(6,43,197,195)(7,44,198,196)(8,45,199,183)(9,46,200,184)(10,47,201,185)(11,48,202,186)(12,49,203,187)(13,50,204,188)(14,51,205,189)(15,57,72,139)(16,58,73,140)(17,59,74,127)(18,60,75,128)(19,61,76,129)(20,62,77,130)(21,63,78,131)(22,64,79,132)(23,65,80,133)(24,66,81,134)(25,67,82,135)(26,68,83,136)(27,69,84,137)(28,70,71,138)(29,85,125,144)(30,86,126,145)(31,87,113,146)(32,88,114,147)(33,89,115,148)(34,90,116,149)(35,91,117,150)(36,92,118,151)(37,93,119,152)(38,94,120,153)(39,95,121,154)(40,96,122,141)(41,97,123,142)(42,98,124,143)(99,178,219,155)(100,179,220,156)(101,180,221,157)(102,181,222,158)(103,182,223,159)(104,169,224,160)(105,170,211,161)(106,171,212,162)(107,172,213,163)(108,173,214,164)(109,174,215,165)(110,175,216,166)(111,176,217,167)(112,177,218,168), (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), (1,137,8,130)(2,136,9,129)(3,135,10,128)(4,134,11,127)(5,133,12,140)(6,132,13,139)(7,131,14,138)(15,195,22,188)(16,194,23,187)(17,193,24,186)(18,192,25,185)(19,191,26,184)(20,190,27,183)(21,189,28,196)(29,182,36,175)(30,181,37,174)(31,180,38,173)(32,179,39,172)(33,178,40,171)(34,177,41,170)(35,176,42,169)(43,79,50,72)(44,78,51,71)(45,77,52,84)(46,76,53,83)(47,75,54,82)(48,74,55,81)(49,73,56,80)(57,197,64,204)(58,210,65,203)(59,209,66,202)(60,208,67,201)(61,207,68,200)(62,206,69,199)(63,205,70,198)(85,103,92,110)(86,102,93,109)(87,101,94,108)(88,100,95,107)(89,99,96,106)(90,112,97,105)(91,111,98,104)(113,157,120,164)(114,156,121,163)(115,155,122,162)(116,168,123,161)(117,167,124,160)(118,166,125,159)(119,165,126,158)(141,212,148,219)(142,211,149,218)(143,224,150,217)(144,223,151,216)(145,222,152,215)(146,221,153,214)(147,220,154,213), (1,169,52,104,206,160,190,224)(2,170,53,105,207,161,191,211)(3,171,54,106,208,162,192,212)(4,172,55,107,209,163,193,213)(5,173,56,108,210,164,194,214)(6,174,43,109,197,165,195,215)(7,175,44,110,198,166,196,216)(8,176,45,111,199,167,183,217)(9,177,46,112,200,168,184,218)(10,178,47,99,201,155,185,219)(11,179,48,100,202,156,186,220)(12,180,49,101,203,157,187,221)(13,181,50,102,204,158,188,222)(14,182,51,103,205,159,189,223)(15,145,139,30,72,86,57,126)(16,146,140,31,73,87,58,113)(17,147,127,32,74,88,59,114)(18,148,128,33,75,89,60,115)(19,149,129,34,76,90,61,116)(20,150,130,35,77,91,62,117)(21,151,131,36,78,92,63,118)(22,152,132,37,79,93,64,119)(23,153,133,38,80,94,65,120)(24,154,134,39,81,95,66,121)(25,141,135,40,82,96,67,122)(26,142,136,41,83,97,68,123)(27,143,137,42,84,98,69,124)(28,144,138,29,71,85,70,125) );
G=PermutationGroup([(1,52,206,190),(2,53,207,191),(3,54,208,192),(4,55,209,193),(5,56,210,194),(6,43,197,195),(7,44,198,196),(8,45,199,183),(9,46,200,184),(10,47,201,185),(11,48,202,186),(12,49,203,187),(13,50,204,188),(14,51,205,189),(15,57,72,139),(16,58,73,140),(17,59,74,127),(18,60,75,128),(19,61,76,129),(20,62,77,130),(21,63,78,131),(22,64,79,132),(23,65,80,133),(24,66,81,134),(25,67,82,135),(26,68,83,136),(27,69,84,137),(28,70,71,138),(29,85,125,144),(30,86,126,145),(31,87,113,146),(32,88,114,147),(33,89,115,148),(34,90,116,149),(35,91,117,150),(36,92,118,151),(37,93,119,152),(38,94,120,153),(39,95,121,154),(40,96,122,141),(41,97,123,142),(42,98,124,143),(99,178,219,155),(100,179,220,156),(101,180,221,157),(102,181,222,158),(103,182,223,159),(104,169,224,160),(105,170,211,161),(106,171,212,162),(107,172,213,163),(108,173,214,164),(109,174,215,165),(110,175,216,166),(111,176,217,167),(112,177,218,168)], [(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)], [(1,137,8,130),(2,136,9,129),(3,135,10,128),(4,134,11,127),(5,133,12,140),(6,132,13,139),(7,131,14,138),(15,195,22,188),(16,194,23,187),(17,193,24,186),(18,192,25,185),(19,191,26,184),(20,190,27,183),(21,189,28,196),(29,182,36,175),(30,181,37,174),(31,180,38,173),(32,179,39,172),(33,178,40,171),(34,177,41,170),(35,176,42,169),(43,79,50,72),(44,78,51,71),(45,77,52,84),(46,76,53,83),(47,75,54,82),(48,74,55,81),(49,73,56,80),(57,197,64,204),(58,210,65,203),(59,209,66,202),(60,208,67,201),(61,207,68,200),(62,206,69,199),(63,205,70,198),(85,103,92,110),(86,102,93,109),(87,101,94,108),(88,100,95,107),(89,99,96,106),(90,112,97,105),(91,111,98,104),(113,157,120,164),(114,156,121,163),(115,155,122,162),(116,168,123,161),(117,167,124,160),(118,166,125,159),(119,165,126,158),(141,212,148,219),(142,211,149,218),(143,224,150,217),(144,223,151,216),(145,222,152,215),(146,221,153,214),(147,220,154,213)], [(1,169,52,104,206,160,190,224),(2,170,53,105,207,161,191,211),(3,171,54,106,208,162,192,212),(4,172,55,107,209,163,193,213),(5,173,56,108,210,164,194,214),(6,174,43,109,197,165,195,215),(7,175,44,110,198,166,196,216),(8,176,45,111,199,167,183,217),(9,177,46,112,200,168,184,218),(10,178,47,99,201,155,185,219),(11,179,48,100,202,156,186,220),(12,180,49,101,203,157,187,221),(13,181,50,102,204,158,188,222),(14,182,51,103,205,159,189,223),(15,145,139,30,72,86,57,126),(16,146,140,31,73,87,58,113),(17,147,127,32,74,88,59,114),(18,148,128,33,75,89,60,115),(19,149,129,34,76,90,61,116),(20,150,130,35,77,91,62,117),(21,151,131,36,78,92,63,118),(22,152,132,37,79,93,64,119),(23,153,133,38,80,94,65,120),(24,154,134,39,81,95,66,121),(25,141,135,40,82,96,67,122),(26,142,136,41,83,97,68,123),(27,143,137,42,84,98,69,124),(28,144,138,29,71,85,70,125)])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | ··· | 8L | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | D4 | Q8 | D7 | D14 | D14 | C8○D4 | Dic14 | C4×D7 | C7⋊D4 | C4×D7 | D28.C4 |
| kernel | C4⋊Dic7.20C4 | Dic7⋊C8 | C22×C7⋊C8 | C23.21D14 | C14×M4(2) | C4⋊Dic7 | C23.D7 | C2×C28 | C2×C28 | C2×M4(2) | C2×C8 | C22×C4 | C14 | C2×C4 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 3 | 6 | 3 | 8 | 12 | 6 | 12 | 6 | 12 |
Matrix representation of C4⋊Dic7.20C4 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 112 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 18 | 25 | 0 | 0 | 0 | 0 |
| 82 | 95 | 0 | 0 | 0 | 0 |
| 0 | 0 | 77 | 23 | 0 | 0 |
| 0 | 0 | 96 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 18 |
| 0 | 0 | 0 | 0 | 47 | 82 |
| 15 | 2 | 0 | 0 | 0 | 0 |
| 106 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 107 | 26 |
| 0 | 0 | 0 | 0 | 3 | 6 |
G:=sub<GL(6,GF(113))| [98,112,0,0,0,0,0,15,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,112,24,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[18,82,0,0,0,0,25,95,0,0,0,0,0,0,77,96,0,0,0,0,23,36,0,0,0,0,0,0,31,47,0,0,0,0,18,82],[15,106,0,0,0,0,2,98,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,107,3,0,0,0,0,26,6] >;
C4⋊Dic7.20C4 in GAP, Magma, Sage, TeX
C_4\rtimes {\rm Dic}_7._{20}C_4 % in TeX
G:=Group("C4:Dic7.20C4"); // GroupNames label
G:=SmallGroup(448,653);
// by ID
G=gap.SmallGroup(448,653);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,477,422,387,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^14=1,c^2=b^7,d^4=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^7*c>;
// generators/relations