metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.164D14, C14.1022- (1+4), C14.1412+ (1+4), C28⋊Q8⋊41C2, C4⋊C4.119D14, C4.D28⋊9C2, C42⋊2C2⋊7D7, D14⋊2Q8⋊42C2, D14⋊Q8⋊45C2, (C4×Dic14)⋊16C2, D14⋊D4.5C2, (C4×C28).36C22, C22⋊C4.82D14, Dic7⋊4D4⋊38C2, D14.5D4⋊43C2, (C2×C28).605C23, (C2×C14).254C24, D14⋊C4.47C22, (C2×D28).37C22, C2.66(D4⋊8D14), C23.60(C22×D7), Dic7.16(C4○D4), Dic7.D4⋊47C2, C22⋊Dic14⋊47C2, C22.D28⋊31C2, C4⋊Dic7.319C22, (C22×C14).68C23, C22.275(C23×D7), C23.D7.69C22, Dic7⋊C4.127C22, (C2×Dic7).267C23, (C4×Dic7).219C22, (C22×D7).113C23, C2.66(D4.10D14), C7⋊10(C22.36C24), (C2×Dic14).256C22, (C22×Dic7).154C22, C4⋊C4⋊D7⋊44C2, C4⋊C4⋊7D7⋊42C2, C2.101(D7×C4○D4), (C7×C42⋊2C2)⋊9C2, C14.212(C2×C4○D4), (C2×C4×D7).136C22, (C7×C4⋊C4).206C22, (C2×C4).210(C22×D7), (C2×C7⋊D4).74C22, (C7×C22⋊C4).79C22, SmallGroup(448,1163)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1036 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C7, C2×C4 [×6], C2×C4 [×10], D4 [×4], Q8 [×4], C23, C23 [×2], D7 [×2], C14 [×3], C14, C42, C42 [×3], C22⋊C4 [×3], C22⋊C4 [×9], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4 [×3], C2×D4 [×3], C2×Q8 [×3], Dic7 [×2], Dic7 [×5], C28 [×6], D14 [×6], C2×C14, C2×C14 [×3], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4 [×3], C42⋊2C2, C42⋊2C2, C4⋊Q8, Dic14 [×4], C4×D7 [×3], D28, C2×Dic7 [×6], C2×Dic7, C7⋊D4 [×3], C2×C28 [×6], C22×D7 [×2], C22×C14, C22.36C24, C4×Dic7 [×3], Dic7⋊C4 [×4], C4⋊Dic7 [×3], D14⋊C4 [×8], C23.D7, C4×C28, C7×C22⋊C4 [×3], C7×C4⋊C4 [×3], C2×Dic14 [×3], C2×C4×D7 [×2], C2×D28, C22×Dic7, C2×C7⋊D4 [×2], C4×Dic14, C4.D28, C22⋊Dic14, Dic7⋊4D4, D14⋊D4, Dic7.D4 [×2], C22.D28, C28⋊Q8, C4⋊C4⋊7D7, D14.5D4, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42⋊2C2, C42.164D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4), 2- (1+4), C22×D7 [×7], C22.36C24, C23×D7, D7×C4○D4, D4⋊8D14, D4.10D14, C42.164D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=ab2, dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 39 95 75)(2 54 96 62)(3 41 97 77)(4 56 98 64)(5 43 99 79)(6 30 100 66)(7 45 101 81)(8 32 102 68)(9 47 103 83)(10 34 104 70)(11 49 105 57)(12 36 106 72)(13 51 107 59)(14 38 108 74)(15 53 109 61)(16 40 110 76)(17 55 111 63)(18 42 112 78)(19 29 85 65)(20 44 86 80)(21 31 87 67)(22 46 88 82)(23 33 89 69)(24 48 90 84)(25 35 91 71)(26 50 92 58)(27 37 93 73)(28 52 94 60)(113 222 165 195)(114 209 166 182)(115 224 167 169)(116 211 168 184)(117 198 141 171)(118 213 142 186)(119 200 143 173)(120 215 144 188)(121 202 145 175)(122 217 146 190)(123 204 147 177)(124 219 148 192)(125 206 149 179)(126 221 150 194)(127 208 151 181)(128 223 152 196)(129 210 153 183)(130 197 154 170)(131 212 155 185)(132 199 156 172)(133 214 157 187)(134 201 158 174)(135 216 159 189)(136 203 160 176)(137 218 161 191)(138 205 162 178)(139 220 163 193)(140 207 164 180)
(1 32 15 46)(2 83 16 69)(3 34 17 48)(4 57 18 71)(5 36 19 50)(6 59 20 73)(7 38 21 52)(8 61 22 75)(9 40 23 54)(10 63 24 77)(11 42 25 56)(12 65 26 79)(13 44 27 30)(14 67 28 81)(29 92 43 106)(31 94 45 108)(33 96 47 110)(35 98 49 112)(37 100 51 86)(39 102 53 88)(41 104 55 90)(58 99 72 85)(60 101 74 87)(62 103 76 89)(64 105 78 91)(66 107 80 93)(68 109 82 95)(70 111 84 97)(113 174 127 188)(114 216 128 202)(115 176 129 190)(116 218 130 204)(117 178 131 192)(118 220 132 206)(119 180 133 194)(120 222 134 208)(121 182 135 196)(122 224 136 210)(123 184 137 170)(124 198 138 212)(125 186 139 172)(126 200 140 214)(141 205 155 219)(142 193 156 179)(143 207 157 221)(144 195 158 181)(145 209 159 223)(146 169 160 183)(147 211 161 197)(148 171 162 185)(149 213 163 199)(150 173 164 187)(151 215 165 201)(152 175 166 189)(153 217 167 203)(154 177 168 191)
(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)
(1 211 15 197)(2 224 16 210)(3 209 17 223)(4 222 18 208)(5 207 19 221)(6 220 20 206)(7 205 21 219)(8 218 22 204)(9 203 23 217)(10 216 24 202)(11 201 25 215)(12 214 26 200)(13 199 27 213)(14 212 28 198)(29 126 43 140)(30 139 44 125)(31 124 45 138)(32 137 46 123)(33 122 47 136)(34 135 48 121)(35 120 49 134)(36 133 50 119)(37 118 51 132)(38 131 52 117)(39 116 53 130)(40 129 54 115)(41 114 55 128)(42 127 56 113)(57 158 71 144)(58 143 72 157)(59 156 73 142)(60 141 74 155)(61 154 75 168)(62 167 76 153)(63 152 77 166)(64 165 78 151)(65 150 79 164)(66 163 80 149)(67 148 81 162)(68 161 82 147)(69 146 83 160)(70 159 84 145)(85 194 99 180)(86 179 100 193)(87 192 101 178)(88 177 102 191)(89 190 103 176)(90 175 104 189)(91 188 105 174)(92 173 106 187)(93 186 107 172)(94 171 108 185)(95 184 109 170)(96 169 110 183)(97 182 111 196)(98 195 112 181)
G:=sub<Sym(224)| (1,39,95,75)(2,54,96,62)(3,41,97,77)(4,56,98,64)(5,43,99,79)(6,30,100,66)(7,45,101,81)(8,32,102,68)(9,47,103,83)(10,34,104,70)(11,49,105,57)(12,36,106,72)(13,51,107,59)(14,38,108,74)(15,53,109,61)(16,40,110,76)(17,55,111,63)(18,42,112,78)(19,29,85,65)(20,44,86,80)(21,31,87,67)(22,46,88,82)(23,33,89,69)(24,48,90,84)(25,35,91,71)(26,50,92,58)(27,37,93,73)(28,52,94,60)(113,222,165,195)(114,209,166,182)(115,224,167,169)(116,211,168,184)(117,198,141,171)(118,213,142,186)(119,200,143,173)(120,215,144,188)(121,202,145,175)(122,217,146,190)(123,204,147,177)(124,219,148,192)(125,206,149,179)(126,221,150,194)(127,208,151,181)(128,223,152,196)(129,210,153,183)(130,197,154,170)(131,212,155,185)(132,199,156,172)(133,214,157,187)(134,201,158,174)(135,216,159,189)(136,203,160,176)(137,218,161,191)(138,205,162,178)(139,220,163,193)(140,207,164,180), (1,32,15,46)(2,83,16,69)(3,34,17,48)(4,57,18,71)(5,36,19,50)(6,59,20,73)(7,38,21,52)(8,61,22,75)(9,40,23,54)(10,63,24,77)(11,42,25,56)(12,65,26,79)(13,44,27,30)(14,67,28,81)(29,92,43,106)(31,94,45,108)(33,96,47,110)(35,98,49,112)(37,100,51,86)(39,102,53,88)(41,104,55,90)(58,99,72,85)(60,101,74,87)(62,103,76,89)(64,105,78,91)(66,107,80,93)(68,109,82,95)(70,111,84,97)(113,174,127,188)(114,216,128,202)(115,176,129,190)(116,218,130,204)(117,178,131,192)(118,220,132,206)(119,180,133,194)(120,222,134,208)(121,182,135,196)(122,224,136,210)(123,184,137,170)(124,198,138,212)(125,186,139,172)(126,200,140,214)(141,205,155,219)(142,193,156,179)(143,207,157,221)(144,195,158,181)(145,209,159,223)(146,169,160,183)(147,211,161,197)(148,171,162,185)(149,213,163,199)(150,173,164,187)(151,215,165,201)(152,175,166,189)(153,217,167,203)(154,177,168,191), (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), (1,211,15,197)(2,224,16,210)(3,209,17,223)(4,222,18,208)(5,207,19,221)(6,220,20,206)(7,205,21,219)(8,218,22,204)(9,203,23,217)(10,216,24,202)(11,201,25,215)(12,214,26,200)(13,199,27,213)(14,212,28,198)(29,126,43,140)(30,139,44,125)(31,124,45,138)(32,137,46,123)(33,122,47,136)(34,135,48,121)(35,120,49,134)(36,133,50,119)(37,118,51,132)(38,131,52,117)(39,116,53,130)(40,129,54,115)(41,114,55,128)(42,127,56,113)(57,158,71,144)(58,143,72,157)(59,156,73,142)(60,141,74,155)(61,154,75,168)(62,167,76,153)(63,152,77,166)(64,165,78,151)(65,150,79,164)(66,163,80,149)(67,148,81,162)(68,161,82,147)(69,146,83,160)(70,159,84,145)(85,194,99,180)(86,179,100,193)(87,192,101,178)(88,177,102,191)(89,190,103,176)(90,175,104,189)(91,188,105,174)(92,173,106,187)(93,186,107,172)(94,171,108,185)(95,184,109,170)(96,169,110,183)(97,182,111,196)(98,195,112,181)>;
G:=Group( (1,39,95,75)(2,54,96,62)(3,41,97,77)(4,56,98,64)(5,43,99,79)(6,30,100,66)(7,45,101,81)(8,32,102,68)(9,47,103,83)(10,34,104,70)(11,49,105,57)(12,36,106,72)(13,51,107,59)(14,38,108,74)(15,53,109,61)(16,40,110,76)(17,55,111,63)(18,42,112,78)(19,29,85,65)(20,44,86,80)(21,31,87,67)(22,46,88,82)(23,33,89,69)(24,48,90,84)(25,35,91,71)(26,50,92,58)(27,37,93,73)(28,52,94,60)(113,222,165,195)(114,209,166,182)(115,224,167,169)(116,211,168,184)(117,198,141,171)(118,213,142,186)(119,200,143,173)(120,215,144,188)(121,202,145,175)(122,217,146,190)(123,204,147,177)(124,219,148,192)(125,206,149,179)(126,221,150,194)(127,208,151,181)(128,223,152,196)(129,210,153,183)(130,197,154,170)(131,212,155,185)(132,199,156,172)(133,214,157,187)(134,201,158,174)(135,216,159,189)(136,203,160,176)(137,218,161,191)(138,205,162,178)(139,220,163,193)(140,207,164,180), (1,32,15,46)(2,83,16,69)(3,34,17,48)(4,57,18,71)(5,36,19,50)(6,59,20,73)(7,38,21,52)(8,61,22,75)(9,40,23,54)(10,63,24,77)(11,42,25,56)(12,65,26,79)(13,44,27,30)(14,67,28,81)(29,92,43,106)(31,94,45,108)(33,96,47,110)(35,98,49,112)(37,100,51,86)(39,102,53,88)(41,104,55,90)(58,99,72,85)(60,101,74,87)(62,103,76,89)(64,105,78,91)(66,107,80,93)(68,109,82,95)(70,111,84,97)(113,174,127,188)(114,216,128,202)(115,176,129,190)(116,218,130,204)(117,178,131,192)(118,220,132,206)(119,180,133,194)(120,222,134,208)(121,182,135,196)(122,224,136,210)(123,184,137,170)(124,198,138,212)(125,186,139,172)(126,200,140,214)(141,205,155,219)(142,193,156,179)(143,207,157,221)(144,195,158,181)(145,209,159,223)(146,169,160,183)(147,211,161,197)(148,171,162,185)(149,213,163,199)(150,173,164,187)(151,215,165,201)(152,175,166,189)(153,217,167,203)(154,177,168,191), (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), (1,211,15,197)(2,224,16,210)(3,209,17,223)(4,222,18,208)(5,207,19,221)(6,220,20,206)(7,205,21,219)(8,218,22,204)(9,203,23,217)(10,216,24,202)(11,201,25,215)(12,214,26,200)(13,199,27,213)(14,212,28,198)(29,126,43,140)(30,139,44,125)(31,124,45,138)(32,137,46,123)(33,122,47,136)(34,135,48,121)(35,120,49,134)(36,133,50,119)(37,118,51,132)(38,131,52,117)(39,116,53,130)(40,129,54,115)(41,114,55,128)(42,127,56,113)(57,158,71,144)(58,143,72,157)(59,156,73,142)(60,141,74,155)(61,154,75,168)(62,167,76,153)(63,152,77,166)(64,165,78,151)(65,150,79,164)(66,163,80,149)(67,148,81,162)(68,161,82,147)(69,146,83,160)(70,159,84,145)(85,194,99,180)(86,179,100,193)(87,192,101,178)(88,177,102,191)(89,190,103,176)(90,175,104,189)(91,188,105,174)(92,173,106,187)(93,186,107,172)(94,171,108,185)(95,184,109,170)(96,169,110,183)(97,182,111,196)(98,195,112,181) );
G=PermutationGroup([(1,39,95,75),(2,54,96,62),(3,41,97,77),(4,56,98,64),(5,43,99,79),(6,30,100,66),(7,45,101,81),(8,32,102,68),(9,47,103,83),(10,34,104,70),(11,49,105,57),(12,36,106,72),(13,51,107,59),(14,38,108,74),(15,53,109,61),(16,40,110,76),(17,55,111,63),(18,42,112,78),(19,29,85,65),(20,44,86,80),(21,31,87,67),(22,46,88,82),(23,33,89,69),(24,48,90,84),(25,35,91,71),(26,50,92,58),(27,37,93,73),(28,52,94,60),(113,222,165,195),(114,209,166,182),(115,224,167,169),(116,211,168,184),(117,198,141,171),(118,213,142,186),(119,200,143,173),(120,215,144,188),(121,202,145,175),(122,217,146,190),(123,204,147,177),(124,219,148,192),(125,206,149,179),(126,221,150,194),(127,208,151,181),(128,223,152,196),(129,210,153,183),(130,197,154,170),(131,212,155,185),(132,199,156,172),(133,214,157,187),(134,201,158,174),(135,216,159,189),(136,203,160,176),(137,218,161,191),(138,205,162,178),(139,220,163,193),(140,207,164,180)], [(1,32,15,46),(2,83,16,69),(3,34,17,48),(4,57,18,71),(5,36,19,50),(6,59,20,73),(7,38,21,52),(8,61,22,75),(9,40,23,54),(10,63,24,77),(11,42,25,56),(12,65,26,79),(13,44,27,30),(14,67,28,81),(29,92,43,106),(31,94,45,108),(33,96,47,110),(35,98,49,112),(37,100,51,86),(39,102,53,88),(41,104,55,90),(58,99,72,85),(60,101,74,87),(62,103,76,89),(64,105,78,91),(66,107,80,93),(68,109,82,95),(70,111,84,97),(113,174,127,188),(114,216,128,202),(115,176,129,190),(116,218,130,204),(117,178,131,192),(118,220,132,206),(119,180,133,194),(120,222,134,208),(121,182,135,196),(122,224,136,210),(123,184,137,170),(124,198,138,212),(125,186,139,172),(126,200,140,214),(141,205,155,219),(142,193,156,179),(143,207,157,221),(144,195,158,181),(145,209,159,223),(146,169,160,183),(147,211,161,197),(148,171,162,185),(149,213,163,199),(150,173,164,187),(151,215,165,201),(152,175,166,189),(153,217,167,203),(154,177,168,191)], [(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)], [(1,211,15,197),(2,224,16,210),(3,209,17,223),(4,222,18,208),(5,207,19,221),(6,220,20,206),(7,205,21,219),(8,218,22,204),(9,203,23,217),(10,216,24,202),(11,201,25,215),(12,214,26,200),(13,199,27,213),(14,212,28,198),(29,126,43,140),(30,139,44,125),(31,124,45,138),(32,137,46,123),(33,122,47,136),(34,135,48,121),(35,120,49,134),(36,133,50,119),(37,118,51,132),(38,131,52,117),(39,116,53,130),(40,129,54,115),(41,114,55,128),(42,127,56,113),(57,158,71,144),(58,143,72,157),(59,156,73,142),(60,141,74,155),(61,154,75,168),(62,167,76,153),(63,152,77,166),(64,165,78,151),(65,150,79,164),(66,163,80,149),(67,148,81,162),(68,161,82,147),(69,146,83,160),(70,159,84,145),(85,194,99,180),(86,179,100,193),(87,192,101,178),(88,177,102,191),(89,190,103,176),(90,175,104,189),(91,188,105,174),(92,173,106,187),(93,186,107,172),(94,171,108,185),(95,184,109,170),(96,169,110,183),(97,182,111,196),(98,195,112,181)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 18 | 0 | 0 | 0 | 0 |
| 13 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 11 |
| 0 | 0 | 0 | 0 | 7 | 3 |
| 28 | 13 | 0 | 0 | 0 | 0 |
| 11 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 4 | 1 |
| 0 | 0 | 18 | 2 | 24 | 15 |
| 0 | 0 | 25 | 8 | 3 | 18 |
| 0 | 0 | 18 | 26 | 22 | 26 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 13 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 8 | 23 |
| 0 | 0 | 21 | 3 | 6 | 0 |
| 0 | 0 | 0 | 0 | 27 | 21 |
| 0 | 0 | 0 | 0 | 16 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 5 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [12,13,0,0,0,0,18,17,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,26,7,0,0,0,0,11,3],[28,11,0,0,0,0,13,1,0,0,0,0,0,0,27,18,25,18,0,0,11,2,8,26,0,0,4,24,3,22,0,0,1,15,18,26],[12,13,0,0,0,0,0,17,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,8,6,27,16,0,0,23,0,21,20],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,11,2,0,0,0,0,27,18,0,0,0,0,0,0,1,0,0,0,0,0,5,28] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 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 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ (1+4) | 2- (1+4) | D7×C4○D4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.164D14 | C4×Dic14 | C4.D28 | C22⋊Dic14 | Dic7⋊4D4 | D14⋊D4 | Dic7.D4 | C22.D28 | C28⋊Q8 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | C42 | C22⋊C4 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 9 | 9 | 1 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{164}D_{14} % in TeX
G:=Group("C4^2.164D14"); // GroupNames label
G:=SmallGroup(448,1163);
// by ID
G=gap.SmallGroup(448,1163);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,675,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀