direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C8⋊3D4, C56⋊21D4, C8⋊3(C7×D4), (C2×D8)⋊9C14, C8⋊C4⋊4C14, C4.5(D4×C14), (C14×D8)⋊23C2, C4⋊1D4⋊4C14, (C2×SD16)⋊3C14, (C2×C28).343D4, C28.312(C2×D4), C4.4D4⋊5C14, (C14×SD16)⋊14C2, C42.29(C2×C14), C14.46(C4⋊1D4), (C4×C28).271C22, (C2×C28).952C23, (C2×C56).275C22, C22.117(D4×C14), C14.147(C8⋊C22), (D4×C14).205C22, (Q8×C14).179C22, (C7×C8⋊C4)⋊13C2, (C2×C4).44(C7×D4), C2.9(C7×C4⋊1D4), (C7×C4⋊1D4)⋊14C2, (C2×C8).27(C2×C14), C2.22(C7×C8⋊C22), (C2×D4).28(C2×C14), (C7×C4.4D4)⋊25C2, (C2×C14).673(C2×D4), (C2×Q8).23(C2×C14), (C2×C4).127(C22×C14), SmallGroup(448,904)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C8⋊3D4
G = < a,b,c,d | a7=b8=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b5, dbd=b-1, dcd=c-1 >
Subgroups: 322 in 144 conjugacy classes, 58 normal (22 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, C2×D4, C2×D4, C2×D4, C2×Q8, C28, C28, C2×C14, C2×C14, C8⋊C4, C4.4D4, C4⋊1D4, C2×D8, C2×SD16, C56, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C8⋊3D4, C4×C28, C7×C22⋊C4, C2×C56, C7×D8, C7×SD16, D4×C14, D4×C14, D4×C14, Q8×C14, C7×C8⋊C4, C7×C4.4D4, C7×C4⋊1D4, C14×D8, C14×SD16, C7×C8⋊3D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C2×C14, C4⋊1D4, C8⋊C22, C7×D4, C22×C14, C8⋊3D4, D4×C14, C7×C4⋊1D4, C7×C8⋊C22, C7×C8⋊3D4
►On 224 points
Generators in S224
(1 43 147 35 139 27 131)(2 44 148 36 140 28 132)(3 45 149 37 141 29 133)(4 46 150 38 142 30 134)(5 47 151 39 143 31 135)(6 48 152 40 144 32 136)(7 41 145 33 137 25 129)(8 42 146 34 138 26 130)(9 58 162 50 154 20 127)(10 59 163 51 155 21 128)(11 60 164 52 156 22 121)(12 61 165 53 157 23 122)(13 62 166 54 158 24 123)(14 63 167 55 159 17 124)(15 64 168 56 160 18 125)(16 57 161 49 153 19 126)(65 169 193 81 185 73 177)(66 170 194 82 186 74 178)(67 171 195 83 187 75 179)(68 172 196 84 188 76 180)(69 173 197 85 189 77 181)(70 174 198 86 190 78 182)(71 175 199 87 191 79 183)(72 176 200 88 192 80 184)(89 119 217 105 209 97 201)(90 120 218 106 210 98 202)(91 113 219 107 211 99 203)(92 114 220 108 212 100 204)(93 115 221 109 213 101 205)(94 116 222 110 214 102 206)(95 117 223 111 215 103 207)(96 118 224 112 216 104 208)
(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 95 175 155)(2 92 176 160)(3 89 169 157)(4 94 170 154)(5 91 171 159)(6 96 172 156)(7 93 173 153)(8 90 174 158)(9 38 110 186)(10 35 111 191)(11 40 112 188)(12 37 105 185)(13 34 106 190)(14 39 107 187)(15 36 108 192)(16 33 109 189)(17 47 113 195)(18 44 114 200)(19 41 115 197)(20 46 116 194)(21 43 117 199)(22 48 118 196)(23 45 119 193)(24 42 120 198)(25 101 181 161)(26 98 182 166)(27 103 183 163)(28 100 184 168)(29 97 177 165)(30 102 178 162)(31 99 179 167)(32 104 180 164)(49 129 205 69)(50 134 206 66)(51 131 207 71)(52 136 208 68)(53 133 201 65)(54 130 202 70)(55 135 203 67)(56 132 204 72)(57 137 213 77)(58 142 214 74)(59 139 215 79)(60 144 216 76)(61 141 209 73)(62 138 210 78)(63 143 211 75)(64 140 212 80)(81 122 149 217)(82 127 150 222)(83 124 151 219)(84 121 152 224)(85 126 145 221)(86 123 146 218)(87 128 147 223)(88 125 148 220)
(1 155)(2 154)(3 153)(4 160)(5 159)(6 158)(7 157)(8 156)(9 36)(10 35)(11 34)(12 33)(13 40)(14 39)(15 38)(16 37)(17 47)(18 46)(19 45)(20 44)(21 43)(22 42)(23 41)(24 48)(25 165)(26 164)(27 163)(28 162)(29 161)(30 168)(31 167)(32 166)(49 133)(50 132)(51 131)(52 130)(53 129)(54 136)(55 135)(56 134)(57 141)(58 140)(59 139)(60 138)(61 137)(62 144)(63 143)(64 142)(65 205)(66 204)(67 203)(68 202)(69 201)(70 208)(71 207)(72 206)(73 213)(74 212)(75 211)(76 210)(77 209)(78 216)(79 215)(80 214)(81 221)(82 220)(83 219)(84 218)(85 217)(86 224)(87 223)(88 222)(89 173)(90 172)(91 171)(92 170)(93 169)(94 176)(95 175)(96 174)(97 181)(98 180)(99 179)(100 178)(101 177)(102 184)(103 183)(104 182)(105 189)(106 188)(107 187)(108 186)(109 185)(110 192)(111 191)(112 190)(113 195)(114 194)(115 193)(116 200)(117 199)(118 198)(119 197)(120 196)(121 146)(122 145)(123 152)(124 151)(125 150)(126 149)(127 148)(128 147)
G:=sub<Sym(224)| (1,43,147,35,139,27,131)(2,44,148,36,140,28,132)(3,45,149,37,141,29,133)(4,46,150,38,142,30,134)(5,47,151,39,143,31,135)(6,48,152,40,144,32,136)(7,41,145,33,137,25,129)(8,42,146,34,138,26,130)(9,58,162,50,154,20,127)(10,59,163,51,155,21,128)(11,60,164,52,156,22,121)(12,61,165,53,157,23,122)(13,62,166,54,158,24,123)(14,63,167,55,159,17,124)(15,64,168,56,160,18,125)(16,57,161,49,153,19,126)(65,169,193,81,185,73,177)(66,170,194,82,186,74,178)(67,171,195,83,187,75,179)(68,172,196,84,188,76,180)(69,173,197,85,189,77,181)(70,174,198,86,190,78,182)(71,175,199,87,191,79,183)(72,176,200,88,192,80,184)(89,119,217,105,209,97,201)(90,120,218,106,210,98,202)(91,113,219,107,211,99,203)(92,114,220,108,212,100,204)(93,115,221,109,213,101,205)(94,116,222,110,214,102,206)(95,117,223,111,215,103,207)(96,118,224,112,216,104,208), (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), (1,95,175,155)(2,92,176,160)(3,89,169,157)(4,94,170,154)(5,91,171,159)(6,96,172,156)(7,93,173,153)(8,90,174,158)(9,38,110,186)(10,35,111,191)(11,40,112,188)(12,37,105,185)(13,34,106,190)(14,39,107,187)(15,36,108,192)(16,33,109,189)(17,47,113,195)(18,44,114,200)(19,41,115,197)(20,46,116,194)(21,43,117,199)(22,48,118,196)(23,45,119,193)(24,42,120,198)(25,101,181,161)(26,98,182,166)(27,103,183,163)(28,100,184,168)(29,97,177,165)(30,102,178,162)(31,99,179,167)(32,104,180,164)(49,129,205,69)(50,134,206,66)(51,131,207,71)(52,136,208,68)(53,133,201,65)(54,130,202,70)(55,135,203,67)(56,132,204,72)(57,137,213,77)(58,142,214,74)(59,139,215,79)(60,144,216,76)(61,141,209,73)(62,138,210,78)(63,143,211,75)(64,140,212,80)(81,122,149,217)(82,127,150,222)(83,124,151,219)(84,121,152,224)(85,126,145,221)(86,123,146,218)(87,128,147,223)(88,125,148,220), (1,155)(2,154)(3,153)(4,160)(5,159)(6,158)(7,157)(8,156)(9,36)(10,35)(11,34)(12,33)(13,40)(14,39)(15,38)(16,37)(17,47)(18,46)(19,45)(20,44)(21,43)(22,42)(23,41)(24,48)(25,165)(26,164)(27,163)(28,162)(29,161)(30,168)(31,167)(32,166)(49,133)(50,132)(51,131)(52,130)(53,129)(54,136)(55,135)(56,134)(57,141)(58,140)(59,139)(60,138)(61,137)(62,144)(63,143)(64,142)(65,205)(66,204)(67,203)(68,202)(69,201)(70,208)(71,207)(72,206)(73,213)(74,212)(75,211)(76,210)(77,209)(78,216)(79,215)(80,214)(81,221)(82,220)(83,219)(84,218)(85,217)(86,224)(87,223)(88,222)(89,173)(90,172)(91,171)(92,170)(93,169)(94,176)(95,175)(96,174)(97,181)(98,180)(99,179)(100,178)(101,177)(102,184)(103,183)(104,182)(105,189)(106,188)(107,187)(108,186)(109,185)(110,192)(111,191)(112,190)(113,195)(114,194)(115,193)(116,200)(117,199)(118,198)(119,197)(120,196)(121,146)(122,145)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)>;
G:=Group( (1,43,147,35,139,27,131)(2,44,148,36,140,28,132)(3,45,149,37,141,29,133)(4,46,150,38,142,30,134)(5,47,151,39,143,31,135)(6,48,152,40,144,32,136)(7,41,145,33,137,25,129)(8,42,146,34,138,26,130)(9,58,162,50,154,20,127)(10,59,163,51,155,21,128)(11,60,164,52,156,22,121)(12,61,165,53,157,23,122)(13,62,166,54,158,24,123)(14,63,167,55,159,17,124)(15,64,168,56,160,18,125)(16,57,161,49,153,19,126)(65,169,193,81,185,73,177)(66,170,194,82,186,74,178)(67,171,195,83,187,75,179)(68,172,196,84,188,76,180)(69,173,197,85,189,77,181)(70,174,198,86,190,78,182)(71,175,199,87,191,79,183)(72,176,200,88,192,80,184)(89,119,217,105,209,97,201)(90,120,218,106,210,98,202)(91,113,219,107,211,99,203)(92,114,220,108,212,100,204)(93,115,221,109,213,101,205)(94,116,222,110,214,102,206)(95,117,223,111,215,103,207)(96,118,224,112,216,104,208), (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), (1,95,175,155)(2,92,176,160)(3,89,169,157)(4,94,170,154)(5,91,171,159)(6,96,172,156)(7,93,173,153)(8,90,174,158)(9,38,110,186)(10,35,111,191)(11,40,112,188)(12,37,105,185)(13,34,106,190)(14,39,107,187)(15,36,108,192)(16,33,109,189)(17,47,113,195)(18,44,114,200)(19,41,115,197)(20,46,116,194)(21,43,117,199)(22,48,118,196)(23,45,119,193)(24,42,120,198)(25,101,181,161)(26,98,182,166)(27,103,183,163)(28,100,184,168)(29,97,177,165)(30,102,178,162)(31,99,179,167)(32,104,180,164)(49,129,205,69)(50,134,206,66)(51,131,207,71)(52,136,208,68)(53,133,201,65)(54,130,202,70)(55,135,203,67)(56,132,204,72)(57,137,213,77)(58,142,214,74)(59,139,215,79)(60,144,216,76)(61,141,209,73)(62,138,210,78)(63,143,211,75)(64,140,212,80)(81,122,149,217)(82,127,150,222)(83,124,151,219)(84,121,152,224)(85,126,145,221)(86,123,146,218)(87,128,147,223)(88,125,148,220), (1,155)(2,154)(3,153)(4,160)(5,159)(6,158)(7,157)(8,156)(9,36)(10,35)(11,34)(12,33)(13,40)(14,39)(15,38)(16,37)(17,47)(18,46)(19,45)(20,44)(21,43)(22,42)(23,41)(24,48)(25,165)(26,164)(27,163)(28,162)(29,161)(30,168)(31,167)(32,166)(49,133)(50,132)(51,131)(52,130)(53,129)(54,136)(55,135)(56,134)(57,141)(58,140)(59,139)(60,138)(61,137)(62,144)(63,143)(64,142)(65,205)(66,204)(67,203)(68,202)(69,201)(70,208)(71,207)(72,206)(73,213)(74,212)(75,211)(76,210)(77,209)(78,216)(79,215)(80,214)(81,221)(82,220)(83,219)(84,218)(85,217)(86,224)(87,223)(88,222)(89,173)(90,172)(91,171)(92,170)(93,169)(94,176)(95,175)(96,174)(97,181)(98,180)(99,179)(100,178)(101,177)(102,184)(103,183)(104,182)(105,189)(106,188)(107,187)(108,186)(109,185)(110,192)(111,191)(112,190)(113,195)(114,194)(115,193)(116,200)(117,199)(118,198)(119,197)(120,196)(121,146)(122,145)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147) );
G=PermutationGroup([[(1,43,147,35,139,27,131),(2,44,148,36,140,28,132),(3,45,149,37,141,29,133),(4,46,150,38,142,30,134),(5,47,151,39,143,31,135),(6,48,152,40,144,32,136),(7,41,145,33,137,25,129),(8,42,146,34,138,26,130),(9,58,162,50,154,20,127),(10,59,163,51,155,21,128),(11,60,164,52,156,22,121),(12,61,165,53,157,23,122),(13,62,166,54,158,24,123),(14,63,167,55,159,17,124),(15,64,168,56,160,18,125),(16,57,161,49,153,19,126),(65,169,193,81,185,73,177),(66,170,194,82,186,74,178),(67,171,195,83,187,75,179),(68,172,196,84,188,76,180),(69,173,197,85,189,77,181),(70,174,198,86,190,78,182),(71,175,199,87,191,79,183),(72,176,200,88,192,80,184),(89,119,217,105,209,97,201),(90,120,218,106,210,98,202),(91,113,219,107,211,99,203),(92,114,220,108,212,100,204),(93,115,221,109,213,101,205),(94,116,222,110,214,102,206),(95,117,223,111,215,103,207),(96,118,224,112,216,104,208)], [(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)], [(1,95,175,155),(2,92,176,160),(3,89,169,157),(4,94,170,154),(5,91,171,159),(6,96,172,156),(7,93,173,153),(8,90,174,158),(9,38,110,186),(10,35,111,191),(11,40,112,188),(12,37,105,185),(13,34,106,190),(14,39,107,187),(15,36,108,192),(16,33,109,189),(17,47,113,195),(18,44,114,200),(19,41,115,197),(20,46,116,194),(21,43,117,199),(22,48,118,196),(23,45,119,193),(24,42,120,198),(25,101,181,161),(26,98,182,166),(27,103,183,163),(28,100,184,168),(29,97,177,165),(30,102,178,162),(31,99,179,167),(32,104,180,164),(49,129,205,69),(50,134,206,66),(51,131,207,71),(52,136,208,68),(53,133,201,65),(54,130,202,70),(55,135,203,67),(56,132,204,72),(57,137,213,77),(58,142,214,74),(59,139,215,79),(60,144,216,76),(61,141,209,73),(62,138,210,78),(63,143,211,75),(64,140,212,80),(81,122,149,217),(82,127,150,222),(83,124,151,219),(84,121,152,224),(85,126,145,221),(86,123,146,218),(87,128,147,223),(88,125,148,220)], [(1,155),(2,154),(3,153),(4,160),(5,159),(6,158),(7,157),(8,156),(9,36),(10,35),(11,34),(12,33),(13,40),(14,39),(15,38),(16,37),(17,47),(18,46),(19,45),(20,44),(21,43),(22,42),(23,41),(24,48),(25,165),(26,164),(27,163),(28,162),(29,161),(30,168),(31,167),(32,166),(49,133),(50,132),(51,131),(52,130),(53,129),(54,136),(55,135),(56,134),(57,141),(58,140),(59,139),(60,138),(61,137),(62,144),(63,143),(64,142),(65,205),(66,204),(67,203),(68,202),(69,201),(70,208),(71,207),(72,206),(73,213),(74,212),(75,211),(76,210),(77,209),(78,216),(79,215),(80,214),(81,221),(82,220),(83,219),(84,218),(85,217),(86,224),(87,223),(88,222),(89,173),(90,172),(91,171),(92,170),(93,169),(94,176),(95,175),(96,174),(97,181),(98,180),(99,179),(100,178),(101,177),(102,184),(103,183),(104,182),(105,189),(106,188),(107,187),(108,186),(109,185),(110,192),(111,191),(112,190),(113,195),(114,194),(115,193),(116,200),(117,199),(118,198),(119,197),(120,196),(121,146),(122,145),(123,152),(124,151),(125,150),(126,149),(127,148),(128,147)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14AJ | 28A | ··· | 28L | 28M | ··· | 28X | 28Y | ··· | 28AD | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 8 | 2 | 2 | 4 | 4 | 8 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 8 | ··· | 8 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C7×D4 | C7×D4 | C8⋊C22 | C7×C8⋊C22 |
| kernel | C7×C8⋊3D4 | C7×C8⋊C4 | C7×C4.4D4 | C7×C4⋊1D4 | C14×D8 | C14×SD16 | C8⋊3D4 | C8⋊C4 | C4.4D4 | C4⋊1D4 | C2×D8 | C2×SD16 | C56 | C2×C28 | C8 | C2×C4 | C14 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 6 | 6 | 6 | 6 | 12 | 12 | 4 | 2 | 24 | 12 | 2 | 12 |
Matrix representation of C7×C8⋊3D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 30 | 0 | 0 | 0 |
| 0 | 0 | 0 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 0 |
| 0 | 0 | 0 | 0 | 0 | 30 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 109 | 50 | 109 | 109 |
| 0 | 0 | 86 | 50 | 109 | 0 |
| 0 | 0 | 0 | 90 | 90 | 27 |
| 0 | 0 | 90 | 90 | 90 | 90 |
| 65 | 111 | 0 | 0 | 0 | 0 |
| 79 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 111 | 0 |
| 0 | 0 | 0 | 0 | 112 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 112 | 1 | 0 |
| 65 | 111 | 0 | 0 | 0 | 0 |
| 78 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 111 | 0 |
| 0 | 0 | 112 | 0 | 112 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 112 | 1 | 0 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,30,0,0,0,0,0,0,30,0,0,0,0,0,0,30,0,0,0,0,0,0,30],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,109,86,0,90,0,0,50,50,90,90,0,0,109,109,90,90,0,0,109,0,27,90],[65,79,0,0,0,0,111,48,0,0,0,0,0,0,112,0,1,1,0,0,0,0,0,112,0,0,111,112,1,1,0,0,0,1,0,0],[65,78,0,0,0,0,111,48,0,0,0,0,0,0,112,112,0,1,0,0,0,0,0,112,0,0,111,112,1,1,0,0,0,112,0,0] >;
C7×C8⋊3D4 in GAP, Magma, Sage, TeX
C_7\times C_8\rtimes_3D_4
% in TeX
G:=Group("C7xC8:3D4"); // GroupNames label
G:=SmallGroup(448,904);
// by ID
G=gap.SmallGroup(448,904);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,813,400,2438,2403,604,9804,172]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^5,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations