direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C8.12D4, C56.75D4, (C4×C8)⋊9C14, (C4×C56)⋊25C2, C8.12(C7×D4), C4.4(D4×C14), (C2×Q16)⋊5C14, (C2×D8).3C14, (C14×Q16)⋊19C2, (C14×D8).10C2, (C2×C28).367D4, C28.311(C2×D4), C4.4D4⋊4C14, (C2×SD16)⋊15C14, (C14×SD16)⋊32C2, C42.82(C2×C14), C14.131(C4○D8), C14.45(C4⋊1D4), (C2×C56).439C22, (C4×C28).366C22, (C2×C28).951C23, C22.116(D4×C14), (D4×C14).204C22, (Q8×C14).178C22, C2.18(C7×C4○D8), (C2×C4).57(C7×D4), C2.8(C7×C4⋊1D4), (C2×C8).81(C2×C14), (C2×D4).27(C2×C14), (C7×C4.4D4)⋊24C2, (C2×C14).672(C2×D4), (C2×Q8).22(C2×C14), (C2×C4).126(C22×C14), SmallGroup(448,903)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C8.12D4
G = < a,b,c,d | a7=b8=c4=1, d2=b4, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b3, dcd-1=b4c-1 >
Subgroups: 258 in 130 conjugacy classes, 58 normal (26 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C2×C8, D8, SD16, Q16, C2×D4, C2×Q8, C28, C28, C2×C14, C2×C14, C4×C8, C4.4D4, C2×D8, C2×SD16, C2×Q16, C56, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C8.12D4, C4×C28, C7×C22⋊C4, C2×C56, C7×D8, C7×SD16, C7×Q16, D4×C14, Q8×C14, C4×C56, C7×C4.4D4, C14×D8, C14×SD16, C14×Q16, C7×C8.12D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C2×C14, C4⋊1D4, C4○D8, C7×D4, C22×C14, C8.12D4, D4×C14, C7×C4⋊1D4, C7×C4○D8, C7×C8.12D4
►On 224 points
Generators in S224
(1 199 85 191 77 183 69)(2 200 86 192 78 184 70)(3 193 87 185 79 177 71)(4 194 88 186 80 178 72)(5 195 81 187 73 179 65)(6 196 82 188 74 180 66)(7 197 83 189 75 181 67)(8 198 84 190 76 182 68)(9 124 139 148 131 17 26)(10 125 140 149 132 18 27)(11 126 141 150 133 19 28)(12 127 142 151 134 20 29)(13 128 143 152 135 21 30)(14 121 144 145 136 22 31)(15 122 137 146 129 23 32)(16 123 138 147 130 24 25)(33 57 163 172 155 41 50)(34 58 164 173 156 42 51)(35 59 165 174 157 43 52)(36 60 166 175 158 44 53)(37 61 167 176 159 45 54)(38 62 168 169 160 46 55)(39 63 161 170 153 47 56)(40 64 162 171 154 48 49)(89 115 219 105 211 97 203)(90 116 220 106 212 98 204)(91 117 221 107 213 99 205)(92 118 222 108 214 100 206)(93 119 223 109 215 101 207)(94 120 224 110 216 102 208)(95 113 217 111 209 103 201)(96 114 218 112 210 104 202)
(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 40 123 93)(2 33 124 94)(3 34 125 95)(4 35 126 96)(5 36 127 89)(6 37 128 90)(7 38 121 91)(8 39 122 92)(9 208 70 50)(10 201 71 51)(11 202 72 52)(12 203 65 53)(13 204 66 54)(14 205 67 55)(15 206 68 56)(16 207 69 49)(17 216 78 155)(18 209 79 156)(19 210 80 157)(20 211 73 158)(21 212 74 159)(22 213 75 160)(23 214 76 153)(24 215 77 154)(25 101 183 48)(26 102 184 41)(27 103 177 42)(28 104 178 43)(29 97 179 44)(30 98 180 45)(31 99 181 46)(32 100 182 47)(57 139 120 200)(58 140 113 193)(59 141 114 194)(60 142 115 195)(61 143 116 196)(62 144 117 197)(63 137 118 198)(64 138 119 199)(81 166 151 219)(82 167 152 220)(83 168 145 221)(84 161 146 222)(85 162 147 223)(86 163 148 224)(87 164 149 217)(88 165 150 218)(105 187 175 134)(106 188 176 135)(107 189 169 136)(108 190 170 129)(109 191 171 130)(110 192 172 131)(111 185 173 132)(112 186 174 133)
(1 8 5 4)(2 3 6 7)(9 10 13 14)(11 16 15 12)(17 18 21 22)(19 24 23 20)(25 32 29 28)(26 27 30 31)(33 91 37 95)(34 94 38 90)(35 89 39 93)(36 92 40 96)(41 99 45 103)(42 102 46 98)(43 97 47 101)(44 100 48 104)(49 202 53 206)(50 205 54 201)(51 208 55 204)(52 203 56 207)(57 117 61 113)(58 120 62 116)(59 115 63 119)(60 118 64 114)(65 72 69 68)(66 67 70 71)(73 80 77 76)(74 75 78 79)(81 88 85 84)(82 83 86 87)(105 170 109 174)(106 173 110 169)(107 176 111 172)(108 171 112 175)(121 124 125 128)(122 127 126 123)(129 134 133 130)(131 132 135 136)(137 142 141 138)(139 140 143 144)(145 148 149 152)(146 151 150 147)(153 215 157 211)(154 210 158 214)(155 213 159 209)(156 216 160 212)(161 223 165 219)(162 218 166 222)(163 221 167 217)(164 224 168 220)(177 180 181 184)(178 183 182 179)(185 188 189 192)(186 191 190 187)(193 196 197 200)(194 199 198 195)
G:=sub<Sym(224)| (1,199,85,191,77,183,69)(2,200,86,192,78,184,70)(3,193,87,185,79,177,71)(4,194,88,186,80,178,72)(5,195,81,187,73,179,65)(6,196,82,188,74,180,66)(7,197,83,189,75,181,67)(8,198,84,190,76,182,68)(9,124,139,148,131,17,26)(10,125,140,149,132,18,27)(11,126,141,150,133,19,28)(12,127,142,151,134,20,29)(13,128,143,152,135,21,30)(14,121,144,145,136,22,31)(15,122,137,146,129,23,32)(16,123,138,147,130,24,25)(33,57,163,172,155,41,50)(34,58,164,173,156,42,51)(35,59,165,174,157,43,52)(36,60,166,175,158,44,53)(37,61,167,176,159,45,54)(38,62,168,169,160,46,55)(39,63,161,170,153,47,56)(40,64,162,171,154,48,49)(89,115,219,105,211,97,203)(90,116,220,106,212,98,204)(91,117,221,107,213,99,205)(92,118,222,108,214,100,206)(93,119,223,109,215,101,207)(94,120,224,110,216,102,208)(95,113,217,111,209,103,201)(96,114,218,112,210,104,202), (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), (1,40,123,93)(2,33,124,94)(3,34,125,95)(4,35,126,96)(5,36,127,89)(6,37,128,90)(7,38,121,91)(8,39,122,92)(9,208,70,50)(10,201,71,51)(11,202,72,52)(12,203,65,53)(13,204,66,54)(14,205,67,55)(15,206,68,56)(16,207,69,49)(17,216,78,155)(18,209,79,156)(19,210,80,157)(20,211,73,158)(21,212,74,159)(22,213,75,160)(23,214,76,153)(24,215,77,154)(25,101,183,48)(26,102,184,41)(27,103,177,42)(28,104,178,43)(29,97,179,44)(30,98,180,45)(31,99,181,46)(32,100,182,47)(57,139,120,200)(58,140,113,193)(59,141,114,194)(60,142,115,195)(61,143,116,196)(62,144,117,197)(63,137,118,198)(64,138,119,199)(81,166,151,219)(82,167,152,220)(83,168,145,221)(84,161,146,222)(85,162,147,223)(86,163,148,224)(87,164,149,217)(88,165,150,218)(105,187,175,134)(106,188,176,135)(107,189,169,136)(108,190,170,129)(109,191,171,130)(110,192,172,131)(111,185,173,132)(112,186,174,133), (1,8,5,4)(2,3,6,7)(9,10,13,14)(11,16,15,12)(17,18,21,22)(19,24,23,20)(25,32,29,28)(26,27,30,31)(33,91,37,95)(34,94,38,90)(35,89,39,93)(36,92,40,96)(41,99,45,103)(42,102,46,98)(43,97,47,101)(44,100,48,104)(49,202,53,206)(50,205,54,201)(51,208,55,204)(52,203,56,207)(57,117,61,113)(58,120,62,116)(59,115,63,119)(60,118,64,114)(65,72,69,68)(66,67,70,71)(73,80,77,76)(74,75,78,79)(81,88,85,84)(82,83,86,87)(105,170,109,174)(106,173,110,169)(107,176,111,172)(108,171,112,175)(121,124,125,128)(122,127,126,123)(129,134,133,130)(131,132,135,136)(137,142,141,138)(139,140,143,144)(145,148,149,152)(146,151,150,147)(153,215,157,211)(154,210,158,214)(155,213,159,209)(156,216,160,212)(161,223,165,219)(162,218,166,222)(163,221,167,217)(164,224,168,220)(177,180,181,184)(178,183,182,179)(185,188,189,192)(186,191,190,187)(193,196,197,200)(194,199,198,195)>;
G:=Group( (1,199,85,191,77,183,69)(2,200,86,192,78,184,70)(3,193,87,185,79,177,71)(4,194,88,186,80,178,72)(5,195,81,187,73,179,65)(6,196,82,188,74,180,66)(7,197,83,189,75,181,67)(8,198,84,190,76,182,68)(9,124,139,148,131,17,26)(10,125,140,149,132,18,27)(11,126,141,150,133,19,28)(12,127,142,151,134,20,29)(13,128,143,152,135,21,30)(14,121,144,145,136,22,31)(15,122,137,146,129,23,32)(16,123,138,147,130,24,25)(33,57,163,172,155,41,50)(34,58,164,173,156,42,51)(35,59,165,174,157,43,52)(36,60,166,175,158,44,53)(37,61,167,176,159,45,54)(38,62,168,169,160,46,55)(39,63,161,170,153,47,56)(40,64,162,171,154,48,49)(89,115,219,105,211,97,203)(90,116,220,106,212,98,204)(91,117,221,107,213,99,205)(92,118,222,108,214,100,206)(93,119,223,109,215,101,207)(94,120,224,110,216,102,208)(95,113,217,111,209,103,201)(96,114,218,112,210,104,202), (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), (1,40,123,93)(2,33,124,94)(3,34,125,95)(4,35,126,96)(5,36,127,89)(6,37,128,90)(7,38,121,91)(8,39,122,92)(9,208,70,50)(10,201,71,51)(11,202,72,52)(12,203,65,53)(13,204,66,54)(14,205,67,55)(15,206,68,56)(16,207,69,49)(17,216,78,155)(18,209,79,156)(19,210,80,157)(20,211,73,158)(21,212,74,159)(22,213,75,160)(23,214,76,153)(24,215,77,154)(25,101,183,48)(26,102,184,41)(27,103,177,42)(28,104,178,43)(29,97,179,44)(30,98,180,45)(31,99,181,46)(32,100,182,47)(57,139,120,200)(58,140,113,193)(59,141,114,194)(60,142,115,195)(61,143,116,196)(62,144,117,197)(63,137,118,198)(64,138,119,199)(81,166,151,219)(82,167,152,220)(83,168,145,221)(84,161,146,222)(85,162,147,223)(86,163,148,224)(87,164,149,217)(88,165,150,218)(105,187,175,134)(106,188,176,135)(107,189,169,136)(108,190,170,129)(109,191,171,130)(110,192,172,131)(111,185,173,132)(112,186,174,133), (1,8,5,4)(2,3,6,7)(9,10,13,14)(11,16,15,12)(17,18,21,22)(19,24,23,20)(25,32,29,28)(26,27,30,31)(33,91,37,95)(34,94,38,90)(35,89,39,93)(36,92,40,96)(41,99,45,103)(42,102,46,98)(43,97,47,101)(44,100,48,104)(49,202,53,206)(50,205,54,201)(51,208,55,204)(52,203,56,207)(57,117,61,113)(58,120,62,116)(59,115,63,119)(60,118,64,114)(65,72,69,68)(66,67,70,71)(73,80,77,76)(74,75,78,79)(81,88,85,84)(82,83,86,87)(105,170,109,174)(106,173,110,169)(107,176,111,172)(108,171,112,175)(121,124,125,128)(122,127,126,123)(129,134,133,130)(131,132,135,136)(137,142,141,138)(139,140,143,144)(145,148,149,152)(146,151,150,147)(153,215,157,211)(154,210,158,214)(155,213,159,209)(156,216,160,212)(161,223,165,219)(162,218,166,222)(163,221,167,217)(164,224,168,220)(177,180,181,184)(178,183,182,179)(185,188,189,192)(186,191,190,187)(193,196,197,200)(194,199,198,195) );
G=PermutationGroup([[(1,199,85,191,77,183,69),(2,200,86,192,78,184,70),(3,193,87,185,79,177,71),(4,194,88,186,80,178,72),(5,195,81,187,73,179,65),(6,196,82,188,74,180,66),(7,197,83,189,75,181,67),(8,198,84,190,76,182,68),(9,124,139,148,131,17,26),(10,125,140,149,132,18,27),(11,126,141,150,133,19,28),(12,127,142,151,134,20,29),(13,128,143,152,135,21,30),(14,121,144,145,136,22,31),(15,122,137,146,129,23,32),(16,123,138,147,130,24,25),(33,57,163,172,155,41,50),(34,58,164,173,156,42,51),(35,59,165,174,157,43,52),(36,60,166,175,158,44,53),(37,61,167,176,159,45,54),(38,62,168,169,160,46,55),(39,63,161,170,153,47,56),(40,64,162,171,154,48,49),(89,115,219,105,211,97,203),(90,116,220,106,212,98,204),(91,117,221,107,213,99,205),(92,118,222,108,214,100,206),(93,119,223,109,215,101,207),(94,120,224,110,216,102,208),(95,113,217,111,209,103,201),(96,114,218,112,210,104,202)], [(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)], [(1,40,123,93),(2,33,124,94),(3,34,125,95),(4,35,126,96),(5,36,127,89),(6,37,128,90),(7,38,121,91),(8,39,122,92),(9,208,70,50),(10,201,71,51),(11,202,72,52),(12,203,65,53),(13,204,66,54),(14,205,67,55),(15,206,68,56),(16,207,69,49),(17,216,78,155),(18,209,79,156),(19,210,80,157),(20,211,73,158),(21,212,74,159),(22,213,75,160),(23,214,76,153),(24,215,77,154),(25,101,183,48),(26,102,184,41),(27,103,177,42),(28,104,178,43),(29,97,179,44),(30,98,180,45),(31,99,181,46),(32,100,182,47),(57,139,120,200),(58,140,113,193),(59,141,114,194),(60,142,115,195),(61,143,116,196),(62,144,117,197),(63,137,118,198),(64,138,119,199),(81,166,151,219),(82,167,152,220),(83,168,145,221),(84,161,146,222),(85,162,147,223),(86,163,148,224),(87,164,149,217),(88,165,150,218),(105,187,175,134),(106,188,176,135),(107,189,169,136),(108,190,170,129),(109,191,171,130),(110,192,172,131),(111,185,173,132),(112,186,174,133)], [(1,8,5,4),(2,3,6,7),(9,10,13,14),(11,16,15,12),(17,18,21,22),(19,24,23,20),(25,32,29,28),(26,27,30,31),(33,91,37,95),(34,94,38,90),(35,89,39,93),(36,92,40,96),(41,99,45,103),(42,102,46,98),(43,97,47,101),(44,100,48,104),(49,202,53,206),(50,205,54,201),(51,208,55,204),(52,203,56,207),(57,117,61,113),(58,120,62,116),(59,115,63,119),(60,118,64,114),(65,72,69,68),(66,67,70,71),(73,80,77,76),(74,75,78,79),(81,88,85,84),(82,83,86,87),(105,170,109,174),(106,173,110,169),(107,176,111,172),(108,171,112,175),(121,124,125,128),(122,127,126,123),(129,134,133,130),(131,132,135,136),(137,142,141,138),(139,140,143,144),(145,148,149,152),(146,151,150,147),(153,215,157,211),(154,210,158,214),(155,213,159,209),(156,216,160,212),(161,223,165,219),(162,218,166,222),(163,221,167,217),(164,224,168,220),(177,180,181,184),(178,183,182,179),(185,188,189,192),(186,191,190,187),(193,196,197,200),(194,199,198,195)]])
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | 4H | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14R | 14S | ··· | 14AD | 28A | ··· | 28AJ | 28AK | ··· | 28AV | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 2 | ··· | 2 | 8 | 8 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 8 | ··· | 8 | 2 | ··· | 2 | 8 | ··· | 8 | 2 | ··· | 2 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C4○D8 | C7×D4 | C7×D4 | C7×C4○D8 |
| kernel | C7×C8.12D4 | C4×C56 | C7×C4.4D4 | C14×D8 | C14×SD16 | C14×Q16 | C8.12D4 | C4×C8 | C4.4D4 | C2×D8 | C2×SD16 | C2×Q16 | C56 | C2×C28 | C14 | C8 | C2×C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 6 | 6 | 12 | 6 | 12 | 6 | 4 | 2 | 8 | 24 | 12 | 48 |
Matrix representation of C7×C8.12D4 ►in GL4(𝔽113) generated by
| 109 | 0 | 0 | 0 |
| 0 | 109 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 100 | 13 | 0 | 0 |
| 100 | 100 | 0 | 0 |
| 0 | 0 | 100 | 13 |
| 0 | 0 | 100 | 100 |
| 0 | 15 | 0 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 13 | 100 | 0 | 0 |
| 100 | 100 | 0 | 0 |
| 0 | 0 | 13 | 100 |
| 0 | 0 | 100 | 100 |
G:=sub<GL(4,GF(113))| [109,0,0,0,0,109,0,0,0,0,1,0,0,0,0,1],[100,100,0,0,13,100,0,0,0,0,100,100,0,0,13,100],[0,98,0,0,15,0,0,0,0,0,15,0,0,0,0,15],[13,100,0,0,100,100,0,0,0,0,13,100,0,0,100,100] >;
C7×C8.12D4 in GAP, Magma, Sage, TeX
C_7\times C_8._{12}D_4 % in TeX
G:=Group("C7xC8.12D4"); // GroupNames label
G:=SmallGroup(448,903);
// by ID
G=gap.SmallGroup(448,903);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,813,400,2438,1780,9804,172]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=1,d^2=b^4,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^3,d*c*d^-1=b^4*c^-1>;
// generators/relations