direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C8.2D4, C56.52D4, C4⋊Q8⋊8C14, C8.2(C7×D4), C8⋊C4⋊5C14, C4.6(D4×C14), (C2×Q16)⋊9C14, (C14×Q16)⋊23C2, C28.313(C2×D4), (C2×C28).344D4, C42.30(C2×C14), (C2×SD16).2C14, (C14×SD16).5C2, C4.4D4.7C14, C14.47(C4⋊1D4), (C2×C56).276C22, (C2×C28).953C23, (C4×C28).272C22, C22.118(D4×C14), (D4×C14).206C22, (Q8×C14).180C22, C14.147(C8.C22), (C7×C4⋊Q8)⋊29C2, (C7×C8⋊C4)⋊14C2, (C2×C4).45(C7×D4), (C2×C8).28(C2×C14), C2.10(C7×C4⋊1D4), (C2×D4).29(C2×C14), (C2×C14).674(C2×D4), (C2×Q8).24(C2×C14), C2.22(C7×C8.C22), (C7×C4.4D4).16C2, (C2×C4).128(C22×C14), SmallGroup(448,905)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C8.2D4
G = < a,b,c,d | a7=b8=d2=1, c4=b4, ab=ba, ac=ca, ad=da, cbc-1=b5, dbd=b3, dcd=c3 >
Subgroups: 226 in 124 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, C4⋊C4, C2×C8, SD16, Q16, C2×D4, C2×Q8, C2×Q8, C28, C28, C2×C14, C2×C14, C8⋊C4, C4.4D4, C4⋊Q8, C2×SD16, C2×Q16, C56, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C8.2D4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C56, C7×SD16, C7×Q16, D4×C14, Q8×C14, Q8×C14, C7×C8⋊C4, C7×C4.4D4, C7×C4⋊Q8, C14×SD16, C14×Q16, C7×C8.2D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C2×C14, C4⋊1D4, C8.C22, C7×D4, C22×C14, C8.2D4, D4×C14, C7×C4⋊1D4, C7×C8.C22, C7×C8.2D4
►On 224 points
Generators in S224
(1 130 74 122 66 114 58)(2 131 75 123 67 115 59)(3 132 76 124 68 116 60)(4 133 77 125 69 117 61)(5 134 78 126 70 118 62)(6 135 79 127 71 119 63)(7 136 80 128 72 120 64)(8 129 73 121 65 113 57)(9 163 195 25 187 17 179)(10 164 196 26 188 18 180)(11 165 197 27 189 19 181)(12 166 198 28 190 20 182)(13 167 199 29 191 21 183)(14 168 200 30 192 22 184)(15 161 193 31 185 23 177)(16 162 194 32 186 24 178)(33 176 219 49 211 41 203)(34 169 220 50 212 42 204)(35 170 221 51 213 43 205)(36 171 222 52 214 44 206)(37 172 223 53 215 45 207)(38 173 224 54 216 46 208)(39 174 217 55 209 47 201)(40 175 218 56 210 48 202)(81 111 159 103 151 95 142)(82 112 160 104 152 96 143)(83 105 153 97 145 89 144)(84 106 154 98 146 90 137)(85 107 155 99 147 91 138)(86 108 156 100 148 92 139)(87 109 157 101 149 93 140)(88 110 158 102 150 94 141)
(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 96 39 166 5 92 35 162)(2 93 40 163 6 89 36 167)(3 90 33 168 7 94 37 164)(4 95 34 165 8 91 38 161)(9 63 145 206 13 59 149 202)(10 60 146 203 14 64 150 207)(11 57 147 208 15 61 151 204)(12 62 148 205 16 58 152 201)(17 71 153 214 21 67 157 210)(18 68 154 211 22 72 158 215)(19 65 155 216 23 69 159 212)(20 70 156 213 24 66 160 209)(25 79 83 222 29 75 87 218)(26 76 84 219 30 80 88 223)(27 73 85 224 31 77 81 220)(28 78 86 221 32 74 82 217)(41 184 120 102 45 180 116 98)(42 181 113 99 46 177 117 103)(43 178 114 104 47 182 118 100)(44 183 115 101 48 179 119 97)(49 192 128 110 53 188 124 106)(50 189 121 107 54 185 125 111)(51 186 122 112 55 190 126 108)(52 191 123 109 56 187 127 105)(129 138 173 193 133 142 169 197)(130 143 174 198 134 139 170 194)(131 140 175 195 135 144 171 199)(132 137 176 200 136 141 172 196)
(1 39)(2 34)(3 37)(4 40)(5 35)(6 38)(7 33)(8 36)(9 11)(10 14)(13 15)(17 19)(18 22)(21 23)(25 27)(26 30)(29 31)(41 120)(42 115)(43 118)(44 113)(45 116)(46 119)(47 114)(48 117)(49 128)(50 123)(51 126)(52 121)(53 124)(54 127)(55 122)(56 125)(57 206)(58 201)(59 204)(60 207)(61 202)(62 205)(63 208)(64 203)(65 214)(66 209)(67 212)(68 215)(69 210)(70 213)(71 216)(72 211)(73 222)(74 217)(75 220)(76 223)(77 218)(78 221)(79 224)(80 219)(81 83)(82 86)(85 87)(89 95)(91 93)(92 96)(97 103)(99 101)(100 104)(105 111)(107 109)(108 112)(129 171)(130 174)(131 169)(132 172)(133 175)(134 170)(135 173)(136 176)(138 140)(139 143)(142 144)(145 151)(147 149)(148 152)(153 159)(155 157)(156 160)(161 167)(163 165)(164 168)(177 183)(179 181)(180 184)(185 191)(187 189)(188 192)(193 199)(195 197)(196 200)
G:=sub<Sym(224)| (1,130,74,122,66,114,58)(2,131,75,123,67,115,59)(3,132,76,124,68,116,60)(4,133,77,125,69,117,61)(5,134,78,126,70,118,62)(6,135,79,127,71,119,63)(7,136,80,128,72,120,64)(8,129,73,121,65,113,57)(9,163,195,25,187,17,179)(10,164,196,26,188,18,180)(11,165,197,27,189,19,181)(12,166,198,28,190,20,182)(13,167,199,29,191,21,183)(14,168,200,30,192,22,184)(15,161,193,31,185,23,177)(16,162,194,32,186,24,178)(33,176,219,49,211,41,203)(34,169,220,50,212,42,204)(35,170,221,51,213,43,205)(36,171,222,52,214,44,206)(37,172,223,53,215,45,207)(38,173,224,54,216,46,208)(39,174,217,55,209,47,201)(40,175,218,56,210,48,202)(81,111,159,103,151,95,142)(82,112,160,104,152,96,143)(83,105,153,97,145,89,144)(84,106,154,98,146,90,137)(85,107,155,99,147,91,138)(86,108,156,100,148,92,139)(87,109,157,101,149,93,140)(88,110,158,102,150,94,141), (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), (1,96,39,166,5,92,35,162)(2,93,40,163,6,89,36,167)(3,90,33,168,7,94,37,164)(4,95,34,165,8,91,38,161)(9,63,145,206,13,59,149,202)(10,60,146,203,14,64,150,207)(11,57,147,208,15,61,151,204)(12,62,148,205,16,58,152,201)(17,71,153,214,21,67,157,210)(18,68,154,211,22,72,158,215)(19,65,155,216,23,69,159,212)(20,70,156,213,24,66,160,209)(25,79,83,222,29,75,87,218)(26,76,84,219,30,80,88,223)(27,73,85,224,31,77,81,220)(28,78,86,221,32,74,82,217)(41,184,120,102,45,180,116,98)(42,181,113,99,46,177,117,103)(43,178,114,104,47,182,118,100)(44,183,115,101,48,179,119,97)(49,192,128,110,53,188,124,106)(50,189,121,107,54,185,125,111)(51,186,122,112,55,190,126,108)(52,191,123,109,56,187,127,105)(129,138,173,193,133,142,169,197)(130,143,174,198,134,139,170,194)(131,140,175,195,135,144,171,199)(132,137,176,200,136,141,172,196), (1,39)(2,34)(3,37)(4,40)(5,35)(6,38)(7,33)(8,36)(9,11)(10,14)(13,15)(17,19)(18,22)(21,23)(25,27)(26,30)(29,31)(41,120)(42,115)(43,118)(44,113)(45,116)(46,119)(47,114)(48,117)(49,128)(50,123)(51,126)(52,121)(53,124)(54,127)(55,122)(56,125)(57,206)(58,201)(59,204)(60,207)(61,202)(62,205)(63,208)(64,203)(65,214)(66,209)(67,212)(68,215)(69,210)(70,213)(71,216)(72,211)(73,222)(74,217)(75,220)(76,223)(77,218)(78,221)(79,224)(80,219)(81,83)(82,86)(85,87)(89,95)(91,93)(92,96)(97,103)(99,101)(100,104)(105,111)(107,109)(108,112)(129,171)(130,174)(131,169)(132,172)(133,175)(134,170)(135,173)(136,176)(138,140)(139,143)(142,144)(145,151)(147,149)(148,152)(153,159)(155,157)(156,160)(161,167)(163,165)(164,168)(177,183)(179,181)(180,184)(185,191)(187,189)(188,192)(193,199)(195,197)(196,200)>;
G:=Group( (1,130,74,122,66,114,58)(2,131,75,123,67,115,59)(3,132,76,124,68,116,60)(4,133,77,125,69,117,61)(5,134,78,126,70,118,62)(6,135,79,127,71,119,63)(7,136,80,128,72,120,64)(8,129,73,121,65,113,57)(9,163,195,25,187,17,179)(10,164,196,26,188,18,180)(11,165,197,27,189,19,181)(12,166,198,28,190,20,182)(13,167,199,29,191,21,183)(14,168,200,30,192,22,184)(15,161,193,31,185,23,177)(16,162,194,32,186,24,178)(33,176,219,49,211,41,203)(34,169,220,50,212,42,204)(35,170,221,51,213,43,205)(36,171,222,52,214,44,206)(37,172,223,53,215,45,207)(38,173,224,54,216,46,208)(39,174,217,55,209,47,201)(40,175,218,56,210,48,202)(81,111,159,103,151,95,142)(82,112,160,104,152,96,143)(83,105,153,97,145,89,144)(84,106,154,98,146,90,137)(85,107,155,99,147,91,138)(86,108,156,100,148,92,139)(87,109,157,101,149,93,140)(88,110,158,102,150,94,141), (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), (1,96,39,166,5,92,35,162)(2,93,40,163,6,89,36,167)(3,90,33,168,7,94,37,164)(4,95,34,165,8,91,38,161)(9,63,145,206,13,59,149,202)(10,60,146,203,14,64,150,207)(11,57,147,208,15,61,151,204)(12,62,148,205,16,58,152,201)(17,71,153,214,21,67,157,210)(18,68,154,211,22,72,158,215)(19,65,155,216,23,69,159,212)(20,70,156,213,24,66,160,209)(25,79,83,222,29,75,87,218)(26,76,84,219,30,80,88,223)(27,73,85,224,31,77,81,220)(28,78,86,221,32,74,82,217)(41,184,120,102,45,180,116,98)(42,181,113,99,46,177,117,103)(43,178,114,104,47,182,118,100)(44,183,115,101,48,179,119,97)(49,192,128,110,53,188,124,106)(50,189,121,107,54,185,125,111)(51,186,122,112,55,190,126,108)(52,191,123,109,56,187,127,105)(129,138,173,193,133,142,169,197)(130,143,174,198,134,139,170,194)(131,140,175,195,135,144,171,199)(132,137,176,200,136,141,172,196), (1,39)(2,34)(3,37)(4,40)(5,35)(6,38)(7,33)(8,36)(9,11)(10,14)(13,15)(17,19)(18,22)(21,23)(25,27)(26,30)(29,31)(41,120)(42,115)(43,118)(44,113)(45,116)(46,119)(47,114)(48,117)(49,128)(50,123)(51,126)(52,121)(53,124)(54,127)(55,122)(56,125)(57,206)(58,201)(59,204)(60,207)(61,202)(62,205)(63,208)(64,203)(65,214)(66,209)(67,212)(68,215)(69,210)(70,213)(71,216)(72,211)(73,222)(74,217)(75,220)(76,223)(77,218)(78,221)(79,224)(80,219)(81,83)(82,86)(85,87)(89,95)(91,93)(92,96)(97,103)(99,101)(100,104)(105,111)(107,109)(108,112)(129,171)(130,174)(131,169)(132,172)(133,175)(134,170)(135,173)(136,176)(138,140)(139,143)(142,144)(145,151)(147,149)(148,152)(153,159)(155,157)(156,160)(161,167)(163,165)(164,168)(177,183)(179,181)(180,184)(185,191)(187,189)(188,192)(193,199)(195,197)(196,200) );
G=PermutationGroup([[(1,130,74,122,66,114,58),(2,131,75,123,67,115,59),(3,132,76,124,68,116,60),(4,133,77,125,69,117,61),(5,134,78,126,70,118,62),(6,135,79,127,71,119,63),(7,136,80,128,72,120,64),(8,129,73,121,65,113,57),(9,163,195,25,187,17,179),(10,164,196,26,188,18,180),(11,165,197,27,189,19,181),(12,166,198,28,190,20,182),(13,167,199,29,191,21,183),(14,168,200,30,192,22,184),(15,161,193,31,185,23,177),(16,162,194,32,186,24,178),(33,176,219,49,211,41,203),(34,169,220,50,212,42,204),(35,170,221,51,213,43,205),(36,171,222,52,214,44,206),(37,172,223,53,215,45,207),(38,173,224,54,216,46,208),(39,174,217,55,209,47,201),(40,175,218,56,210,48,202),(81,111,159,103,151,95,142),(82,112,160,104,152,96,143),(83,105,153,97,145,89,144),(84,106,154,98,146,90,137),(85,107,155,99,147,91,138),(86,108,156,100,148,92,139),(87,109,157,101,149,93,140),(88,110,158,102,150,94,141)], [(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)], [(1,96,39,166,5,92,35,162),(2,93,40,163,6,89,36,167),(3,90,33,168,7,94,37,164),(4,95,34,165,8,91,38,161),(9,63,145,206,13,59,149,202),(10,60,146,203,14,64,150,207),(11,57,147,208,15,61,151,204),(12,62,148,205,16,58,152,201),(17,71,153,214,21,67,157,210),(18,68,154,211,22,72,158,215),(19,65,155,216,23,69,159,212),(20,70,156,213,24,66,160,209),(25,79,83,222,29,75,87,218),(26,76,84,219,30,80,88,223),(27,73,85,224,31,77,81,220),(28,78,86,221,32,74,82,217),(41,184,120,102,45,180,116,98),(42,181,113,99,46,177,117,103),(43,178,114,104,47,182,118,100),(44,183,115,101,48,179,119,97),(49,192,128,110,53,188,124,106),(50,189,121,107,54,185,125,111),(51,186,122,112,55,190,126,108),(52,191,123,109,56,187,127,105),(129,138,173,193,133,142,169,197),(130,143,174,198,134,139,170,194),(131,140,175,195,135,144,171,199),(132,137,176,200,136,141,172,196)], [(1,39),(2,34),(3,37),(4,40),(5,35),(6,38),(7,33),(8,36),(9,11),(10,14),(13,15),(17,19),(18,22),(21,23),(25,27),(26,30),(29,31),(41,120),(42,115),(43,118),(44,113),(45,116),(46,119),(47,114),(48,117),(49,128),(50,123),(51,126),(52,121),(53,124),(54,127),(55,122),(56,125),(57,206),(58,201),(59,204),(60,207),(61,202),(62,205),(63,208),(64,203),(65,214),(66,209),(67,212),(68,215),(69,210),(70,213),(71,216),(72,211),(73,222),(74,217),(75,220),(76,223),(77,218),(78,221),(79,224),(80,219),(81,83),(82,86),(85,87),(89,95),(91,93),(92,96),(97,103),(99,101),(100,104),(105,111),(107,109),(108,112),(129,171),(130,174),(131,169),(132,172),(133,175),(134,170),(135,173),(136,176),(138,140),(139,143),(142,144),(145,151),(147,149),(148,152),(153,159),(155,157),(156,160),(161,167),(163,165),(164,168),(177,183),(179,181),(180,184),(185,191),(187,189),(188,192),(193,199),(195,197),(196,200)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14X | 28A | ··· | 28L | 28M | ··· | 28X | 28Y | ··· | 28AP | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 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 | 2 | 2 | 4 | 4 | 8 | 8 | 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×C8.2D4 | C7×C8⋊C4 | C7×C4.4D4 | C7×C4⋊Q8 | C14×SD16 | C14×Q16 | C8.2D4 | C8⋊C4 | C4.4D4 | C4⋊Q8 | C2×SD16 | C2×Q16 | 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×C8.2D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 109 | 0 | 0 | 0 |
| 0 | 0 | 0 | 109 | 0 | 0 |
| 0 | 0 | 0 | 0 | 109 | 0 |
| 0 | 0 | 0 | 0 | 0 | 109 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 45 | 32 | 81 |
| 0 | 0 | 18 | 45 | 0 | 81 |
| 0 | 0 | 0 | 50 | 18 | 95 |
| 0 | 0 | 50 | 18 | 18 | 50 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 81 | 45 | 68 |
| 0 | 0 | 50 | 81 | 0 | 68 |
| 0 | 0 | 0 | 95 | 50 | 63 |
| 0 | 0 | 95 | 50 | 50 | 95 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 2 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 112 |
| 0 | 0 | 0 | 112 | 112 | 0 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,109,0,0,0,0,0,0,109,0,0,0,0,0,0,109,0,0,0,0,0,0,109],[0,1,0,0,0,0,112,0,0,0,0,0,0,0,0,18,0,50,0,0,45,45,50,18,0,0,32,0,18,18,0,0,81,81,95,50],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,50,0,95,0,0,81,81,95,50,0,0,45,0,50,50,0,0,68,68,63,95],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,2,1,112,112,0,0,0,0,0,112,0,0,0,0,112,0] >;
C7×C8.2D4 in GAP, Magma, Sage, TeX
C_7\times C_8._2D_4
% in TeX
G:=Group("C7xC8.2D4"); // GroupNames label
G:=SmallGroup(448,905);
// by ID
G=gap.SmallGroup(448,905);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,1568,813,400,2438,2403,604,9804,172]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=d^2=1,c^4=b^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^5,d*b*d=b^3,d*c*d=c^3>;
// generators/relations