metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C8×D7)⋊2C4, C8.27(C4×D7), (C4×D7).6Q8, C4.30(Q8×D7), C2.D8⋊14D7, C56.17(C2×C4), C56⋊1C4⋊21C2, C28.21(C2×Q8), C4⋊C4.170D14, D14.5(C4⋊C4), (C2×C8).230D14, C22.90(D4×D7), C14.28(C4○D8), C2.4(D8⋊3D7), (C2×C56).82C22, C28.49(C22×C4), C4.Dic14⋊19C2, (C22×D7).54D4, C2.4(Q8.D14), Dic7.12(C4⋊C4), (C2×C28).296C23, (C2×Dic7).209D4, C7⋊2(C23.25D4), C4⋊Dic7.122C22, (D7×C2×C8).3C2, C4.80(C2×C4×D7), C7⋊C8.17(C2×C4), C2.15(D7×C4⋊C4), (C7×C2.D8)⋊4C2, C14.14(C2×C4⋊C4), C4⋊C4⋊7D7.7C2, (C4×D7).28(C2×C4), (C2×C14).301(C2×D4), (C7×C4⋊C4).89C22, (C2×C7⋊C8).234C22, (C2×C4×D7).235C22, (C2×C4).399(C22×D7), SmallGroup(448,414)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C8.27(C4×D7)
G = < a,b,c,d | a8=b4=c7=d2=1, bab-1=a-1, ac=ca, ad=da, bc=cb, dbd=a4b, dcd=c-1 >
Subgroups: 492 in 114 conjugacy classes, 55 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C4.Q8, C2.D8, 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, C4.Dic14, C56⋊1C4, C7×C2.D8, C4⋊C4⋊7D7, D7×C2×C8, C8.27(C4×D7)
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, D8⋊3D7, Q8.D14, C8.27(C4×D7)
►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)
(1 156 65 109)(2 155 66 108)(3 154 67 107)(4 153 68 106)(5 160 69 105)(6 159 70 112)(7 158 71 111)(8 157 72 110)(9 200 59 54)(10 199 60 53)(11 198 61 52)(12 197 62 51)(13 196 63 50)(14 195 64 49)(15 194 57 56)(16 193 58 55)(17 90 183 40)(18 89 184 39)(19 96 177 38)(20 95 178 37)(21 94 179 36)(22 93 180 35)(23 92 181 34)(24 91 182 33)(25 127 212 78)(26 126 213 77)(27 125 214 76)(28 124 215 75)(29 123 216 74)(30 122 209 73)(31 121 210 80)(32 128 211 79)(41 218 88 190)(42 217 81 189)(43 224 82 188)(44 223 83 187)(45 222 84 186)(46 221 85 185)(47 220 86 192)(48 219 87 191)(97 141 152 115)(98 140 145 114)(99 139 146 113)(100 138 147 120)(101 137 148 119)(102 144 149 118)(103 143 150 117)(104 142 151 116)(129 202 161 174)(130 201 162 173)(131 208 163 172)(132 207 164 171)(133 206 165 170)(134 205 166 169)(135 204 167 176)(136 203 168 175)
(1 83 199 146 28 36 174)(2 84 200 147 29 37 175)(3 85 193 148 30 38 176)(4 86 194 149 31 39 169)(5 87 195 150 32 40 170)(6 88 196 151 25 33 171)(7 81 197 152 26 34 172)(8 82 198 145 27 35 173)(9 138 74 178 168 108 222)(10 139 75 179 161 109 223)(11 140 76 180 162 110 224)(12 141 77 181 163 111 217)(13 142 78 182 164 112 218)(14 143 79 183 165 105 219)(15 144 80 184 166 106 220)(16 137 73 177 167 107 221)(17 133 160 191 64 117 128)(18 134 153 192 57 118 121)(19 135 154 185 58 119 122)(20 136 155 186 59 120 123)(21 129 156 187 60 113 124)(22 130 157 188 61 114 125)(23 131 158 189 62 115 126)(24 132 159 190 63 116 127)(41 50 104 212 91 207 70)(42 51 97 213 92 208 71)(43 52 98 214 93 201 72)(44 53 99 215 94 202 65)(45 54 100 216 95 203 66)(46 55 101 209 96 204 67)(47 56 102 210 89 205 68)(48 49 103 211 90 206 69)
(1 202)(2 203)(3 204)(4 205)(5 206)(6 207)(7 208)(8 201)(9 127)(10 128)(11 121)(12 122)(13 123)(14 124)(15 125)(16 126)(17 223)(18 224)(19 217)(20 218)(21 219)(22 220)(23 221)(24 222)(25 50)(26 51)(27 52)(28 53)(29 54)(30 55)(31 56)(32 49)(33 41)(34 42)(35 43)(36 44)(37 45)(38 46)(39 47)(40 48)(57 76)(58 77)(59 78)(60 79)(61 80)(62 73)(63 74)(64 75)(65 174)(66 175)(67 176)(68 169)(69 170)(70 171)(71 172)(72 173)(81 92)(82 93)(83 94)(84 95)(85 96)(86 89)(87 90)(88 91)(97 152)(98 145)(99 146)(100 147)(101 148)(102 149)(103 150)(104 151)(105 129)(106 130)(107 131)(108 132)(109 133)(110 134)(111 135)(112 136)(113 143)(114 144)(115 137)(116 138)(117 139)(118 140)(119 141)(120 142)(153 162)(154 163)(155 164)(156 165)(157 166)(158 167)(159 168)(160 161)(177 189)(178 190)(179 191)(180 192)(181 185)(182 186)(183 187)(184 188)(193 209)(194 210)(195 211)(196 212)(197 213)(198 214)(199 215)(200 216)
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), (1,156,65,109)(2,155,66,108)(3,154,67,107)(4,153,68,106)(5,160,69,105)(6,159,70,112)(7,158,71,111)(8,157,72,110)(9,200,59,54)(10,199,60,53)(11,198,61,52)(12,197,62,51)(13,196,63,50)(14,195,64,49)(15,194,57,56)(16,193,58,55)(17,90,183,40)(18,89,184,39)(19,96,177,38)(20,95,178,37)(21,94,179,36)(22,93,180,35)(23,92,181,34)(24,91,182,33)(25,127,212,78)(26,126,213,77)(27,125,214,76)(28,124,215,75)(29,123,216,74)(30,122,209,73)(31,121,210,80)(32,128,211,79)(41,218,88,190)(42,217,81,189)(43,224,82,188)(44,223,83,187)(45,222,84,186)(46,221,85,185)(47,220,86,192)(48,219,87,191)(97,141,152,115)(98,140,145,114)(99,139,146,113)(100,138,147,120)(101,137,148,119)(102,144,149,118)(103,143,150,117)(104,142,151,116)(129,202,161,174)(130,201,162,173)(131,208,163,172)(132,207,164,171)(133,206,165,170)(134,205,166,169)(135,204,167,176)(136,203,168,175), (1,83,199,146,28,36,174)(2,84,200,147,29,37,175)(3,85,193,148,30,38,176)(4,86,194,149,31,39,169)(5,87,195,150,32,40,170)(6,88,196,151,25,33,171)(7,81,197,152,26,34,172)(8,82,198,145,27,35,173)(9,138,74,178,168,108,222)(10,139,75,179,161,109,223)(11,140,76,180,162,110,224)(12,141,77,181,163,111,217)(13,142,78,182,164,112,218)(14,143,79,183,165,105,219)(15,144,80,184,166,106,220)(16,137,73,177,167,107,221)(17,133,160,191,64,117,128)(18,134,153,192,57,118,121)(19,135,154,185,58,119,122)(20,136,155,186,59,120,123)(21,129,156,187,60,113,124)(22,130,157,188,61,114,125)(23,131,158,189,62,115,126)(24,132,159,190,63,116,127)(41,50,104,212,91,207,70)(42,51,97,213,92,208,71)(43,52,98,214,93,201,72)(44,53,99,215,94,202,65)(45,54,100,216,95,203,66)(46,55,101,209,96,204,67)(47,56,102,210,89,205,68)(48,49,103,211,90,206,69), (1,202)(2,203)(3,204)(4,205)(5,206)(6,207)(7,208)(8,201)(9,127)(10,128)(11,121)(12,122)(13,123)(14,124)(15,125)(16,126)(17,223)(18,224)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,50)(26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,49)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(57,76)(58,77)(59,78)(60,79)(61,80)(62,73)(63,74)(64,75)(65,174)(66,175)(67,176)(68,169)(69,170)(70,171)(71,172)(72,173)(81,92)(82,93)(83,94)(84,95)(85,96)(86,89)(87,90)(88,91)(97,152)(98,145)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,143)(114,144)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161)(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)(184,188)(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)(200,216)>;
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), (1,156,65,109)(2,155,66,108)(3,154,67,107)(4,153,68,106)(5,160,69,105)(6,159,70,112)(7,158,71,111)(8,157,72,110)(9,200,59,54)(10,199,60,53)(11,198,61,52)(12,197,62,51)(13,196,63,50)(14,195,64,49)(15,194,57,56)(16,193,58,55)(17,90,183,40)(18,89,184,39)(19,96,177,38)(20,95,178,37)(21,94,179,36)(22,93,180,35)(23,92,181,34)(24,91,182,33)(25,127,212,78)(26,126,213,77)(27,125,214,76)(28,124,215,75)(29,123,216,74)(30,122,209,73)(31,121,210,80)(32,128,211,79)(41,218,88,190)(42,217,81,189)(43,224,82,188)(44,223,83,187)(45,222,84,186)(46,221,85,185)(47,220,86,192)(48,219,87,191)(97,141,152,115)(98,140,145,114)(99,139,146,113)(100,138,147,120)(101,137,148,119)(102,144,149,118)(103,143,150,117)(104,142,151,116)(129,202,161,174)(130,201,162,173)(131,208,163,172)(132,207,164,171)(133,206,165,170)(134,205,166,169)(135,204,167,176)(136,203,168,175), (1,83,199,146,28,36,174)(2,84,200,147,29,37,175)(3,85,193,148,30,38,176)(4,86,194,149,31,39,169)(5,87,195,150,32,40,170)(6,88,196,151,25,33,171)(7,81,197,152,26,34,172)(8,82,198,145,27,35,173)(9,138,74,178,168,108,222)(10,139,75,179,161,109,223)(11,140,76,180,162,110,224)(12,141,77,181,163,111,217)(13,142,78,182,164,112,218)(14,143,79,183,165,105,219)(15,144,80,184,166,106,220)(16,137,73,177,167,107,221)(17,133,160,191,64,117,128)(18,134,153,192,57,118,121)(19,135,154,185,58,119,122)(20,136,155,186,59,120,123)(21,129,156,187,60,113,124)(22,130,157,188,61,114,125)(23,131,158,189,62,115,126)(24,132,159,190,63,116,127)(41,50,104,212,91,207,70)(42,51,97,213,92,208,71)(43,52,98,214,93,201,72)(44,53,99,215,94,202,65)(45,54,100,216,95,203,66)(46,55,101,209,96,204,67)(47,56,102,210,89,205,68)(48,49,103,211,90,206,69), (1,202)(2,203)(3,204)(4,205)(5,206)(6,207)(7,208)(8,201)(9,127)(10,128)(11,121)(12,122)(13,123)(14,124)(15,125)(16,126)(17,223)(18,224)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,50)(26,51)(27,52)(28,53)(29,54)(30,55)(31,56)(32,49)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(57,76)(58,77)(59,78)(60,79)(61,80)(62,73)(63,74)(64,75)(65,174)(66,175)(67,176)(68,169)(69,170)(70,171)(71,172)(72,173)(81,92)(82,93)(83,94)(84,95)(85,96)(86,89)(87,90)(88,91)(97,152)(98,145)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,143)(114,144)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161)(177,189)(178,190)(179,191)(180,192)(181,185)(182,186)(183,187)(184,188)(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)(200,216) );
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)], [(1,156,65,109),(2,155,66,108),(3,154,67,107),(4,153,68,106),(5,160,69,105),(6,159,70,112),(7,158,71,111),(8,157,72,110),(9,200,59,54),(10,199,60,53),(11,198,61,52),(12,197,62,51),(13,196,63,50),(14,195,64,49),(15,194,57,56),(16,193,58,55),(17,90,183,40),(18,89,184,39),(19,96,177,38),(20,95,178,37),(21,94,179,36),(22,93,180,35),(23,92,181,34),(24,91,182,33),(25,127,212,78),(26,126,213,77),(27,125,214,76),(28,124,215,75),(29,123,216,74),(30,122,209,73),(31,121,210,80),(32,128,211,79),(41,218,88,190),(42,217,81,189),(43,224,82,188),(44,223,83,187),(45,222,84,186),(46,221,85,185),(47,220,86,192),(48,219,87,191),(97,141,152,115),(98,140,145,114),(99,139,146,113),(100,138,147,120),(101,137,148,119),(102,144,149,118),(103,143,150,117),(104,142,151,116),(129,202,161,174),(130,201,162,173),(131,208,163,172),(132,207,164,171),(133,206,165,170),(134,205,166,169),(135,204,167,176),(136,203,168,175)], [(1,83,199,146,28,36,174),(2,84,200,147,29,37,175),(3,85,193,148,30,38,176),(4,86,194,149,31,39,169),(5,87,195,150,32,40,170),(6,88,196,151,25,33,171),(7,81,197,152,26,34,172),(8,82,198,145,27,35,173),(9,138,74,178,168,108,222),(10,139,75,179,161,109,223),(11,140,76,180,162,110,224),(12,141,77,181,163,111,217),(13,142,78,182,164,112,218),(14,143,79,183,165,105,219),(15,144,80,184,166,106,220),(16,137,73,177,167,107,221),(17,133,160,191,64,117,128),(18,134,153,192,57,118,121),(19,135,154,185,58,119,122),(20,136,155,186,59,120,123),(21,129,156,187,60,113,124),(22,130,157,188,61,114,125),(23,131,158,189,62,115,126),(24,132,159,190,63,116,127),(41,50,104,212,91,207,70),(42,51,97,213,92,208,71),(43,52,98,214,93,201,72),(44,53,99,215,94,202,65),(45,54,100,216,95,203,66),(46,55,101,209,96,204,67),(47,56,102,210,89,205,68),(48,49,103,211,90,206,69)], [(1,202),(2,203),(3,204),(4,205),(5,206),(6,207),(7,208),(8,201),(9,127),(10,128),(11,121),(12,122),(13,123),(14,124),(15,125),(16,126),(17,223),(18,224),(19,217),(20,218),(21,219),(22,220),(23,221),(24,222),(25,50),(26,51),(27,52),(28,53),(29,54),(30,55),(31,56),(32,49),(33,41),(34,42),(35,43),(36,44),(37,45),(38,46),(39,47),(40,48),(57,76),(58,77),(59,78),(60,79),(61,80),(62,73),(63,74),(64,75),(65,174),(66,175),(67,176),(68,169),(69,170),(70,171),(71,172),(72,173),(81,92),(82,93),(83,94),(84,95),(85,96),(86,89),(87,90),(88,91),(97,152),(98,145),(99,146),(100,147),(101,148),(102,149),(103,150),(104,151),(105,129),(106,130),(107,131),(108,132),(109,133),(110,134),(111,135),(112,136),(113,143),(114,144),(115,137),(116,138),(117,139),(118,140),(119,141),(120,142),(153,162),(154,163),(155,164),(156,165),(157,166),(158,167),(159,168),(160,161),(177,189),(178,190),(179,191),(180,192),(181,185),(182,186),(183,187),(184,188),(193,209),(194,210),(195,211),(196,212),(197,213),(198,214),(199,215),(200,216)]])
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 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | - | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | Q8 | D4 | D4 | D7 | D14 | D14 | C4○D8 | C4×D7 | Q8×D7 | D4×D7 | D8⋊3D7 | Q8.D14 |
| kernel | C8.27(C4×D7) | C4.Dic14 | C56⋊1C4 | C7×C2.D8 | C4⋊C4⋊7D7 | D7×C2×C8 | C8×D7 | C4×D7 | C2×Dic7 | C22×D7 | C2.D8 | C4⋊C4 | C2×C8 | C14 | C8 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 1 | 8 | 2 | 1 | 1 | 3 | 6 | 3 | 8 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of C8.27(C4×D7) ►in GL5(𝔽113)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 95 | 0 | 0 | 0 |
| 0 | 0 | 69 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 89 | 112 |
| 0 | 0 | 0 | 2 | 33 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 81 | 33 |
| 0 | 0 | 0 | 82 | 32 |
G:=sub<GL(5,GF(113))| [1,0,0,0,0,0,95,0,0,0,0,0,69,0,0,0,0,0,1,0,0,0,0,0,1],[15,0,0,0,0,0,0,98,0,0,0,98,0,0,0,0,0,0,112,0,0,0,0,0,112],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,89,2,0,0,0,112,33],[1,0,0,0,0,0,112,0,0,0,0,0,1,0,0,0,0,0,81,82,0,0,0,33,32] >;
C8.27(C4×D7) in GAP, Magma, Sage, TeX
C_8._{27}(C_4\times D_7) % in TeX
G:=Group("C8.27(C4xD7)"); // GroupNames label
G:=SmallGroup(448,414);
// by ID
G=gap.SmallGroup(448,414);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,58,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^4=c^7=d^2=1,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^4*b,d*c*d=c^-1>;
// generators/relations