metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.158D14, C14.322- (1+4), C14.1362+ (1+4), C28⋊1D4⋊35C2, C4⋊C4.115D14, C42.C2⋊14D7, D14⋊Q8⋊38C2, C4.D28⋊32C2, D14.5D4⋊37C2, (C4×C28).225C22, (C2×C14).244C24, (C2×C28).191C23, D14⋊C4.74C22, C2.61(D4⋊8D14), (C2×D28).167C22, Dic7⋊C4.55C22, C22.265(C23×D7), C7⋊5(C22.56C24), (C2×Dic14).42C22, (C2×Dic7).126C23, (C22×D7).109C23, C2.33(Q8.10D14), (C7×C42.C2)⋊17C2, (C2×C4×D7).134C22, (C7×C4⋊C4).199C22, (C2×C4).208(C22×D7), SmallGroup(448,1153)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1244 in 220 conjugacy classes, 91 normal (13 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×11], C22, C22 [×12], C7, C2×C4, C2×C4 [×6], C2×C4 [×8], D4 [×6], Q8 [×2], C23 [×4], D7 [×4], C14, C14 [×2], C42, C22⋊C4 [×12], C4⋊C4 [×6], C4⋊C4 [×4], C22×C4 [×4], C2×D4 [×6], C2×Q8 [×2], Dic7 [×4], C28 [×7], D14 [×12], C2×C14, C4⋊D4 [×4], C22⋊Q8 [×4], C22.D4 [×4], C4.4D4 [×2], C42.C2, Dic14 [×2], C4×D7 [×4], D28 [×6], C2×Dic7 [×4], C2×C28, C2×C28 [×6], C22×D7 [×4], C22.56C24, Dic7⋊C4 [×4], D14⋊C4 [×12], C4×C28, C7×C4⋊C4 [×6], C2×Dic14 [×2], C2×C4×D7 [×4], C2×D28 [×6], C4.D28 [×2], D14.5D4 [×4], C28⋊1D4 [×4], D14⋊Q8 [×4], C7×C42.C2, C42.158D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C24, D14 [×7], 2+ (1+4) [×2], 2- (1+4), C22×D7 [×7], C22.56C24, C23×D7, Q8.10D14, D4⋊8D14 [×2], C42.158D14
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-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 128 15 114)(2 178 16 192)(3 130 17 116)(4 180 18 194)(5 132 19 118)(6 182 20 196)(7 134 21 120)(8 184 22 170)(9 136 23 122)(10 186 24 172)(11 138 25 124)(12 188 26 174)(13 140 27 126)(14 190 28 176)(29 103 43 89)(30 67 44 81)(31 105 45 91)(32 69 46 83)(33 107 47 93)(34 71 48 57)(35 109 49 95)(36 73 50 59)(37 111 51 97)(38 75 52 61)(39 85 53 99)(40 77 54 63)(41 87 55 101)(42 79 56 65)(58 148 72 162)(60 150 74 164)(62 152 76 166)(64 154 78 168)(66 156 80 142)(68 158 82 144)(70 160 84 146)(86 167 100 153)(88 141 102 155)(90 143 104 157)(92 145 106 159)(94 147 108 161)(96 149 110 163)(98 151 112 165)(113 207 127 221)(115 209 129 223)(117 211 131 197)(119 213 133 199)(121 215 135 201)(123 217 137 203)(125 219 139 205)(169 214 183 200)(171 216 185 202)(173 218 187 204)(175 220 189 206)(177 222 191 208)(179 224 193 210)(181 198 195 212)
(1 88 222 65)(2 66 223 89)(3 90 224 67)(4 68 197 91)(5 92 198 69)(6 70 199 93)(7 94 200 71)(8 72 201 95)(9 96 202 73)(10 74 203 97)(11 98 204 75)(12 76 205 99)(13 100 206 77)(14 78 207 101)(15 102 208 79)(16 80 209 103)(17 104 210 81)(18 82 211 105)(19 106 212 83)(20 84 213 107)(21 108 214 57)(22 58 215 109)(23 110 216 59)(24 60 217 111)(25 112 218 61)(26 62 219 85)(27 86 220 63)(28 64 221 87)(29 178 156 115)(30 116 157 179)(31 180 158 117)(32 118 159 181)(33 182 160 119)(34 120 161 183)(35 184 162 121)(36 122 163 185)(37 186 164 123)(38 124 165 187)(39 188 166 125)(40 126 167 189)(41 190 168 127)(42 128 141 191)(43 192 142 129)(44 130 143 193)(45 194 144 131)(46 132 145 195)(47 196 146 133)(48 134 147 169)(49 170 148 135)(50 136 149 171)(51 172 150 137)(52 138 151 173)(53 174 152 139)(54 140 153 175)(55 176 154 113)(56 114 155 177)
(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 48 15 34)(2 33 16 47)(3 46 17 32)(4 31 18 45)(5 44 19 30)(6 29 20 43)(7 42 21 56)(8 55 22 41)(9 40 23 54)(10 53 24 39)(11 38 25 52)(12 51 26 37)(13 36 27 50)(14 49 28 35)(57 128 71 114)(58 113 72 127)(59 126 73 140)(60 139 74 125)(61 124 75 138)(62 137 76 123)(63 122 77 136)(64 135 78 121)(65 120 79 134)(66 133 80 119)(67 118 81 132)(68 131 82 117)(69 116 83 130)(70 129 84 115)(85 172 99 186)(86 185 100 171)(87 170 101 184)(88 183 102 169)(89 196 103 182)(90 181 104 195)(91 194 105 180)(92 179 106 193)(93 192 107 178)(94 177 108 191)(95 190 109 176)(96 175 110 189)(97 188 111 174)(98 173 112 187)(141 214 155 200)(142 199 156 213)(143 212 157 198)(144 197 158 211)(145 210 159 224)(146 223 160 209)(147 208 161 222)(148 221 162 207)(149 206 163 220)(150 219 164 205)(151 204 165 218)(152 217 166 203)(153 202 167 216)(154 215 168 201)
G:=sub<Sym(224)| (1,128,15,114)(2,178,16,192)(3,130,17,116)(4,180,18,194)(5,132,19,118)(6,182,20,196)(7,134,21,120)(8,184,22,170)(9,136,23,122)(10,186,24,172)(11,138,25,124)(12,188,26,174)(13,140,27,126)(14,190,28,176)(29,103,43,89)(30,67,44,81)(31,105,45,91)(32,69,46,83)(33,107,47,93)(34,71,48,57)(35,109,49,95)(36,73,50,59)(37,111,51,97)(38,75,52,61)(39,85,53,99)(40,77,54,63)(41,87,55,101)(42,79,56,65)(58,148,72,162)(60,150,74,164)(62,152,76,166)(64,154,78,168)(66,156,80,142)(68,158,82,144)(70,160,84,146)(86,167,100,153)(88,141,102,155)(90,143,104,157)(92,145,106,159)(94,147,108,161)(96,149,110,163)(98,151,112,165)(113,207,127,221)(115,209,129,223)(117,211,131,197)(119,213,133,199)(121,215,135,201)(123,217,137,203)(125,219,139,205)(169,214,183,200)(171,216,185,202)(173,218,187,204)(175,220,189,206)(177,222,191,208)(179,224,193,210)(181,198,195,212), (1,88,222,65)(2,66,223,89)(3,90,224,67)(4,68,197,91)(5,92,198,69)(6,70,199,93)(7,94,200,71)(8,72,201,95)(9,96,202,73)(10,74,203,97)(11,98,204,75)(12,76,205,99)(13,100,206,77)(14,78,207,101)(15,102,208,79)(16,80,209,103)(17,104,210,81)(18,82,211,105)(19,106,212,83)(20,84,213,107)(21,108,214,57)(22,58,215,109)(23,110,216,59)(24,60,217,111)(25,112,218,61)(26,62,219,85)(27,86,220,63)(28,64,221,87)(29,178,156,115)(30,116,157,179)(31,180,158,117)(32,118,159,181)(33,182,160,119)(34,120,161,183)(35,184,162,121)(36,122,163,185)(37,186,164,123)(38,124,165,187)(39,188,166,125)(40,126,167,189)(41,190,168,127)(42,128,141,191)(43,192,142,129)(44,130,143,193)(45,194,144,131)(46,132,145,195)(47,196,146,133)(48,134,147,169)(49,170,148,135)(50,136,149,171)(51,172,150,137)(52,138,151,173)(53,174,152,139)(54,140,153,175)(55,176,154,113)(56,114,155,177), (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), (1,48,15,34)(2,33,16,47)(3,46,17,32)(4,31,18,45)(5,44,19,30)(6,29,20,43)(7,42,21,56)(8,55,22,41)(9,40,23,54)(10,53,24,39)(11,38,25,52)(12,51,26,37)(13,36,27,50)(14,49,28,35)(57,128,71,114)(58,113,72,127)(59,126,73,140)(60,139,74,125)(61,124,75,138)(62,137,76,123)(63,122,77,136)(64,135,78,121)(65,120,79,134)(66,133,80,119)(67,118,81,132)(68,131,82,117)(69,116,83,130)(70,129,84,115)(85,172,99,186)(86,185,100,171)(87,170,101,184)(88,183,102,169)(89,196,103,182)(90,181,104,195)(91,194,105,180)(92,179,106,193)(93,192,107,178)(94,177,108,191)(95,190,109,176)(96,175,110,189)(97,188,111,174)(98,173,112,187)(141,214,155,200)(142,199,156,213)(143,212,157,198)(144,197,158,211)(145,210,159,224)(146,223,160,209)(147,208,161,222)(148,221,162,207)(149,206,163,220)(150,219,164,205)(151,204,165,218)(152,217,166,203)(153,202,167,216)(154,215,168,201)>;
G:=Group( (1,128,15,114)(2,178,16,192)(3,130,17,116)(4,180,18,194)(5,132,19,118)(6,182,20,196)(7,134,21,120)(8,184,22,170)(9,136,23,122)(10,186,24,172)(11,138,25,124)(12,188,26,174)(13,140,27,126)(14,190,28,176)(29,103,43,89)(30,67,44,81)(31,105,45,91)(32,69,46,83)(33,107,47,93)(34,71,48,57)(35,109,49,95)(36,73,50,59)(37,111,51,97)(38,75,52,61)(39,85,53,99)(40,77,54,63)(41,87,55,101)(42,79,56,65)(58,148,72,162)(60,150,74,164)(62,152,76,166)(64,154,78,168)(66,156,80,142)(68,158,82,144)(70,160,84,146)(86,167,100,153)(88,141,102,155)(90,143,104,157)(92,145,106,159)(94,147,108,161)(96,149,110,163)(98,151,112,165)(113,207,127,221)(115,209,129,223)(117,211,131,197)(119,213,133,199)(121,215,135,201)(123,217,137,203)(125,219,139,205)(169,214,183,200)(171,216,185,202)(173,218,187,204)(175,220,189,206)(177,222,191,208)(179,224,193,210)(181,198,195,212), (1,88,222,65)(2,66,223,89)(3,90,224,67)(4,68,197,91)(5,92,198,69)(6,70,199,93)(7,94,200,71)(8,72,201,95)(9,96,202,73)(10,74,203,97)(11,98,204,75)(12,76,205,99)(13,100,206,77)(14,78,207,101)(15,102,208,79)(16,80,209,103)(17,104,210,81)(18,82,211,105)(19,106,212,83)(20,84,213,107)(21,108,214,57)(22,58,215,109)(23,110,216,59)(24,60,217,111)(25,112,218,61)(26,62,219,85)(27,86,220,63)(28,64,221,87)(29,178,156,115)(30,116,157,179)(31,180,158,117)(32,118,159,181)(33,182,160,119)(34,120,161,183)(35,184,162,121)(36,122,163,185)(37,186,164,123)(38,124,165,187)(39,188,166,125)(40,126,167,189)(41,190,168,127)(42,128,141,191)(43,192,142,129)(44,130,143,193)(45,194,144,131)(46,132,145,195)(47,196,146,133)(48,134,147,169)(49,170,148,135)(50,136,149,171)(51,172,150,137)(52,138,151,173)(53,174,152,139)(54,140,153,175)(55,176,154,113)(56,114,155,177), (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), (1,48,15,34)(2,33,16,47)(3,46,17,32)(4,31,18,45)(5,44,19,30)(6,29,20,43)(7,42,21,56)(8,55,22,41)(9,40,23,54)(10,53,24,39)(11,38,25,52)(12,51,26,37)(13,36,27,50)(14,49,28,35)(57,128,71,114)(58,113,72,127)(59,126,73,140)(60,139,74,125)(61,124,75,138)(62,137,76,123)(63,122,77,136)(64,135,78,121)(65,120,79,134)(66,133,80,119)(67,118,81,132)(68,131,82,117)(69,116,83,130)(70,129,84,115)(85,172,99,186)(86,185,100,171)(87,170,101,184)(88,183,102,169)(89,196,103,182)(90,181,104,195)(91,194,105,180)(92,179,106,193)(93,192,107,178)(94,177,108,191)(95,190,109,176)(96,175,110,189)(97,188,111,174)(98,173,112,187)(141,214,155,200)(142,199,156,213)(143,212,157,198)(144,197,158,211)(145,210,159,224)(146,223,160,209)(147,208,161,222)(148,221,162,207)(149,206,163,220)(150,219,164,205)(151,204,165,218)(152,217,166,203)(153,202,167,216)(154,215,168,201) );
G=PermutationGroup([(1,128,15,114),(2,178,16,192),(3,130,17,116),(4,180,18,194),(5,132,19,118),(6,182,20,196),(7,134,21,120),(8,184,22,170),(9,136,23,122),(10,186,24,172),(11,138,25,124),(12,188,26,174),(13,140,27,126),(14,190,28,176),(29,103,43,89),(30,67,44,81),(31,105,45,91),(32,69,46,83),(33,107,47,93),(34,71,48,57),(35,109,49,95),(36,73,50,59),(37,111,51,97),(38,75,52,61),(39,85,53,99),(40,77,54,63),(41,87,55,101),(42,79,56,65),(58,148,72,162),(60,150,74,164),(62,152,76,166),(64,154,78,168),(66,156,80,142),(68,158,82,144),(70,160,84,146),(86,167,100,153),(88,141,102,155),(90,143,104,157),(92,145,106,159),(94,147,108,161),(96,149,110,163),(98,151,112,165),(113,207,127,221),(115,209,129,223),(117,211,131,197),(119,213,133,199),(121,215,135,201),(123,217,137,203),(125,219,139,205),(169,214,183,200),(171,216,185,202),(173,218,187,204),(175,220,189,206),(177,222,191,208),(179,224,193,210),(181,198,195,212)], [(1,88,222,65),(2,66,223,89),(3,90,224,67),(4,68,197,91),(5,92,198,69),(6,70,199,93),(7,94,200,71),(8,72,201,95),(9,96,202,73),(10,74,203,97),(11,98,204,75),(12,76,205,99),(13,100,206,77),(14,78,207,101),(15,102,208,79),(16,80,209,103),(17,104,210,81),(18,82,211,105),(19,106,212,83),(20,84,213,107),(21,108,214,57),(22,58,215,109),(23,110,216,59),(24,60,217,111),(25,112,218,61),(26,62,219,85),(27,86,220,63),(28,64,221,87),(29,178,156,115),(30,116,157,179),(31,180,158,117),(32,118,159,181),(33,182,160,119),(34,120,161,183),(35,184,162,121),(36,122,163,185),(37,186,164,123),(38,124,165,187),(39,188,166,125),(40,126,167,189),(41,190,168,127),(42,128,141,191),(43,192,142,129),(44,130,143,193),(45,194,144,131),(46,132,145,195),(47,196,146,133),(48,134,147,169),(49,170,148,135),(50,136,149,171),(51,172,150,137),(52,138,151,173),(53,174,152,139),(54,140,153,175),(55,176,154,113),(56,114,155,177)], [(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)], [(1,48,15,34),(2,33,16,47),(3,46,17,32),(4,31,18,45),(5,44,19,30),(6,29,20,43),(7,42,21,56),(8,55,22,41),(9,40,23,54),(10,53,24,39),(11,38,25,52),(12,51,26,37),(13,36,27,50),(14,49,28,35),(57,128,71,114),(58,113,72,127),(59,126,73,140),(60,139,74,125),(61,124,75,138),(62,137,76,123),(63,122,77,136),(64,135,78,121),(65,120,79,134),(66,133,80,119),(67,118,81,132),(68,131,82,117),(69,116,83,130),(70,129,84,115),(85,172,99,186),(86,185,100,171),(87,170,101,184),(88,183,102,169),(89,196,103,182),(90,181,104,195),(91,194,105,180),(92,179,106,193),(93,192,107,178),(94,177,108,191),(95,190,109,176),(96,175,110,189),(97,188,111,174),(98,173,112,187),(141,214,155,200),(142,199,156,213),(143,212,157,198),(144,197,158,211),(145,210,159,224),(146,223,160,209),(147,208,161,222),(148,221,162,207),(149,206,163,220),(150,219,164,205),(151,204,165,218),(152,217,166,203),(153,202,167,216),(154,215,168,201)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 5 | 4 | 27 | 0 | 0 | 0 | 0 | 0 |
| 15 | 5 | 0 | 27 | 0 | 0 | 0 | 0 |
| 14 | 20 | 24 | 25 | 0 | 0 | 0 | 0 |
| 17 | 14 | 14 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 28 | 17 | 10 | 22 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 14 | 8 | 13 | 12 |
| 18 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 27 | 15 | 18 | 14 | 0 | 0 | 0 | 0 |
| 9 | 2 | 8 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 16 | 9 | 22 |
| 0 | 0 | 0 | 0 | 12 | 13 | 20 | 20 |
| 26 | 14 | 14 | 6 | 0 | 0 | 0 | 0 |
| 14 | 10 | 20 | 11 | 0 | 0 | 0 | 0 |
| 6 | 5 | 27 | 9 | 0 | 0 | 0 | 0 |
| 8 | 25 | 23 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 26 | 6 | 2 |
| 0 | 0 | 0 | 0 | 21 | 0 | 14 | 0 |
| 0 | 0 | 0 | 0 | 24 | 25 | 25 | 3 |
| 9 | 25 | 6 | 20 | 0 | 0 | 0 | 0 |
| 21 | 19 | 27 | 23 | 0 | 0 | 0 | 0 |
| 8 | 4 | 11 | 9 | 0 | 0 | 0 | 0 |
| 18 | 16 | 11 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 13 | 12 | 10 |
| 0 | 0 | 0 | 0 | 28 | 17 | 10 | 22 |
| 0 | 0 | 0 | 0 | 1 | 13 | 20 | 7 |
| 0 | 0 | 0 | 0 | 9 | 4 | 18 | 4 |
G:=sub<GL(8,GF(29))| [5,15,14,17,0,0,0,0,4,5,20,14,0,0,0,0,27,0,24,14,0,0,0,0,0,27,25,24,0,0,0,0,0,0,0,0,1,28,0,14,0,0,0,0,0,17,0,8,0,0,0,0,11,10,28,13,0,0,0,0,0,22,0,12],[18,8,27,9,0,0,0,0,14,11,15,2,0,0,0,0,0,0,18,8,0,0,0,0,0,0,14,11,0,0,0,0,0,0,0,0,28,13,28,12,0,0,0,0,11,1,16,13,0,0,0,0,0,0,9,20,0,0,0,0,0,0,22,20],[26,14,6,8,0,0,0,0,14,10,5,25,0,0,0,0,14,20,27,23,0,0,0,0,6,11,9,24,0,0,0,0,0,0,0,0,15,0,21,24,0,0,0,0,0,26,0,25,0,0,0,0,28,6,14,25,0,0,0,0,0,2,0,3],[9,21,8,18,0,0,0,0,25,19,4,16,0,0,0,0,6,27,11,11,0,0,0,0,20,23,9,19,0,0,0,0,0,0,0,0,17,28,1,9,0,0,0,0,13,17,13,4,0,0,0,0,12,10,20,18,0,0,0,0,10,22,7,4] >;
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4G | 4H | 4I | 4J | 4K | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 4 | ··· | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | 2+ (1+4) | 2- (1+4) | Q8.10D14 | D4⋊8D14 |
| kernel | C42.158D14 | C4.D28 | D14.5D4 | C28⋊1D4 | D14⋊Q8 | C7×C42.C2 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 3 | 18 | 2 | 1 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{158}D_{14} % in TeX
G:=Group("C4^2.158D14"); // GroupNames label
G:=SmallGroup(448,1153);
// by ID
G=gap.SmallGroup(448,1153);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,555,100,675,570,136,18822]);
// 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^-1,d*c*d^-1=c^13>;
// generators/relations
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