metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C8×D7)⋊4C4, C8.30(C4×D7), (C4×D7).4Q8, C4.24(Q8×D7), C4.Q8⋊14D7, C56.34(C2×C4), C8⋊Dic7⋊25C2, C28.13(C2×Q8), D14.3(C4⋊C4), C4⋊C4.161D14, (C2×C8).259D14, C22.84(D4×D7), C14.54(C4○D8), C28.Q8⋊14C2, C28.43(C22×C4), (C22×D7).52D4, Dic7.11(C4⋊C4), (C2×C56).160C22, (C2×C28).276C23, (C2×Dic7).206D4, C7⋊1(C23.25D4), C2.6(SD16⋊3D7), C4⋊Dic7.108C22, (D7×C2×C8).8C2, C4.77(C2×C4×D7), C7⋊C8.16(C2×C4), C2.12(D7×C4⋊C4), (C7×C4.Q8)⋊8C2, C14.11(C2×C4⋊C4), C4⋊C4⋊7D7.4C2, (C4×D7).26(C2×C4), (C2×C14).281(C2×D4), (C7×C4⋊C4).69C22, (C2×C7⋊C8).227C22, (C2×C4×D7).232C22, (C2×C4).379(C22×D7), SmallGroup(448,394)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C8×D7)⋊C4
G = < a,b,c,d | a8=b7=c2=d4=1, ab=ba, ac=ca, dad-1=a3, cbc=b-1, bd=db, dcd-1=a4c >
Subgroups: 492 in 114 conjugacy classes, 55 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C4.Q8, C4.Q8, C2.D8, C42⋊C2, C22×C8, C7⋊C8, C56, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C23.25D4, C8×D7, C2×C7⋊C8, C4×Dic7, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×C4×D7, C28.Q8, C8⋊Dic7, C7×C4.Q8, C4⋊C4⋊7D7, D7×C2×C8, (C8×D7)⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, D14, C2×C4⋊C4, C4○D8, C4×D7, C22×D7, C23.25D4, C2×C4×D7, D4×D7, Q8×D7, D7×C4⋊C4, SD16⋊3D7, (C8×D7)⋊C4
►On 224 points
Generators in S224
(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 83 199 55 31 143 153)(2 84 200 56 32 144 154)(3 85 193 49 25 137 155)(4 86 194 50 26 138 156)(5 87 195 51 27 139 157)(6 88 196 52 28 140 158)(7 81 197 53 29 141 159)(8 82 198 54 30 142 160)(9 20 113 130 40 188 173)(10 21 114 131 33 189 174)(11 22 115 132 34 190 175)(12 23 116 133 35 191 176)(13 24 117 134 36 192 169)(14 17 118 135 37 185 170)(15 18 119 136 38 186 171)(16 19 120 129 39 187 172)(41 60 94 209 208 99 177)(42 61 95 210 201 100 178)(43 62 96 211 202 101 179)(44 63 89 212 203 102 180)(45 64 90 213 204 103 181)(46 57 91 214 205 104 182)(47 58 92 215 206 97 183)(48 59 93 216 207 98 184)(65 168 73 107 221 128 147)(66 161 74 108 222 121 148)(67 162 75 109 223 122 149)(68 163 76 110 224 123 150)(69 164 77 111 217 124 151)(70 165 78 112 218 125 152)(71 166 79 105 219 126 145)(72 167 80 106 220 127 146)
(1 101)(2 102)(3 103)(4 104)(5 97)(6 98)(7 99)(8 100)(9 150)(10 151)(11 152)(12 145)(13 146)(14 147)(15 148)(16 149)(17 128)(18 121)(19 122)(20 123)(21 124)(22 125)(23 126)(24 127)(25 64)(26 57)(27 58)(28 59)(29 60)(30 61)(31 62)(32 63)(33 77)(34 78)(35 79)(36 80)(37 73)(38 74)(39 75)(40 76)(41 141)(42 142)(43 143)(44 144)(45 137)(46 138)(47 139)(48 140)(49 90)(50 91)(51 92)(52 93)(53 94)(54 95)(55 96)(56 89)(65 170)(66 171)(67 172)(68 173)(69 174)(70 175)(71 176)(72 169)(81 208)(82 201)(83 202)(84 203)(85 204)(86 205)(87 206)(88 207)(105 133)(106 134)(107 135)(108 136)(109 129)(110 130)(111 131)(112 132)(113 224)(114 217)(115 218)(116 219)(117 220)(118 221)(119 222)(120 223)(153 179)(154 180)(155 181)(156 182)(157 183)(158 184)(159 177)(160 178)(161 186)(162 187)(163 188)(164 189)(165 190)(166 191)(167 192)(168 185)(193 213)(194 214)(195 215)(196 216)(197 209)(198 210)(199 211)(200 212)
(1 39 183 109)(2 34 184 112)(3 37 177 107)(4 40 178 110)(5 35 179 105)(6 38 180 108)(7 33 181 111)(8 36 182 106)(9 95 150 50)(10 90 151 53)(11 93 152 56)(12 96 145 51)(13 91 146 54)(14 94 147 49)(15 89 148 52)(16 92 149 55)(17 209 65 25)(18 212 66 28)(19 215 67 31)(20 210 68 26)(21 213 69 29)(22 216 70 32)(23 211 71 27)(24 214 72 30)(41 221 85 185)(42 224 86 188)(43 219 87 191)(44 222 88 186)(45 217 81 189)(46 220 82 192)(47 223 83 187)(48 218 84 190)(57 127 198 169)(58 122 199 172)(59 125 200 175)(60 128 193 170)(61 123 194 173)(62 126 195 176)(63 121 196 171)(64 124 197 174)(73 155 135 99)(74 158 136 102)(75 153 129 97)(76 156 130 100)(77 159 131 103)(78 154 132 98)(79 157 133 101)(80 160 134 104)(113 201 163 138)(114 204 164 141)(115 207 165 144)(116 202 166 139)(117 205 167 142)(118 208 168 137)(119 203 161 140)(120 206 162 143)
G:=sub<Sym(224)| (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), (1,83,199,55,31,143,153)(2,84,200,56,32,144,154)(3,85,193,49,25,137,155)(4,86,194,50,26,138,156)(5,87,195,51,27,139,157)(6,88,196,52,28,140,158)(7,81,197,53,29,141,159)(8,82,198,54,30,142,160)(9,20,113,130,40,188,173)(10,21,114,131,33,189,174)(11,22,115,132,34,190,175)(12,23,116,133,35,191,176)(13,24,117,134,36,192,169)(14,17,118,135,37,185,170)(15,18,119,136,38,186,171)(16,19,120,129,39,187,172)(41,60,94,209,208,99,177)(42,61,95,210,201,100,178)(43,62,96,211,202,101,179)(44,63,89,212,203,102,180)(45,64,90,213,204,103,181)(46,57,91,214,205,104,182)(47,58,92,215,206,97,183)(48,59,93,216,207,98,184)(65,168,73,107,221,128,147)(66,161,74,108,222,121,148)(67,162,75,109,223,122,149)(68,163,76,110,224,123,150)(69,164,77,111,217,124,151)(70,165,78,112,218,125,152)(71,166,79,105,219,126,145)(72,167,80,106,220,127,146), (1,101)(2,102)(3,103)(4,104)(5,97)(6,98)(7,99)(8,100)(9,150)(10,151)(11,152)(12,145)(13,146)(14,147)(15,148)(16,149)(17,128)(18,121)(19,122)(20,123)(21,124)(22,125)(23,126)(24,127)(25,64)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,77)(34,78)(35,79)(36,80)(37,73)(38,74)(39,75)(40,76)(41,141)(42,142)(43,143)(44,144)(45,137)(46,138)(47,139)(48,140)(49,90)(50,91)(51,92)(52,93)(53,94)(54,95)(55,96)(56,89)(65,170)(66,171)(67,172)(68,173)(69,174)(70,175)(71,176)(72,169)(81,208)(82,201)(83,202)(84,203)(85,204)(86,205)(87,206)(88,207)(105,133)(106,134)(107,135)(108,136)(109,129)(110,130)(111,131)(112,132)(113,224)(114,217)(115,218)(116,219)(117,220)(118,221)(119,222)(120,223)(153,179)(154,180)(155,181)(156,182)(157,183)(158,184)(159,177)(160,178)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,185)(193,213)(194,214)(195,215)(196,216)(197,209)(198,210)(199,211)(200,212), (1,39,183,109)(2,34,184,112)(3,37,177,107)(4,40,178,110)(5,35,179,105)(6,38,180,108)(7,33,181,111)(8,36,182,106)(9,95,150,50)(10,90,151,53)(11,93,152,56)(12,96,145,51)(13,91,146,54)(14,94,147,49)(15,89,148,52)(16,92,149,55)(17,209,65,25)(18,212,66,28)(19,215,67,31)(20,210,68,26)(21,213,69,29)(22,216,70,32)(23,211,71,27)(24,214,72,30)(41,221,85,185)(42,224,86,188)(43,219,87,191)(44,222,88,186)(45,217,81,189)(46,220,82,192)(47,223,83,187)(48,218,84,190)(57,127,198,169)(58,122,199,172)(59,125,200,175)(60,128,193,170)(61,123,194,173)(62,126,195,176)(63,121,196,171)(64,124,197,174)(73,155,135,99)(74,158,136,102)(75,153,129,97)(76,156,130,100)(77,159,131,103)(78,154,132,98)(79,157,133,101)(80,160,134,104)(113,201,163,138)(114,204,164,141)(115,207,165,144)(116,202,166,139)(117,205,167,142)(118,208,168,137)(119,203,161,140)(120,206,162,143)>;
G:=Group( (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), (1,83,199,55,31,143,153)(2,84,200,56,32,144,154)(3,85,193,49,25,137,155)(4,86,194,50,26,138,156)(5,87,195,51,27,139,157)(6,88,196,52,28,140,158)(7,81,197,53,29,141,159)(8,82,198,54,30,142,160)(9,20,113,130,40,188,173)(10,21,114,131,33,189,174)(11,22,115,132,34,190,175)(12,23,116,133,35,191,176)(13,24,117,134,36,192,169)(14,17,118,135,37,185,170)(15,18,119,136,38,186,171)(16,19,120,129,39,187,172)(41,60,94,209,208,99,177)(42,61,95,210,201,100,178)(43,62,96,211,202,101,179)(44,63,89,212,203,102,180)(45,64,90,213,204,103,181)(46,57,91,214,205,104,182)(47,58,92,215,206,97,183)(48,59,93,216,207,98,184)(65,168,73,107,221,128,147)(66,161,74,108,222,121,148)(67,162,75,109,223,122,149)(68,163,76,110,224,123,150)(69,164,77,111,217,124,151)(70,165,78,112,218,125,152)(71,166,79,105,219,126,145)(72,167,80,106,220,127,146), (1,101)(2,102)(3,103)(4,104)(5,97)(6,98)(7,99)(8,100)(9,150)(10,151)(11,152)(12,145)(13,146)(14,147)(15,148)(16,149)(17,128)(18,121)(19,122)(20,123)(21,124)(22,125)(23,126)(24,127)(25,64)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62)(32,63)(33,77)(34,78)(35,79)(36,80)(37,73)(38,74)(39,75)(40,76)(41,141)(42,142)(43,143)(44,144)(45,137)(46,138)(47,139)(48,140)(49,90)(50,91)(51,92)(52,93)(53,94)(54,95)(55,96)(56,89)(65,170)(66,171)(67,172)(68,173)(69,174)(70,175)(71,176)(72,169)(81,208)(82,201)(83,202)(84,203)(85,204)(86,205)(87,206)(88,207)(105,133)(106,134)(107,135)(108,136)(109,129)(110,130)(111,131)(112,132)(113,224)(114,217)(115,218)(116,219)(117,220)(118,221)(119,222)(120,223)(153,179)(154,180)(155,181)(156,182)(157,183)(158,184)(159,177)(160,178)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,185)(193,213)(194,214)(195,215)(196,216)(197,209)(198,210)(199,211)(200,212), (1,39,183,109)(2,34,184,112)(3,37,177,107)(4,40,178,110)(5,35,179,105)(6,38,180,108)(7,33,181,111)(8,36,182,106)(9,95,150,50)(10,90,151,53)(11,93,152,56)(12,96,145,51)(13,91,146,54)(14,94,147,49)(15,89,148,52)(16,92,149,55)(17,209,65,25)(18,212,66,28)(19,215,67,31)(20,210,68,26)(21,213,69,29)(22,216,70,32)(23,211,71,27)(24,214,72,30)(41,221,85,185)(42,224,86,188)(43,219,87,191)(44,222,88,186)(45,217,81,189)(46,220,82,192)(47,223,83,187)(48,218,84,190)(57,127,198,169)(58,122,199,172)(59,125,200,175)(60,128,193,170)(61,123,194,173)(62,126,195,176)(63,121,196,171)(64,124,197,174)(73,155,135,99)(74,158,136,102)(75,153,129,97)(76,156,130,100)(77,159,131,103)(78,154,132,98)(79,157,133,101)(80,160,134,104)(113,201,163,138)(114,204,164,141)(115,207,165,144)(116,202,166,139)(117,205,167,142)(118,208,168,137)(119,203,161,140)(120,206,162,143) );
G=PermutationGroup([[(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)], [(1,83,199,55,31,143,153),(2,84,200,56,32,144,154),(3,85,193,49,25,137,155),(4,86,194,50,26,138,156),(5,87,195,51,27,139,157),(6,88,196,52,28,140,158),(7,81,197,53,29,141,159),(8,82,198,54,30,142,160),(9,20,113,130,40,188,173),(10,21,114,131,33,189,174),(11,22,115,132,34,190,175),(12,23,116,133,35,191,176),(13,24,117,134,36,192,169),(14,17,118,135,37,185,170),(15,18,119,136,38,186,171),(16,19,120,129,39,187,172),(41,60,94,209,208,99,177),(42,61,95,210,201,100,178),(43,62,96,211,202,101,179),(44,63,89,212,203,102,180),(45,64,90,213,204,103,181),(46,57,91,214,205,104,182),(47,58,92,215,206,97,183),(48,59,93,216,207,98,184),(65,168,73,107,221,128,147),(66,161,74,108,222,121,148),(67,162,75,109,223,122,149),(68,163,76,110,224,123,150),(69,164,77,111,217,124,151),(70,165,78,112,218,125,152),(71,166,79,105,219,126,145),(72,167,80,106,220,127,146)], [(1,101),(2,102),(3,103),(4,104),(5,97),(6,98),(7,99),(8,100),(9,150),(10,151),(11,152),(12,145),(13,146),(14,147),(15,148),(16,149),(17,128),(18,121),(19,122),(20,123),(21,124),(22,125),(23,126),(24,127),(25,64),(26,57),(27,58),(28,59),(29,60),(30,61),(31,62),(32,63),(33,77),(34,78),(35,79),(36,80),(37,73),(38,74),(39,75),(40,76),(41,141),(42,142),(43,143),(44,144),(45,137),(46,138),(47,139),(48,140),(49,90),(50,91),(51,92),(52,93),(53,94),(54,95),(55,96),(56,89),(65,170),(66,171),(67,172),(68,173),(69,174),(70,175),(71,176),(72,169),(81,208),(82,201),(83,202),(84,203),(85,204),(86,205),(87,206),(88,207),(105,133),(106,134),(107,135),(108,136),(109,129),(110,130),(111,131),(112,132),(113,224),(114,217),(115,218),(116,219),(117,220),(118,221),(119,222),(120,223),(153,179),(154,180),(155,181),(156,182),(157,183),(158,184),(159,177),(160,178),(161,186),(162,187),(163,188),(164,189),(165,190),(166,191),(167,192),(168,185),(193,213),(194,214),(195,215),(196,216),(197,209),(198,210),(199,211),(200,212)], [(1,39,183,109),(2,34,184,112),(3,37,177,107),(4,40,178,110),(5,35,179,105),(6,38,180,108),(7,33,181,111),(8,36,182,106),(9,95,150,50),(10,90,151,53),(11,93,152,56),(12,96,145,51),(13,91,146,54),(14,94,147,49),(15,89,148,52),(16,92,149,55),(17,209,65,25),(18,212,66,28),(19,215,67,31),(20,210,68,26),(21,213,69,29),(22,216,70,32),(23,211,71,27),(24,214,72,30),(41,221,85,185),(42,224,86,188),(43,219,87,191),(44,222,88,186),(45,217,81,189),(46,220,82,192),(47,223,83,187),(48,218,84,190),(57,127,198,169),(58,122,199,172),(59,125,200,175),(60,128,193,170),(61,123,194,173),(62,126,195,176),(63,121,196,171),(64,124,197,174),(73,155,135,99),(74,158,136,102),(75,153,129,97),(76,156,130,100),(77,159,131,103),(78,154,132,98),(79,157,133,101),(80,160,134,104),(113,201,163,138),(114,204,164,141),(115,207,165,144),(116,202,166,139),(117,205,167,142),(118,208,168,137),(119,203,161,140),(120,206,162,143)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | Q8 | D4 | D4 | D7 | D14 | D14 | C4○D8 | C4×D7 | Q8×D7 | D4×D7 | SD16⋊3D7 |
| kernel | (C8×D7)⋊C4 | C28.Q8 | C8⋊Dic7 | C7×C4.Q8 | C4⋊C4⋊7D7 | D7×C2×C8 | C8×D7 | C4×D7 | C2×Dic7 | C22×D7 | C4.Q8 | C4⋊C4 | C2×C8 | C14 | C8 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 1 | 8 | 2 | 1 | 1 | 3 | 6 | 3 | 8 | 12 | 3 | 3 | 12 |
Matrix representation of (C8×D7)⋊C4 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 69 | 0 |
| 0 | 0 | 77 | 18 |
| 0 | 112 | 0 | 0 |
| 1 | 24 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 24 | 1 | 0 | 0 |
| 103 | 89 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 28 | 1 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 1 | 105 |
| 0 | 0 | 0 | 112 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,69,77,0,0,0,18],[0,1,0,0,112,24,0,0,0,0,1,0,0,0,0,1],[24,103,0,0,1,89,0,0,0,0,112,28,0,0,0,1],[98,0,0,0,0,98,0,0,0,0,1,0,0,0,105,112] >;
(C8×D7)⋊C4 in GAP, Magma, Sage, TeX
(C_8\times D_7)\rtimes C_4
% in TeX
G:=Group("(C8xD7):C4"); // GroupNames label
G:=SmallGroup(448,394);
// by ID
G=gap.SmallGroup(448,394);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,555,58,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^7=c^2=d^4=1,a*b=b*a,a*c=c*a,d*a*d^-1=a^3,c*b*c=b^-1,b*d=d*b,d*c*d^-1=a^4*c>;
// generators/relations