metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.154D14, C14.302- (1+4), C28⋊Q8⋊37C2, C4⋊C4.210D14, C42.C2⋊10D7, (C4×Dic14)⋊49C2, Dic7.Q8⋊35C2, D14⋊Q8.3C2, C4.Dic14⋊36C2, C42⋊2D7.1C2, Dic7⋊3Q8⋊37C2, (C4×C28).199C22, (C2×C28).602C23, (C2×C14).240C24, D14⋊C4.42C22, Dic7.13(C4○D4), C4⋊Dic7.316C22, C22.261(C23×D7), Dic7⋊C4.162C22, C7⋊4(C22.35C24), (C2×Dic7).260C23, (C4×Dic7).216C22, (C22×D7).105C23, C2.59(D4.10D14), C2.31(Q8.10D14), (C2×Dic14).252C22, C2.91(D7×C4○D4), C4⋊C4⋊D7.2C2, C4⋊C4⋊7D7.13C2, C14.202(C2×C4○D4), (C7×C42.C2)⋊13C2, (C2×C4×D7).130C22, (C7×C4⋊C4).195C22, (C2×C4).205(C22×D7), SmallGroup(448,1149)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 764 in 192 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2, C4 [×15], C22, C22 [×3], C7, C2×C4 [×7], C2×C4 [×9], Q8 [×4], C23, D7, C14 [×3], C42, C42 [×5], C22⋊C4 [×6], C4⋊C4 [×6], C4⋊C4 [×14], C22×C4, C2×Q8 [×2], Dic7 [×2], Dic7 [×6], C28 [×7], D14 [×3], C2×C14, C42⋊C2, C4×Q8 [×2], C22⋊Q8 [×2], C42.C2, C42.C2 [×4], C42⋊2C2 [×4], C4⋊Q8, Dic14 [×4], C4×D7 [×2], C2×Dic7 [×7], C2×C28 [×7], C22×D7, C22.35C24, C4×Dic7 [×5], Dic7⋊C4 [×10], C4⋊Dic7 [×4], D14⋊C4 [×6], C4×C28, C7×C4⋊C4 [×6], C2×Dic14 [×2], C2×C4×D7, C4×Dic14, C42⋊2D7, Dic7⋊3Q8, C28⋊Q8, Dic7.Q8 [×3], C4.Dic14, C4⋊C4⋊7D7, D14⋊Q8 [×2], C4⋊C4⋊D7 [×3], C7×C42.C2, C42.154D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2- (1+4) [×2], C22×D7 [×7], C22.35C24, C23×D7, Q8.10D14, D7×C4○D4, D4.10D14, C42.154D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 113 15 127)(2 176 16 190)(3 115 17 129)(4 178 18 192)(5 117 19 131)(6 180 20 194)(7 119 21 133)(8 182 22 196)(9 121 23 135)(10 184 24 170)(11 123 25 137)(12 186 26 172)(13 125 27 139)(14 188 28 174)(29 193 43 179)(30 132 44 118)(31 195 45 181)(32 134 46 120)(33 169 47 183)(34 136 48 122)(35 171 49 185)(36 138 50 124)(37 173 51 187)(38 140 52 126)(39 175 53 189)(40 114 54 128)(41 177 55 191)(42 116 56 130)(57 87 71 101)(58 168 72 154)(59 89 73 103)(60 142 74 156)(61 91 75 105)(62 144 76 158)(63 93 77 107)(64 146 78 160)(65 95 79 109)(66 148 80 162)(67 97 81 111)(68 150 82 164)(69 99 83 85)(70 152 84 166)(86 215 100 201)(88 217 102 203)(90 219 104 205)(92 221 106 207)(94 223 108 209)(96 197 110 211)(98 199 112 213)(141 218 155 204)(143 220 157 206)(145 222 159 208)(147 224 161 210)(149 198 163 212)(151 200 165 214)(153 202 167 216)
(1 77 53 208)(2 209 54 78)(3 79 55 210)(4 211 56 80)(5 81 29 212)(6 213 30 82)(7 83 31 214)(8 215 32 84)(9 57 33 216)(10 217 34 58)(11 59 35 218)(12 219 36 60)(13 61 37 220)(14 221 38 62)(15 63 39 222)(16 223 40 64)(17 65 41 224)(18 197 42 66)(19 67 43 198)(20 199 44 68)(21 69 45 200)(22 201 46 70)(23 71 47 202)(24 203 48 72)(25 73 49 204)(26 205 50 74)(27 75 51 206)(28 207 52 76)(85 195 151 119)(86 120 152 196)(87 169 153 121)(88 122 154 170)(89 171 155 123)(90 124 156 172)(91 173 157 125)(92 126 158 174)(93 175 159 127)(94 128 160 176)(95 177 161 129)(96 130 162 178)(97 179 163 131)(98 132 164 180)(99 181 165 133)(100 134 166 182)(101 183 167 135)(102 136 168 184)(103 185 141 137)(104 138 142 186)(105 187 143 139)(106 140 144 188)(107 189 145 113)(108 114 146 190)(109 191 147 115)(110 116 148 192)(111 193 149 117)(112 118 150 194)
(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 34 43 48)(30 47 44 33)(31 32 45 46)(35 56 49 42)(36 41 50 55)(37 54 51 40)(38 39 52 53)(57 199 71 213)(58 212 72 198)(59 197 73 211)(60 210 74 224)(61 223 75 209)(62 208 76 222)(63 221 77 207)(64 206 78 220)(65 219 79 205)(66 204 80 218)(67 217 81 203)(68 202 82 216)(69 215 83 201)(70 200 84 214)(85 100 99 86)(87 98 101 112)(88 111 102 97)(89 96 103 110)(90 109 104 95)(91 94 105 108)(92 107 106 93)(113 174 127 188)(114 187 128 173)(115 172 129 186)(116 185 130 171)(117 170 131 184)(118 183 132 169)(119 196 133 182)(120 181 134 195)(121 194 135 180)(122 179 136 193)(123 192 137 178)(124 177 138 191)(125 190 139 176)(126 175 140 189)(141 148 155 162)(142 161 156 147)(143 146 157 160)(144 159 158 145)(149 168 163 154)(150 153 164 167)(151 166 165 152)
G:=sub<Sym(224)| (1,113,15,127)(2,176,16,190)(3,115,17,129)(4,178,18,192)(5,117,19,131)(6,180,20,194)(7,119,21,133)(8,182,22,196)(9,121,23,135)(10,184,24,170)(11,123,25,137)(12,186,26,172)(13,125,27,139)(14,188,28,174)(29,193,43,179)(30,132,44,118)(31,195,45,181)(32,134,46,120)(33,169,47,183)(34,136,48,122)(35,171,49,185)(36,138,50,124)(37,173,51,187)(38,140,52,126)(39,175,53,189)(40,114,54,128)(41,177,55,191)(42,116,56,130)(57,87,71,101)(58,168,72,154)(59,89,73,103)(60,142,74,156)(61,91,75,105)(62,144,76,158)(63,93,77,107)(64,146,78,160)(65,95,79,109)(66,148,80,162)(67,97,81,111)(68,150,82,164)(69,99,83,85)(70,152,84,166)(86,215,100,201)(88,217,102,203)(90,219,104,205)(92,221,106,207)(94,223,108,209)(96,197,110,211)(98,199,112,213)(141,218,155,204)(143,220,157,206)(145,222,159,208)(147,224,161,210)(149,198,163,212)(151,200,165,214)(153,202,167,216), (1,77,53,208)(2,209,54,78)(3,79,55,210)(4,211,56,80)(5,81,29,212)(6,213,30,82)(7,83,31,214)(8,215,32,84)(9,57,33,216)(10,217,34,58)(11,59,35,218)(12,219,36,60)(13,61,37,220)(14,221,38,62)(15,63,39,222)(16,223,40,64)(17,65,41,224)(18,197,42,66)(19,67,43,198)(20,199,44,68)(21,69,45,200)(22,201,46,70)(23,71,47,202)(24,203,48,72)(25,73,49,204)(26,205,50,74)(27,75,51,206)(28,207,52,76)(85,195,151,119)(86,120,152,196)(87,169,153,121)(88,122,154,170)(89,171,155,123)(90,124,156,172)(91,173,157,125)(92,126,158,174)(93,175,159,127)(94,128,160,176)(95,177,161,129)(96,130,162,178)(97,179,163,131)(98,132,164,180)(99,181,165,133)(100,134,166,182)(101,183,167,135)(102,136,168,184)(103,185,141,137)(104,138,142,186)(105,187,143,139)(106,140,144,188)(107,189,145,113)(108,114,146,190)(109,191,147,115)(110,116,148,192)(111,193,149,117)(112,118,150,194), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,34,43,48)(30,47,44,33)(31,32,45,46)(35,56,49,42)(36,41,50,55)(37,54,51,40)(38,39,52,53)(57,199,71,213)(58,212,72,198)(59,197,73,211)(60,210,74,224)(61,223,75,209)(62,208,76,222)(63,221,77,207)(64,206,78,220)(65,219,79,205)(66,204,80,218)(67,217,81,203)(68,202,82,216)(69,215,83,201)(70,200,84,214)(85,100,99,86)(87,98,101,112)(88,111,102,97)(89,96,103,110)(90,109,104,95)(91,94,105,108)(92,107,106,93)(113,174,127,188)(114,187,128,173)(115,172,129,186)(116,185,130,171)(117,170,131,184)(118,183,132,169)(119,196,133,182)(120,181,134,195)(121,194,135,180)(122,179,136,193)(123,192,137,178)(124,177,138,191)(125,190,139,176)(126,175,140,189)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152)>;
G:=Group( (1,113,15,127)(2,176,16,190)(3,115,17,129)(4,178,18,192)(5,117,19,131)(6,180,20,194)(7,119,21,133)(8,182,22,196)(9,121,23,135)(10,184,24,170)(11,123,25,137)(12,186,26,172)(13,125,27,139)(14,188,28,174)(29,193,43,179)(30,132,44,118)(31,195,45,181)(32,134,46,120)(33,169,47,183)(34,136,48,122)(35,171,49,185)(36,138,50,124)(37,173,51,187)(38,140,52,126)(39,175,53,189)(40,114,54,128)(41,177,55,191)(42,116,56,130)(57,87,71,101)(58,168,72,154)(59,89,73,103)(60,142,74,156)(61,91,75,105)(62,144,76,158)(63,93,77,107)(64,146,78,160)(65,95,79,109)(66,148,80,162)(67,97,81,111)(68,150,82,164)(69,99,83,85)(70,152,84,166)(86,215,100,201)(88,217,102,203)(90,219,104,205)(92,221,106,207)(94,223,108,209)(96,197,110,211)(98,199,112,213)(141,218,155,204)(143,220,157,206)(145,222,159,208)(147,224,161,210)(149,198,163,212)(151,200,165,214)(153,202,167,216), (1,77,53,208)(2,209,54,78)(3,79,55,210)(4,211,56,80)(5,81,29,212)(6,213,30,82)(7,83,31,214)(8,215,32,84)(9,57,33,216)(10,217,34,58)(11,59,35,218)(12,219,36,60)(13,61,37,220)(14,221,38,62)(15,63,39,222)(16,223,40,64)(17,65,41,224)(18,197,42,66)(19,67,43,198)(20,199,44,68)(21,69,45,200)(22,201,46,70)(23,71,47,202)(24,203,48,72)(25,73,49,204)(26,205,50,74)(27,75,51,206)(28,207,52,76)(85,195,151,119)(86,120,152,196)(87,169,153,121)(88,122,154,170)(89,171,155,123)(90,124,156,172)(91,173,157,125)(92,126,158,174)(93,175,159,127)(94,128,160,176)(95,177,161,129)(96,130,162,178)(97,179,163,131)(98,132,164,180)(99,181,165,133)(100,134,166,182)(101,183,167,135)(102,136,168,184)(103,185,141,137)(104,138,142,186)(105,187,143,139)(106,140,144,188)(107,189,145,113)(108,114,146,190)(109,191,147,115)(110,116,148,192)(111,193,149,117)(112,118,150,194), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,34,43,48)(30,47,44,33)(31,32,45,46)(35,56,49,42)(36,41,50,55)(37,54,51,40)(38,39,52,53)(57,199,71,213)(58,212,72,198)(59,197,73,211)(60,210,74,224)(61,223,75,209)(62,208,76,222)(63,221,77,207)(64,206,78,220)(65,219,79,205)(66,204,80,218)(67,217,81,203)(68,202,82,216)(69,215,83,201)(70,200,84,214)(85,100,99,86)(87,98,101,112)(88,111,102,97)(89,96,103,110)(90,109,104,95)(91,94,105,108)(92,107,106,93)(113,174,127,188)(114,187,128,173)(115,172,129,186)(116,185,130,171)(117,170,131,184)(118,183,132,169)(119,196,133,182)(120,181,134,195)(121,194,135,180)(122,179,136,193)(123,192,137,178)(124,177,138,191)(125,190,139,176)(126,175,140,189)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152) );
G=PermutationGroup([(1,113,15,127),(2,176,16,190),(3,115,17,129),(4,178,18,192),(5,117,19,131),(6,180,20,194),(7,119,21,133),(8,182,22,196),(9,121,23,135),(10,184,24,170),(11,123,25,137),(12,186,26,172),(13,125,27,139),(14,188,28,174),(29,193,43,179),(30,132,44,118),(31,195,45,181),(32,134,46,120),(33,169,47,183),(34,136,48,122),(35,171,49,185),(36,138,50,124),(37,173,51,187),(38,140,52,126),(39,175,53,189),(40,114,54,128),(41,177,55,191),(42,116,56,130),(57,87,71,101),(58,168,72,154),(59,89,73,103),(60,142,74,156),(61,91,75,105),(62,144,76,158),(63,93,77,107),(64,146,78,160),(65,95,79,109),(66,148,80,162),(67,97,81,111),(68,150,82,164),(69,99,83,85),(70,152,84,166),(86,215,100,201),(88,217,102,203),(90,219,104,205),(92,221,106,207),(94,223,108,209),(96,197,110,211),(98,199,112,213),(141,218,155,204),(143,220,157,206),(145,222,159,208),(147,224,161,210),(149,198,163,212),(151,200,165,214),(153,202,167,216)], [(1,77,53,208),(2,209,54,78),(3,79,55,210),(4,211,56,80),(5,81,29,212),(6,213,30,82),(7,83,31,214),(8,215,32,84),(9,57,33,216),(10,217,34,58),(11,59,35,218),(12,219,36,60),(13,61,37,220),(14,221,38,62),(15,63,39,222),(16,223,40,64),(17,65,41,224),(18,197,42,66),(19,67,43,198),(20,199,44,68),(21,69,45,200),(22,201,46,70),(23,71,47,202),(24,203,48,72),(25,73,49,204),(26,205,50,74),(27,75,51,206),(28,207,52,76),(85,195,151,119),(86,120,152,196),(87,169,153,121),(88,122,154,170),(89,171,155,123),(90,124,156,172),(91,173,157,125),(92,126,158,174),(93,175,159,127),(94,128,160,176),(95,177,161,129),(96,130,162,178),(97,179,163,131),(98,132,164,180),(99,181,165,133),(100,134,166,182),(101,183,167,135),(102,136,168,184),(103,185,141,137),(104,138,142,186),(105,187,143,139),(106,140,144,188),(107,189,145,113),(108,114,146,190),(109,191,147,115),(110,116,148,192),(111,193,149,117),(112,118,150,194)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,34,43,48),(30,47,44,33),(31,32,45,46),(35,56,49,42),(36,41,50,55),(37,54,51,40),(38,39,52,53),(57,199,71,213),(58,212,72,198),(59,197,73,211),(60,210,74,224),(61,223,75,209),(62,208,76,222),(63,221,77,207),(64,206,78,220),(65,219,79,205),(66,204,80,218),(67,217,81,203),(68,202,82,216),(69,215,83,201),(70,200,84,214),(85,100,99,86),(87,98,101,112),(88,111,102,97),(89,96,103,110),(90,109,104,95),(91,94,105,108),(92,107,106,93),(113,174,127,188),(114,187,128,173),(115,172,129,186),(116,185,130,171),(117,170,131,184),(118,183,132,169),(119,196,133,182),(120,181,134,195),(121,194,135,180),(122,179,136,193),(123,192,137,178),(124,177,138,191),(125,190,139,176),(126,175,140,189),(141,148,155,162),(142,161,156,147),(143,146,157,160),(144,159,158,145),(149,168,163,154),(150,153,164,167),(151,166,165,152)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 24 | 22 | 13 | 11 | 0 | 0 | 0 | 0 |
| 4 | 0 | 6 | 9 | 0 | 0 | 0 | 0 |
| 18 | 16 | 21 | 7 | 0 | 0 | 0 | 0 |
| 16 | 28 | 6 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 24 | 25 | 7 |
| 0 | 0 | 0 | 0 | 5 | 27 | 23 | 20 |
| 0 | 0 | 0 | 0 | 23 | 16 | 11 | 10 |
| 0 | 0 | 0 | 0 | 13 | 0 | 24 | 25 |
| 2 | 26 | 18 | 13 | 0 | 0 | 0 | 0 |
| 10 | 0 | 15 | 8 | 0 | 0 | 0 | 0 |
| 16 | 11 | 9 | 3 | 0 | 0 | 0 | 0 |
| 11 | 12 | 15 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 26 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 2 | 3 |
| 0 | 27 | 4 | 15 | 0 | 0 | 0 | 0 |
| 24 | 5 | 17 | 17 | 0 | 0 | 0 | 0 |
| 12 | 2 | 1 | 2 | 0 | 0 | 0 | 0 |
| 13 | 6 | 2 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 1 | 19 | 8 |
| 0 | 0 | 0 | 0 | 28 | 18 | 9 | 12 |
| 0 | 0 | 0 | 0 | 4 | 22 | 15 | 27 |
| 0 | 0 | 0 | 0 | 4 | 17 | 1 | 18 |
| 9 | 18 | 14 | 25 | 0 | 0 | 0 | 0 |
| 5 | 24 | 12 | 12 | 0 | 0 | 0 | 0 |
| 2 | 10 | 27 | 28 | 0 | 0 | 0 | 0 |
| 6 | 24 | 6 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 7 | 15 | 14 |
| 0 | 0 | 0 | 0 | 18 | 28 | 16 | 10 |
| 0 | 0 | 0 | 0 | 22 | 4 | 13 | 22 |
| 0 | 0 | 0 | 0 | 17 | 4 | 6 | 16 |
G:=sub<GL(8,GF(29))| [24,4,18,16,0,0,0,0,22,0,16,28,0,0,0,0,13,6,21,6,0,0,0,0,11,9,7,13,0,0,0,0,0,0,0,0,24,5,23,13,0,0,0,0,24,27,16,0,0,0,0,0,25,23,11,24,0,0,0,0,7,20,10,25],[2,10,16,11,0,0,0,0,26,0,11,12,0,0,0,0,18,15,9,15,0,0,0,0,13,8,3,18,0,0,0,0,0,0,0,0,11,2,0,0,0,0,0,0,27,18,0,0,0,0,0,0,0,0,26,2,0,0,0,0,0,0,25,3],[0,24,12,13,0,0,0,0,27,5,2,6,0,0,0,0,4,17,1,2,0,0,0,0,15,17,2,23,0,0,0,0,0,0,0,0,7,28,4,4,0,0,0,0,1,18,22,17,0,0,0,0,19,9,15,1,0,0,0,0,8,12,27,18],[9,5,2,6,0,0,0,0,18,24,10,24,0,0,0,0,14,12,27,6,0,0,0,0,25,12,28,27,0,0,0,0,0,0,0,0,1,18,22,17,0,0,0,0,7,28,4,4,0,0,0,0,15,16,13,6,0,0,0,0,14,10,22,16] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2- (1+4) | Q8.10D14 | D7×C4○D4 | D4.10D14 |
| kernel | C42.154D14 | C4×Dic14 | C42⋊2D7 | Dic7⋊3Q8 | C28⋊Q8 | Dic7.Q8 | C4.Dic14 | C4⋊C4⋊7D7 | D14⋊Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | Dic7 | C42 | C4⋊C4 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 2 | 3 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{154}D_{14} % in TeX
G:=Group("C4^2.154D14"); // GroupNames label
G:=SmallGroup(448,1149);
// by ID
G=gap.SmallGroup(448,1149);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,555,100,1571,570,136,18822]);
// 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=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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