metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8.1D4, C4⋊C4.30D14, C4.169(D4×D7), C7⋊1(C8.D4), Q8⋊C4⋊19D7, C28.127(C2×D4), (C2×C8).178D14, (C2×Q8).22D14, C28.22(C4○D4), C4.35(C4○D28), D14⋊3Q8.6C2, D14⋊2Q8.3C2, C4.Dic14⋊13C2, (C2×Dic7).34D4, (C22×D7).22D4, C22.206(D4×D7), C28.44D4⋊25C2, C14.26(C4⋊D4), (C2×C28).256C23, (C2×C56).203C22, (Q8×C14).39C22, C2.29(D14⋊D4), C2.18(Q16⋊D7), C2.19(SD16⋊D7), C14.64(C8.C22), C4⋊Dic7.100C22, (C2×Dic14).74C22, (C2×C7⋊Q16)⋊6C2, (C2×C8⋊D7).7C2, (C2×C7⋊C8).46C22, (C2×C4×D7).28C22, (C7×Q8⋊C4)⋊25C2, (C2×C14).269(C2×D4), (C7×C4⋊C4).57C22, (C2×C4).363(C22×D7), SmallGroup(448,350)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8.D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=dad=a-1, ac=ca, cbc-1=b3, dbd=b5, dcd=b4c-1 >
Subgroups: 564 in 110 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), Q16, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, Q8⋊C4, Q8⋊C4, C4.Q8, C22⋊Q8, C2×M4(2), C2×Q16, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C8.D4, C8⋊D7, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7⋊Q16, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, Q8×C14, C4.Dic14, C28.44D4, C7×Q8⋊C4, D14⋊2Q8, C2×C8⋊D7, C2×C7⋊Q16, D14⋊3Q8, C7⋊C8.D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C8.C22, C22×D7, C8.D4, C4○D28, D4×D7, D14⋊D4, SD16⋊D7, Q16⋊D7, C7⋊C8.D4
►On 224 points
Generators in S224
(1 136 92 53 42 184 201)(2 202 177 43 54 93 129)(3 130 94 55 44 178 203)(4 204 179 45 56 95 131)(5 132 96 49 46 180 205)(6 206 181 47 50 89 133)(7 134 90 51 48 182 207)(8 208 183 41 52 91 135)(9 36 211 125 105 67 172)(10 173 68 106 126 212 37)(11 38 213 127 107 69 174)(12 175 70 108 128 214 39)(13 40 215 121 109 71 176)(14 169 72 110 122 216 33)(15 34 209 123 111 65 170)(16 171 66 112 124 210 35)(17 28 168 101 63 153 116)(18 117 154 64 102 161 29)(19 30 162 103 57 155 118)(20 119 156 58 104 163 31)(21 32 164 97 59 157 120)(22 113 158 60 98 165 25)(23 26 166 99 61 159 114)(24 115 160 62 100 167 27)(73 150 190 193 218 140 88)(74 81 141 219 194 191 151)(75 152 192 195 220 142 82)(76 83 143 221 196 185 145)(77 146 186 197 222 144 84)(78 85 137 223 198 187 147)(79 148 188 199 224 138 86)(80 87 139 217 200 189 149)
(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)
(1 126 221 164)(2 121 222 167)(3 124 223 162)(4 127 224 165)(5 122 217 168)(6 125 218 163)(7 128 219 166)(8 123 220 161)(9 150 156 50)(10 145 157 53)(11 148 158 56)(12 151 159 51)(13 146 160 54)(14 149 153 49)(15 152 154 52)(16 147 155 55)(17 180 72 87)(18 183 65 82)(19 178 66 85)(20 181 67 88)(21 184 68 83)(22 179 69 86)(23 182 70 81)(24 177 71 84)(25 204 107 138)(26 207 108 141)(27 202 109 144)(28 205 110 139)(29 208 111 142)(30 203 112 137)(31 206 105 140)(32 201 106 143)(33 189 63 96)(34 192 64 91)(35 187 57 94)(36 190 58 89)(37 185 59 92)(38 188 60 95)(39 191 61 90)(40 186 62 93)(41 170 75 117)(42 173 76 120)(43 176 77 115)(44 171 78 118)(45 174 79 113)(46 169 80 116)(47 172 73 119)(48 175 74 114)(97 136 212 196)(98 131 213 199)(99 134 214 194)(100 129 215 197)(101 132 216 200)(102 135 209 195)(103 130 210 198)(104 133 211 193)
(1 217)(2 222)(3 219)(4 224)(5 221)(6 218)(7 223)(8 220)(9 176)(10 173)(11 170)(12 175)(13 172)(14 169)(15 174)(16 171)(17 63)(18 60)(19 57)(20 62)(21 59)(22 64)(23 61)(24 58)(25 102)(26 99)(27 104)(28 101)(29 98)(30 103)(31 100)(32 97)(33 72)(34 69)(35 66)(36 71)(37 68)(38 65)(39 70)(40 67)(41 152)(42 149)(43 146)(44 151)(45 148)(46 145)(47 150)(48 147)(49 76)(50 73)(51 78)(52 75)(53 80)(54 77)(55 74)(56 79)(81 94)(82 91)(83 96)(84 93)(85 90)(86 95)(87 92)(88 89)(105 215)(106 212)(107 209)(108 214)(109 211)(110 216)(111 213)(112 210)(113 154)(114 159)(115 156)(116 153)(117 158)(118 155)(119 160)(120 157)(121 125)(123 127)(129 144)(130 141)(131 138)(132 143)(133 140)(134 137)(135 142)(136 139)(161 165)(163 167)(177 186)(178 191)(179 188)(180 185)(181 190)(182 187)(183 192)(184 189)(193 206)(194 203)(195 208)(196 205)(197 202)(198 207)(199 204)(200 201)
G:=sub<Sym(224)| (1,136,92,53,42,184,201)(2,202,177,43,54,93,129)(3,130,94,55,44,178,203)(4,204,179,45,56,95,131)(5,132,96,49,46,180,205)(6,206,181,47,50,89,133)(7,134,90,51,48,182,207)(8,208,183,41,52,91,135)(9,36,211,125,105,67,172)(10,173,68,106,126,212,37)(11,38,213,127,107,69,174)(12,175,70,108,128,214,39)(13,40,215,121,109,71,176)(14,169,72,110,122,216,33)(15,34,209,123,111,65,170)(16,171,66,112,124,210,35)(17,28,168,101,63,153,116)(18,117,154,64,102,161,29)(19,30,162,103,57,155,118)(20,119,156,58,104,163,31)(21,32,164,97,59,157,120)(22,113,158,60,98,165,25)(23,26,166,99,61,159,114)(24,115,160,62,100,167,27)(73,150,190,193,218,140,88)(74,81,141,219,194,191,151)(75,152,192,195,220,142,82)(76,83,143,221,196,185,145)(77,146,186,197,222,144,84)(78,85,137,223,198,187,147)(79,148,188,199,224,138,86)(80,87,139,217,200,189,149), (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), (1,126,221,164)(2,121,222,167)(3,124,223,162)(4,127,224,165)(5,122,217,168)(6,125,218,163)(7,128,219,166)(8,123,220,161)(9,150,156,50)(10,145,157,53)(11,148,158,56)(12,151,159,51)(13,146,160,54)(14,149,153,49)(15,152,154,52)(16,147,155,55)(17,180,72,87)(18,183,65,82)(19,178,66,85)(20,181,67,88)(21,184,68,83)(22,179,69,86)(23,182,70,81)(24,177,71,84)(25,204,107,138)(26,207,108,141)(27,202,109,144)(28,205,110,139)(29,208,111,142)(30,203,112,137)(31,206,105,140)(32,201,106,143)(33,189,63,96)(34,192,64,91)(35,187,57,94)(36,190,58,89)(37,185,59,92)(38,188,60,95)(39,191,61,90)(40,186,62,93)(41,170,75,117)(42,173,76,120)(43,176,77,115)(44,171,78,118)(45,174,79,113)(46,169,80,116)(47,172,73,119)(48,175,74,114)(97,136,212,196)(98,131,213,199)(99,134,214,194)(100,129,215,197)(101,132,216,200)(102,135,209,195)(103,130,210,198)(104,133,211,193), (1,217)(2,222)(3,219)(4,224)(5,221)(6,218)(7,223)(8,220)(9,176)(10,173)(11,170)(12,175)(13,172)(14,169)(15,174)(16,171)(17,63)(18,60)(19,57)(20,62)(21,59)(22,64)(23,61)(24,58)(25,102)(26,99)(27,104)(28,101)(29,98)(30,103)(31,100)(32,97)(33,72)(34,69)(35,66)(36,71)(37,68)(38,65)(39,70)(40,67)(41,152)(42,149)(43,146)(44,151)(45,148)(46,145)(47,150)(48,147)(49,76)(50,73)(51,78)(52,75)(53,80)(54,77)(55,74)(56,79)(81,94)(82,91)(83,96)(84,93)(85,90)(86,95)(87,92)(88,89)(105,215)(106,212)(107,209)(108,214)(109,211)(110,216)(111,213)(112,210)(113,154)(114,159)(115,156)(116,153)(117,158)(118,155)(119,160)(120,157)(121,125)(123,127)(129,144)(130,141)(131,138)(132,143)(133,140)(134,137)(135,142)(136,139)(161,165)(163,167)(177,186)(178,191)(179,188)(180,185)(181,190)(182,187)(183,192)(184,189)(193,206)(194,203)(195,208)(196,205)(197,202)(198,207)(199,204)(200,201)>;
G:=Group( (1,136,92,53,42,184,201)(2,202,177,43,54,93,129)(3,130,94,55,44,178,203)(4,204,179,45,56,95,131)(5,132,96,49,46,180,205)(6,206,181,47,50,89,133)(7,134,90,51,48,182,207)(8,208,183,41,52,91,135)(9,36,211,125,105,67,172)(10,173,68,106,126,212,37)(11,38,213,127,107,69,174)(12,175,70,108,128,214,39)(13,40,215,121,109,71,176)(14,169,72,110,122,216,33)(15,34,209,123,111,65,170)(16,171,66,112,124,210,35)(17,28,168,101,63,153,116)(18,117,154,64,102,161,29)(19,30,162,103,57,155,118)(20,119,156,58,104,163,31)(21,32,164,97,59,157,120)(22,113,158,60,98,165,25)(23,26,166,99,61,159,114)(24,115,160,62,100,167,27)(73,150,190,193,218,140,88)(74,81,141,219,194,191,151)(75,152,192,195,220,142,82)(76,83,143,221,196,185,145)(77,146,186,197,222,144,84)(78,85,137,223,198,187,147)(79,148,188,199,224,138,86)(80,87,139,217,200,189,149), (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), (1,126,221,164)(2,121,222,167)(3,124,223,162)(4,127,224,165)(5,122,217,168)(6,125,218,163)(7,128,219,166)(8,123,220,161)(9,150,156,50)(10,145,157,53)(11,148,158,56)(12,151,159,51)(13,146,160,54)(14,149,153,49)(15,152,154,52)(16,147,155,55)(17,180,72,87)(18,183,65,82)(19,178,66,85)(20,181,67,88)(21,184,68,83)(22,179,69,86)(23,182,70,81)(24,177,71,84)(25,204,107,138)(26,207,108,141)(27,202,109,144)(28,205,110,139)(29,208,111,142)(30,203,112,137)(31,206,105,140)(32,201,106,143)(33,189,63,96)(34,192,64,91)(35,187,57,94)(36,190,58,89)(37,185,59,92)(38,188,60,95)(39,191,61,90)(40,186,62,93)(41,170,75,117)(42,173,76,120)(43,176,77,115)(44,171,78,118)(45,174,79,113)(46,169,80,116)(47,172,73,119)(48,175,74,114)(97,136,212,196)(98,131,213,199)(99,134,214,194)(100,129,215,197)(101,132,216,200)(102,135,209,195)(103,130,210,198)(104,133,211,193), (1,217)(2,222)(3,219)(4,224)(5,221)(6,218)(7,223)(8,220)(9,176)(10,173)(11,170)(12,175)(13,172)(14,169)(15,174)(16,171)(17,63)(18,60)(19,57)(20,62)(21,59)(22,64)(23,61)(24,58)(25,102)(26,99)(27,104)(28,101)(29,98)(30,103)(31,100)(32,97)(33,72)(34,69)(35,66)(36,71)(37,68)(38,65)(39,70)(40,67)(41,152)(42,149)(43,146)(44,151)(45,148)(46,145)(47,150)(48,147)(49,76)(50,73)(51,78)(52,75)(53,80)(54,77)(55,74)(56,79)(81,94)(82,91)(83,96)(84,93)(85,90)(86,95)(87,92)(88,89)(105,215)(106,212)(107,209)(108,214)(109,211)(110,216)(111,213)(112,210)(113,154)(114,159)(115,156)(116,153)(117,158)(118,155)(119,160)(120,157)(121,125)(123,127)(129,144)(130,141)(131,138)(132,143)(133,140)(134,137)(135,142)(136,139)(161,165)(163,167)(177,186)(178,191)(179,188)(180,185)(181,190)(182,187)(183,192)(184,189)(193,206)(194,203)(195,208)(196,205)(197,202)(198,207)(199,204)(200,201) );
G=PermutationGroup([[(1,136,92,53,42,184,201),(2,202,177,43,54,93,129),(3,130,94,55,44,178,203),(4,204,179,45,56,95,131),(5,132,96,49,46,180,205),(6,206,181,47,50,89,133),(7,134,90,51,48,182,207),(8,208,183,41,52,91,135),(9,36,211,125,105,67,172),(10,173,68,106,126,212,37),(11,38,213,127,107,69,174),(12,175,70,108,128,214,39),(13,40,215,121,109,71,176),(14,169,72,110,122,216,33),(15,34,209,123,111,65,170),(16,171,66,112,124,210,35),(17,28,168,101,63,153,116),(18,117,154,64,102,161,29),(19,30,162,103,57,155,118),(20,119,156,58,104,163,31),(21,32,164,97,59,157,120),(22,113,158,60,98,165,25),(23,26,166,99,61,159,114),(24,115,160,62,100,167,27),(73,150,190,193,218,140,88),(74,81,141,219,194,191,151),(75,152,192,195,220,142,82),(76,83,143,221,196,185,145),(77,146,186,197,222,144,84),(78,85,137,223,198,187,147),(79,148,188,199,224,138,86),(80,87,139,217,200,189,149)], [(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)], [(1,126,221,164),(2,121,222,167),(3,124,223,162),(4,127,224,165),(5,122,217,168),(6,125,218,163),(7,128,219,166),(8,123,220,161),(9,150,156,50),(10,145,157,53),(11,148,158,56),(12,151,159,51),(13,146,160,54),(14,149,153,49),(15,152,154,52),(16,147,155,55),(17,180,72,87),(18,183,65,82),(19,178,66,85),(20,181,67,88),(21,184,68,83),(22,179,69,86),(23,182,70,81),(24,177,71,84),(25,204,107,138),(26,207,108,141),(27,202,109,144),(28,205,110,139),(29,208,111,142),(30,203,112,137),(31,206,105,140),(32,201,106,143),(33,189,63,96),(34,192,64,91),(35,187,57,94),(36,190,58,89),(37,185,59,92),(38,188,60,95),(39,191,61,90),(40,186,62,93),(41,170,75,117),(42,173,76,120),(43,176,77,115),(44,171,78,118),(45,174,79,113),(46,169,80,116),(47,172,73,119),(48,175,74,114),(97,136,212,196),(98,131,213,199),(99,134,214,194),(100,129,215,197),(101,132,216,200),(102,135,209,195),(103,130,210,198),(104,133,211,193)], [(1,217),(2,222),(3,219),(4,224),(5,221),(6,218),(7,223),(8,220),(9,176),(10,173),(11,170),(12,175),(13,172),(14,169),(15,174),(16,171),(17,63),(18,60),(19,57),(20,62),(21,59),(22,64),(23,61),(24,58),(25,102),(26,99),(27,104),(28,101),(29,98),(30,103),(31,100),(32,97),(33,72),(34,69),(35,66),(36,71),(37,68),(38,65),(39,70),(40,67),(41,152),(42,149),(43,146),(44,151),(45,148),(46,145),(47,150),(48,147),(49,76),(50,73),(51,78),(52,75),(53,80),(54,77),(55,74),(56,79),(81,94),(82,91),(83,96),(84,93),(85,90),(86,95),(87,92),(88,89),(105,215),(106,212),(107,209),(108,214),(109,211),(110,216),(111,213),(112,210),(113,154),(114,159),(115,156),(116,153),(117,158),(118,155),(119,160),(120,157),(121,125),(123,127),(129,144),(130,141),(131,138),(132,143),(133,140),(134,137),(135,142),(136,139),(161,165),(163,167),(177,186),(178,191),(179,188),(180,185),(181,190),(182,187),(183,192),(184,189),(193,206),(194,203),(195,208),(196,205),(197,202),(198,207),(199,204),(200,201)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 8 | 8 | 28 | 56 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 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 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | C8.C22 | D4×D7 | D4×D7 | SD16⋊D7 | Q16⋊D7 |
| kernel | C7⋊C8.D4 | C4.Dic14 | C28.44D4 | C7×Q8⋊C4 | D14⋊2Q8 | C2×C8⋊D7 | C2×C7⋊Q16 | D14⋊3Q8 | C7⋊C8 | C2×Dic7 | C22×D7 | Q8⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 3 | 3 | 3 | 12 | 2 | 3 | 3 | 6 | 6 |
Matrix representation of C7⋊C8.D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 79 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 79 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 106 | 86 |
| 0 | 0 | 0 | 0 | 98 | 7 |
| 0 | 0 | 60 | 70 | 106 | 86 |
| 0 | 0 | 64 | 53 | 98 | 7 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 91 | 12 | 44 | 89 |
| 0 | 0 | 101 | 22 | 24 | 69 |
| 0 | 0 | 0 | 0 | 22 | 101 |
| 0 | 0 | 0 | 0 | 12 | 91 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 34 | 1 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,79,1,0,0,0,0,112,0,0,0,0,0,0,0,79,1,0,0,0,0,112,0],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,60,64,0,0,0,0,70,53,0,0,106,98,106,98,0,0,86,7,86,7],[0,1,0,0,0,0,112,0,0,0,0,0,0,0,91,101,0,0,0,0,12,22,0,0,0,0,44,24,22,12,0,0,89,69,101,91],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,34,0,0,0,0,0,1,0,0,0,0,0,0,112,34,0,0,0,0,0,1] >;
C7⋊C8.D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8.D_4
% in TeX
G:=Group("C7:C8.D4"); // GroupNames label
G:=SmallGroup(448,350);
// by ID
G=gap.SmallGroup(448,350);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,1094,135,184,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,b*a*b^-1=d*a*d=a^-1,a*c=c*a,c*b*c^-1=b^3,d*b*d=b^5,d*c*d=b^4*c^-1>;
// generators/relations