metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.163D14, C14.1402+ (1+4), (C4×D28)⋊16C2, C28⋊1D4⋊37C2, C4⋊C4.214D14, C42⋊D7⋊8C2, C42⋊2C2⋊6D7, D28⋊C4⋊42C2, D14⋊D4⋊45C2, Dic7.Q8⋊39C2, (C4×C28).35C22, (C2×C28).96C23, C22⋊C4.81D14, Dic7⋊4D4⋊37C2, D14.33(C4○D4), D14.5D4⋊42C2, (C2×C14).253C24, D14⋊C4.46C22, C2.65(D4⋊8D14), C23.59(C22×D7), Dic7.33(C4○D4), (C2×D28).169C22, C22.D28⋊30C2, C4⋊Dic7.318C22, (C22×C14).67C23, C22.274(C23×D7), Dic7⋊C4.147C22, (C2×Dic7).266C23, (C4×Dic7).152C22, (C22×D7).112C23, C7⋊11(C22.47C24), (C22×Dic7).153C22, (D7×C4⋊C4)⋊43C2, C4⋊C4⋊D7⋊43C2, C2.100(D7×C4○D4), (C7×C42⋊2C2)⋊8C2, C14.211(C2×C4○D4), (C2×C4×D7).135C22, (C2×C4).89(C22×D7), (C7×C4⋊C4).205C22, (C2×C7⋊D4).73C22, (C7×C22⋊C4).78C22, SmallGroup(448,1162)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1196 in 238 conjugacy classes, 95 normal (91 characteristic)
C1, C2 [×3], C2 [×5], C4 [×12], C22, C22 [×13], C7, C2×C4 [×6], C2×C4 [×13], D4 [×10], C23, C23 [×3], D7 [×4], C14 [×3], C14, C42, C42 [×2], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4 [×6], C2×D4 [×6], Dic7 [×2], Dic7 [×4], C28 [×6], D14 [×2], D14 [×8], C2×C14, C2×C14 [×3], C2×C4⋊C4, C42⋊C2, C4×D4 [×4], C4⋊D4 [×4], C22.D4 [×2], C42.C2, C42⋊2C2, C42⋊2C2, C4×D7 [×7], D28 [×5], C2×Dic7 [×5], C2×Dic7, C7⋊D4 [×5], C2×C28 [×6], C22×D7 [×3], C22×C14, C22.47C24, C4×Dic7 [×2], Dic7⋊C4 [×5], C4⋊Dic7 [×2], D14⋊C4 [×7], C4×C28, C7×C22⋊C4 [×3], C7×C4⋊C4 [×3], C2×C4×D7 [×5], C2×D28 [×3], C22×Dic7, C2×C7⋊D4 [×3], C42⋊D7, C4×D28, Dic7⋊4D4 [×2], D14⋊D4 [×3], C22.D28, Dic7.Q8, D7×C4⋊C4, D28⋊C4, D14.5D4, C28⋊1D4, C4⋊C4⋊D7, C7×C42⋊2C2, C42.163D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.47C24, C23×D7, D7×C4○D4 [×2], D4⋊8D14, C42.163D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=a2b, dbd-1=a2b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 87 15 101)(2 129 16 115)(3 89 17 103)(4 131 18 117)(5 91 19 105)(6 133 20 119)(7 93 21 107)(8 135 22 121)(9 95 23 109)(10 137 24 123)(11 97 25 111)(12 139 26 125)(13 99 27 85)(14 113 28 127)(29 165 43 151)(30 57 44 71)(31 167 45 153)(32 59 46 73)(33 141 47 155)(34 61 48 75)(35 143 49 157)(36 63 50 77)(37 145 51 159)(38 65 52 79)(39 147 53 161)(40 67 54 81)(41 149 55 163)(42 69 56 83)(58 170 72 184)(60 172 74 186)(62 174 76 188)(64 176 78 190)(66 178 80 192)(68 180 82 194)(70 182 84 196)(86 207 100 221)(88 209 102 223)(90 211 104 197)(92 213 106 199)(94 215 108 201)(96 217 110 203)(98 219 112 205)(114 222 128 208)(116 224 130 210)(118 198 132 212)(120 200 134 214)(122 202 136 216)(124 204 138 218)(126 206 140 220)(142 173 156 187)(144 175 158 189)(146 177 160 191)(148 179 162 193)(150 181 164 195)(152 183 166 169)(154 185 168 171)
(1 191 208 52)(2 178 209 39)(3 193 210 54)(4 180 211 41)(5 195 212 56)(6 182 213 43)(7 169 214 30)(8 184 215 45)(9 171 216 32)(10 186 217 47)(11 173 218 34)(12 188 219 49)(13 175 220 36)(14 190 221 51)(15 177 222 38)(16 192 223 53)(17 179 224 40)(18 194 197 55)(19 181 198 42)(20 196 199 29)(21 183 200 44)(22 170 201 31)(23 185 202 46)(24 172 203 33)(25 187 204 48)(26 174 205 35)(27 189 206 50)(28 176 207 37)(57 93 152 120)(58 108 153 135)(59 95 154 122)(60 110 155 137)(61 97 156 124)(62 112 157 139)(63 99 158 126)(64 86 159 113)(65 101 160 128)(66 88 161 115)(67 103 162 130)(68 90 163 117)(69 105 164 132)(70 92 165 119)(71 107 166 134)(72 94 167 121)(73 109 168 136)(74 96 141 123)(75 111 142 138)(76 98 143 125)(77 85 144 140)(78 100 145 127)(79 87 146 114)(80 102 147 129)(81 89 148 116)(82 104 149 131)(83 91 150 118)(84 106 151 133)
(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 28 15 14)(2 13 16 27)(3 26 17 12)(4 11 18 25)(5 24 19 10)(6 9 20 23)(7 22 21 8)(29 171 43 185)(30 184 44 170)(31 169 45 183)(32 182 46 196)(33 195 47 181)(34 180 48 194)(35 193 49 179)(36 178 50 192)(37 191 51 177)(38 176 52 190)(39 189 53 175)(40 174 54 188)(41 187 55 173)(42 172 56 186)(57 167 71 153)(58 152 72 166)(59 165 73 151)(60 150 74 164)(61 163 75 149)(62 148 76 162)(63 161 77 147)(64 146 78 160)(65 159 79 145)(66 144 80 158)(67 157 81 143)(68 142 82 156)(69 155 83 141)(70 168 84 154)(85 88 99 102)(86 101 100 87)(89 112 103 98)(90 97 104 111)(91 110 105 96)(92 95 106 109)(93 108 107 94)(113 128 127 114)(115 126 129 140)(116 139 130 125)(117 124 131 138)(118 137 132 123)(119 122 133 136)(120 135 134 121)(197 204 211 218)(198 217 212 203)(199 202 213 216)(200 215 214 201)(205 224 219 210)(206 209 220 223)(207 222 221 208)
G:=sub<Sym(224)| (1,87,15,101)(2,129,16,115)(3,89,17,103)(4,131,18,117)(5,91,19,105)(6,133,20,119)(7,93,21,107)(8,135,22,121)(9,95,23,109)(10,137,24,123)(11,97,25,111)(12,139,26,125)(13,99,27,85)(14,113,28,127)(29,165,43,151)(30,57,44,71)(31,167,45,153)(32,59,46,73)(33,141,47,155)(34,61,48,75)(35,143,49,157)(36,63,50,77)(37,145,51,159)(38,65,52,79)(39,147,53,161)(40,67,54,81)(41,149,55,163)(42,69,56,83)(58,170,72,184)(60,172,74,186)(62,174,76,188)(64,176,78,190)(66,178,80,192)(68,180,82,194)(70,182,84,196)(86,207,100,221)(88,209,102,223)(90,211,104,197)(92,213,106,199)(94,215,108,201)(96,217,110,203)(98,219,112,205)(114,222,128,208)(116,224,130,210)(118,198,132,212)(120,200,134,214)(122,202,136,216)(124,204,138,218)(126,206,140,220)(142,173,156,187)(144,175,158,189)(146,177,160,191)(148,179,162,193)(150,181,164,195)(152,183,166,169)(154,185,168,171), (1,191,208,52)(2,178,209,39)(3,193,210,54)(4,180,211,41)(5,195,212,56)(6,182,213,43)(7,169,214,30)(8,184,215,45)(9,171,216,32)(10,186,217,47)(11,173,218,34)(12,188,219,49)(13,175,220,36)(14,190,221,51)(15,177,222,38)(16,192,223,53)(17,179,224,40)(18,194,197,55)(19,181,198,42)(20,196,199,29)(21,183,200,44)(22,170,201,31)(23,185,202,46)(24,172,203,33)(25,187,204,48)(26,174,205,35)(27,189,206,50)(28,176,207,37)(57,93,152,120)(58,108,153,135)(59,95,154,122)(60,110,155,137)(61,97,156,124)(62,112,157,139)(63,99,158,126)(64,86,159,113)(65,101,160,128)(66,88,161,115)(67,103,162,130)(68,90,163,117)(69,105,164,132)(70,92,165,119)(71,107,166,134)(72,94,167,121)(73,109,168,136)(74,96,141,123)(75,111,142,138)(76,98,143,125)(77,85,144,140)(78,100,145,127)(79,87,146,114)(80,102,147,129)(81,89,148,116)(82,104,149,131)(83,91,150,118)(84,106,151,133), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,171,43,185)(30,184,44,170)(31,169,45,183)(32,182,46,196)(33,195,47,181)(34,180,48,194)(35,193,49,179)(36,178,50,192)(37,191,51,177)(38,176,52,190)(39,189,53,175)(40,174,54,188)(41,187,55,173)(42,172,56,186)(57,167,71,153)(58,152,72,166)(59,165,73,151)(60,150,74,164)(61,163,75,149)(62,148,76,162)(63,161,77,147)(64,146,78,160)(65,159,79,145)(66,144,80,158)(67,157,81,143)(68,142,82,156)(69,155,83,141)(70,168,84,154)(85,88,99,102)(86,101,100,87)(89,112,103,98)(90,97,104,111)(91,110,105,96)(92,95,106,109)(93,108,107,94)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(197,204,211,218)(198,217,212,203)(199,202,213,216)(200,215,214,201)(205,224,219,210)(206,209,220,223)(207,222,221,208)>;
G:=Group( (1,87,15,101)(2,129,16,115)(3,89,17,103)(4,131,18,117)(5,91,19,105)(6,133,20,119)(7,93,21,107)(8,135,22,121)(9,95,23,109)(10,137,24,123)(11,97,25,111)(12,139,26,125)(13,99,27,85)(14,113,28,127)(29,165,43,151)(30,57,44,71)(31,167,45,153)(32,59,46,73)(33,141,47,155)(34,61,48,75)(35,143,49,157)(36,63,50,77)(37,145,51,159)(38,65,52,79)(39,147,53,161)(40,67,54,81)(41,149,55,163)(42,69,56,83)(58,170,72,184)(60,172,74,186)(62,174,76,188)(64,176,78,190)(66,178,80,192)(68,180,82,194)(70,182,84,196)(86,207,100,221)(88,209,102,223)(90,211,104,197)(92,213,106,199)(94,215,108,201)(96,217,110,203)(98,219,112,205)(114,222,128,208)(116,224,130,210)(118,198,132,212)(120,200,134,214)(122,202,136,216)(124,204,138,218)(126,206,140,220)(142,173,156,187)(144,175,158,189)(146,177,160,191)(148,179,162,193)(150,181,164,195)(152,183,166,169)(154,185,168,171), (1,191,208,52)(2,178,209,39)(3,193,210,54)(4,180,211,41)(5,195,212,56)(6,182,213,43)(7,169,214,30)(8,184,215,45)(9,171,216,32)(10,186,217,47)(11,173,218,34)(12,188,219,49)(13,175,220,36)(14,190,221,51)(15,177,222,38)(16,192,223,53)(17,179,224,40)(18,194,197,55)(19,181,198,42)(20,196,199,29)(21,183,200,44)(22,170,201,31)(23,185,202,46)(24,172,203,33)(25,187,204,48)(26,174,205,35)(27,189,206,50)(28,176,207,37)(57,93,152,120)(58,108,153,135)(59,95,154,122)(60,110,155,137)(61,97,156,124)(62,112,157,139)(63,99,158,126)(64,86,159,113)(65,101,160,128)(66,88,161,115)(67,103,162,130)(68,90,163,117)(69,105,164,132)(70,92,165,119)(71,107,166,134)(72,94,167,121)(73,109,168,136)(74,96,141,123)(75,111,142,138)(76,98,143,125)(77,85,144,140)(78,100,145,127)(79,87,146,114)(80,102,147,129)(81,89,148,116)(82,104,149,131)(83,91,150,118)(84,106,151,133), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,171,43,185)(30,184,44,170)(31,169,45,183)(32,182,46,196)(33,195,47,181)(34,180,48,194)(35,193,49,179)(36,178,50,192)(37,191,51,177)(38,176,52,190)(39,189,53,175)(40,174,54,188)(41,187,55,173)(42,172,56,186)(57,167,71,153)(58,152,72,166)(59,165,73,151)(60,150,74,164)(61,163,75,149)(62,148,76,162)(63,161,77,147)(64,146,78,160)(65,159,79,145)(66,144,80,158)(67,157,81,143)(68,142,82,156)(69,155,83,141)(70,168,84,154)(85,88,99,102)(86,101,100,87)(89,112,103,98)(90,97,104,111)(91,110,105,96)(92,95,106,109)(93,108,107,94)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(197,204,211,218)(198,217,212,203)(199,202,213,216)(200,215,214,201)(205,224,219,210)(206,209,220,223)(207,222,221,208) );
G=PermutationGroup([(1,87,15,101),(2,129,16,115),(3,89,17,103),(4,131,18,117),(5,91,19,105),(6,133,20,119),(7,93,21,107),(8,135,22,121),(9,95,23,109),(10,137,24,123),(11,97,25,111),(12,139,26,125),(13,99,27,85),(14,113,28,127),(29,165,43,151),(30,57,44,71),(31,167,45,153),(32,59,46,73),(33,141,47,155),(34,61,48,75),(35,143,49,157),(36,63,50,77),(37,145,51,159),(38,65,52,79),(39,147,53,161),(40,67,54,81),(41,149,55,163),(42,69,56,83),(58,170,72,184),(60,172,74,186),(62,174,76,188),(64,176,78,190),(66,178,80,192),(68,180,82,194),(70,182,84,196),(86,207,100,221),(88,209,102,223),(90,211,104,197),(92,213,106,199),(94,215,108,201),(96,217,110,203),(98,219,112,205),(114,222,128,208),(116,224,130,210),(118,198,132,212),(120,200,134,214),(122,202,136,216),(124,204,138,218),(126,206,140,220),(142,173,156,187),(144,175,158,189),(146,177,160,191),(148,179,162,193),(150,181,164,195),(152,183,166,169),(154,185,168,171)], [(1,191,208,52),(2,178,209,39),(3,193,210,54),(4,180,211,41),(5,195,212,56),(6,182,213,43),(7,169,214,30),(8,184,215,45),(9,171,216,32),(10,186,217,47),(11,173,218,34),(12,188,219,49),(13,175,220,36),(14,190,221,51),(15,177,222,38),(16,192,223,53),(17,179,224,40),(18,194,197,55),(19,181,198,42),(20,196,199,29),(21,183,200,44),(22,170,201,31),(23,185,202,46),(24,172,203,33),(25,187,204,48),(26,174,205,35),(27,189,206,50),(28,176,207,37),(57,93,152,120),(58,108,153,135),(59,95,154,122),(60,110,155,137),(61,97,156,124),(62,112,157,139),(63,99,158,126),(64,86,159,113),(65,101,160,128),(66,88,161,115),(67,103,162,130),(68,90,163,117),(69,105,164,132),(70,92,165,119),(71,107,166,134),(72,94,167,121),(73,109,168,136),(74,96,141,123),(75,111,142,138),(76,98,143,125),(77,85,144,140),(78,100,145,127),(79,87,146,114),(80,102,147,129),(81,89,148,116),(82,104,149,131),(83,91,150,118),(84,106,151,133)], [(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)], [(1,28,15,14),(2,13,16,27),(3,26,17,12),(4,11,18,25),(5,24,19,10),(6,9,20,23),(7,22,21,8),(29,171,43,185),(30,184,44,170),(31,169,45,183),(32,182,46,196),(33,195,47,181),(34,180,48,194),(35,193,49,179),(36,178,50,192),(37,191,51,177),(38,176,52,190),(39,189,53,175),(40,174,54,188),(41,187,55,173),(42,172,56,186),(57,167,71,153),(58,152,72,166),(59,165,73,151),(60,150,74,164),(61,163,75,149),(62,148,76,162),(63,161,77,147),(64,146,78,160),(65,159,79,145),(66,144,80,158),(67,157,81,143),(68,142,82,156),(69,155,83,141),(70,168,84,154),(85,88,99,102),(86,101,100,87),(89,112,103,98),(90,97,104,111),(91,110,105,96),(92,95,106,109),(93,108,107,94),(113,128,127,114),(115,126,129,140),(116,139,130,125),(117,124,131,138),(118,137,132,123),(119,122,133,136),(120,135,134,121),(197,204,211,218),(198,217,212,203),(199,202,213,216),(200,215,214,201),(205,224,219,210),(206,209,220,223),(207,222,221,208)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 3 |
| 0 | 0 | 0 | 0 | 2 | 15 |
| 28 | 2 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 7 |
| 0 | 0 | 0 | 0 | 24 | 6 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 17 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 21 | 0 | 0 |
| 0 | 0 | 11 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 24 |
| 0 | 0 | 0 | 0 | 26 | 19 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 21 | 0 | 0 |
| 0 | 0 | 15 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 5 |
| 0 | 0 | 0 | 0 | 3 | 10 |
G:=sub<GL(6,GF(29))| [17,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,14,2,0,0,0,0,3,15],[28,28,0,0,0,0,2,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,23,24,0,0,0,0,7,6],[17,17,0,0,0,0,0,12,0,0,0,0,0,0,0,11,0,0,0,0,21,18,0,0,0,0,0,0,10,26,0,0,0,0,24,19],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,11,15,0,0,0,0,21,18,0,0,0,0,0,0,19,3,0,0,0,0,5,10] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | 2+ (1+4) | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.163D14 | C42⋊D7 | C4×D28 | Dic7⋊4D4 | D14⋊D4 | C22.D28 | Dic7.Q8 | D7×C4⋊C4 | D28⋊C4 | D14.5D4 | C28⋊1D4 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | D14 | C42 | C22⋊C4 | C4⋊C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 9 | 9 | 1 | 12 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{163}D_{14} % in TeX
G:=Group("C4^2.163D14"); // GroupNames label
G:=SmallGroup(448,1162);
// by ID
G=gap.SmallGroup(448,1162);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,219,184,1571,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=a^2*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations
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