metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.143D14, C14.1272+ 1+4, (C4×D28)⋊46C2, (Q8×Dic7)⋊20C2, (D4×Dic7)⋊31C2, C4.4D4⋊14D7, C28⋊D4.9C2, (C4×Dic14)⋊46C2, (C2×D4).176D14, (C2×Q8).139D14, C22⋊C4.36D14, Dic7⋊4D4⋊34C2, D14.D4⋊46C2, C28.126(C4○D4), C28.23D4⋊23C2, C4.16(D4⋊2D7), (C4×C28).188C22, (C2×C14).225C24, (C2×C28).505C23, D14⋊C4.37C22, C2.51(D4⋊8D14), C23.47(C22×D7), Dic7.39(C4○D4), Dic7.D4⋊41C2, (C2×D28).266C22, (D4×C14).158C22, C22.D28⋊26C2, C4⋊Dic7.235C22, (C22×C14).55C23, (Q8×C14).129C22, (C22×D7).97C23, C22.246(C23×D7), C23.D7.58C22, Dic7⋊C4.142C22, C7⋊4(C22.53C24), (C4×Dic7).135C22, (C2×Dic7).256C23, (C2×Dic14).250C22, (C22×Dic7).145C22, C2.81(D7×C4○D4), C14.192(C2×C4○D4), C2.57(C2×D4⋊2D7), (C7×C4.4D4)⋊17C2, (C2×C4×D7).216C22, (C2×C4).198(C22×D7), (C2×C7⋊D4).63C22, (C7×C22⋊C4).67C22, SmallGroup(448,1134)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.143D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b, dbd-1=b-1, dcd-1=a2c-1 >
Subgroups: 1100 in 236 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C22.D4, C4.4D4, C4.4D4, C4⋊1D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C22.53C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C4×Dic14, C4×D28, Dic7⋊4D4, D14.D4, Dic7.D4, C22.D28, D4×Dic7, C28⋊D4, Q8×Dic7, C28.23D4, C7×C4.4D4, C42.143D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.53C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D7×C4○D4, D4⋊8D14, C42.143D14
►On 224 points
Generators in S224
(1 202 28 33)(2 174 15 136)(3 204 16 35)(4 176 17 138)(5 206 18 37)(6 178 19 140)(7 208 20 39)(8 180 21 128)(9 210 22 41)(10 182 23 130)(11 198 24 29)(12 170 25 132)(13 200 26 31)(14 172 27 134)(30 104 199 144)(32 106 201 146)(34 108 203 148)(36 110 205 150)(38 112 207 152)(40 100 209 154)(42 102 197 142)(43 221 193 124)(44 84 194 96)(45 223 195 126)(46 72 196 98)(47 211 183 114)(48 74 184 86)(49 213 185 116)(50 76 186 88)(51 215 187 118)(52 78 188 90)(53 217 189 120)(54 80 190 92)(55 219 191 122)(56 82 192 94)(57 81 158 93)(58 220 159 123)(59 83 160 95)(60 222 161 125)(61 71 162 97)(62 224 163 113)(63 73 164 85)(64 212 165 115)(65 75 166 87)(66 214 167 117)(67 77 168 89)(68 216 155 119)(69 79 156 91)(70 218 157 121)(99 179 153 127)(101 181 141 129)(103 169 143 131)(105 171 145 133)(107 173 147 135)(109 175 149 137)(111 177 151 139)
(1 124 107 95)(2 222 108 84)(3 126 109 97)(4 224 110 72)(5 114 111 85)(6 212 112 74)(7 116 99 87)(8 214 100 76)(9 118 101 89)(10 216 102 78)(11 120 103 91)(12 218 104 80)(13 122 105 93)(14 220 106 82)(15 125 148 96)(16 223 149 71)(17 113 150 98)(18 211 151 73)(19 115 152 86)(20 213 153 75)(21 117 154 88)(22 215 141 77)(23 119 142 90)(24 217 143 79)(25 121 144 92)(26 219 145 81)(27 123 146 94)(28 221 147 83)(29 189 131 156)(30 54 132 70)(31 191 133 158)(32 56 134 58)(33 193 135 160)(34 44 136 60)(35 195 137 162)(36 46 138 62)(37 183 139 164)(38 48 140 64)(39 185 127 166)(40 50 128 66)(41 187 129 168)(42 52 130 68)(43 173 59 202)(45 175 61 204)(47 177 63 206)(49 179 65 208)(51 181 67 210)(53 169 69 198)(55 171 57 200)(155 197 188 182)(157 199 190 170)(159 201 192 172)(161 203 194 174)(163 205 196 176)(165 207 184 178)(167 209 186 180)
(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)
(1 159 28 58)(2 57 15 158)(3 157 16 70)(4 69 17 156)(5 155 18 68)(6 67 19 168)(7 167 20 66)(8 65 21 166)(9 165 22 64)(10 63 23 164)(11 163 24 62)(12 61 25 162)(13 161 26 60)(14 59 27 160)(29 72 198 98)(30 97 199 71)(31 84 200 96)(32 95 201 83)(33 82 202 94)(34 93 203 81)(35 80 204 92)(36 91 205 79)(37 78 206 90)(38 89 207 77)(39 76 208 88)(40 87 209 75)(41 74 210 86)(42 85 197 73)(43 146 193 106)(44 105 194 145)(45 144 195 104)(46 103 196 143)(47 142 183 102)(48 101 184 141)(49 154 185 100)(50 99 186 153)(51 152 187 112)(52 111 188 151)(53 150 189 110)(54 109 190 149)(55 148 191 108)(56 107 192 147)(113 131 224 169)(114 182 211 130)(115 129 212 181)(116 180 213 128)(117 127 214 179)(118 178 215 140)(119 139 216 177)(120 176 217 138)(121 137 218 175)(122 174 219 136)(123 135 220 173)(124 172 221 134)(125 133 222 171)(126 170 223 132)
G:=sub<Sym(224)| (1,202,28,33)(2,174,15,136)(3,204,16,35)(4,176,17,138)(5,206,18,37)(6,178,19,140)(7,208,20,39)(8,180,21,128)(9,210,22,41)(10,182,23,130)(11,198,24,29)(12,170,25,132)(13,200,26,31)(14,172,27,134)(30,104,199,144)(32,106,201,146)(34,108,203,148)(36,110,205,150)(38,112,207,152)(40,100,209,154)(42,102,197,142)(43,221,193,124)(44,84,194,96)(45,223,195,126)(46,72,196,98)(47,211,183,114)(48,74,184,86)(49,213,185,116)(50,76,186,88)(51,215,187,118)(52,78,188,90)(53,217,189,120)(54,80,190,92)(55,219,191,122)(56,82,192,94)(57,81,158,93)(58,220,159,123)(59,83,160,95)(60,222,161,125)(61,71,162,97)(62,224,163,113)(63,73,164,85)(64,212,165,115)(65,75,166,87)(66,214,167,117)(67,77,168,89)(68,216,155,119)(69,79,156,91)(70,218,157,121)(99,179,153,127)(101,181,141,129)(103,169,143,131)(105,171,145,133)(107,173,147,135)(109,175,149,137)(111,177,151,139), (1,124,107,95)(2,222,108,84)(3,126,109,97)(4,224,110,72)(5,114,111,85)(6,212,112,74)(7,116,99,87)(8,214,100,76)(9,118,101,89)(10,216,102,78)(11,120,103,91)(12,218,104,80)(13,122,105,93)(14,220,106,82)(15,125,148,96)(16,223,149,71)(17,113,150,98)(18,211,151,73)(19,115,152,86)(20,213,153,75)(21,117,154,88)(22,215,141,77)(23,119,142,90)(24,217,143,79)(25,121,144,92)(26,219,145,81)(27,123,146,94)(28,221,147,83)(29,189,131,156)(30,54,132,70)(31,191,133,158)(32,56,134,58)(33,193,135,160)(34,44,136,60)(35,195,137,162)(36,46,138,62)(37,183,139,164)(38,48,140,64)(39,185,127,166)(40,50,128,66)(41,187,129,168)(42,52,130,68)(43,173,59,202)(45,175,61,204)(47,177,63,206)(49,179,65,208)(51,181,67,210)(53,169,69,198)(55,171,57,200)(155,197,188,182)(157,199,190,170)(159,201,192,172)(161,203,194,174)(163,205,196,176)(165,207,184,178)(167,209,186,180), (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), (1,159,28,58)(2,57,15,158)(3,157,16,70)(4,69,17,156)(5,155,18,68)(6,67,19,168)(7,167,20,66)(8,65,21,166)(9,165,22,64)(10,63,23,164)(11,163,24,62)(12,61,25,162)(13,161,26,60)(14,59,27,160)(29,72,198,98)(30,97,199,71)(31,84,200,96)(32,95,201,83)(33,82,202,94)(34,93,203,81)(35,80,204,92)(36,91,205,79)(37,78,206,90)(38,89,207,77)(39,76,208,88)(40,87,209,75)(41,74,210,86)(42,85,197,73)(43,146,193,106)(44,105,194,145)(45,144,195,104)(46,103,196,143)(47,142,183,102)(48,101,184,141)(49,154,185,100)(50,99,186,153)(51,152,187,112)(52,111,188,151)(53,150,189,110)(54,109,190,149)(55,148,191,108)(56,107,192,147)(113,131,224,169)(114,182,211,130)(115,129,212,181)(116,180,213,128)(117,127,214,179)(118,178,215,140)(119,139,216,177)(120,176,217,138)(121,137,218,175)(122,174,219,136)(123,135,220,173)(124,172,221,134)(125,133,222,171)(126,170,223,132)>;
G:=Group( (1,202,28,33)(2,174,15,136)(3,204,16,35)(4,176,17,138)(5,206,18,37)(6,178,19,140)(7,208,20,39)(8,180,21,128)(9,210,22,41)(10,182,23,130)(11,198,24,29)(12,170,25,132)(13,200,26,31)(14,172,27,134)(30,104,199,144)(32,106,201,146)(34,108,203,148)(36,110,205,150)(38,112,207,152)(40,100,209,154)(42,102,197,142)(43,221,193,124)(44,84,194,96)(45,223,195,126)(46,72,196,98)(47,211,183,114)(48,74,184,86)(49,213,185,116)(50,76,186,88)(51,215,187,118)(52,78,188,90)(53,217,189,120)(54,80,190,92)(55,219,191,122)(56,82,192,94)(57,81,158,93)(58,220,159,123)(59,83,160,95)(60,222,161,125)(61,71,162,97)(62,224,163,113)(63,73,164,85)(64,212,165,115)(65,75,166,87)(66,214,167,117)(67,77,168,89)(68,216,155,119)(69,79,156,91)(70,218,157,121)(99,179,153,127)(101,181,141,129)(103,169,143,131)(105,171,145,133)(107,173,147,135)(109,175,149,137)(111,177,151,139), (1,124,107,95)(2,222,108,84)(3,126,109,97)(4,224,110,72)(5,114,111,85)(6,212,112,74)(7,116,99,87)(8,214,100,76)(9,118,101,89)(10,216,102,78)(11,120,103,91)(12,218,104,80)(13,122,105,93)(14,220,106,82)(15,125,148,96)(16,223,149,71)(17,113,150,98)(18,211,151,73)(19,115,152,86)(20,213,153,75)(21,117,154,88)(22,215,141,77)(23,119,142,90)(24,217,143,79)(25,121,144,92)(26,219,145,81)(27,123,146,94)(28,221,147,83)(29,189,131,156)(30,54,132,70)(31,191,133,158)(32,56,134,58)(33,193,135,160)(34,44,136,60)(35,195,137,162)(36,46,138,62)(37,183,139,164)(38,48,140,64)(39,185,127,166)(40,50,128,66)(41,187,129,168)(42,52,130,68)(43,173,59,202)(45,175,61,204)(47,177,63,206)(49,179,65,208)(51,181,67,210)(53,169,69,198)(55,171,57,200)(155,197,188,182)(157,199,190,170)(159,201,192,172)(161,203,194,174)(163,205,196,176)(165,207,184,178)(167,209,186,180), (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), (1,159,28,58)(2,57,15,158)(3,157,16,70)(4,69,17,156)(5,155,18,68)(6,67,19,168)(7,167,20,66)(8,65,21,166)(9,165,22,64)(10,63,23,164)(11,163,24,62)(12,61,25,162)(13,161,26,60)(14,59,27,160)(29,72,198,98)(30,97,199,71)(31,84,200,96)(32,95,201,83)(33,82,202,94)(34,93,203,81)(35,80,204,92)(36,91,205,79)(37,78,206,90)(38,89,207,77)(39,76,208,88)(40,87,209,75)(41,74,210,86)(42,85,197,73)(43,146,193,106)(44,105,194,145)(45,144,195,104)(46,103,196,143)(47,142,183,102)(48,101,184,141)(49,154,185,100)(50,99,186,153)(51,152,187,112)(52,111,188,151)(53,150,189,110)(54,109,190,149)(55,148,191,108)(56,107,192,147)(113,131,224,169)(114,182,211,130)(115,129,212,181)(116,180,213,128)(117,127,214,179)(118,178,215,140)(119,139,216,177)(120,176,217,138)(121,137,218,175)(122,174,219,136)(123,135,220,173)(124,172,221,134)(125,133,222,171)(126,170,223,132) );
G=PermutationGroup([[(1,202,28,33),(2,174,15,136),(3,204,16,35),(4,176,17,138),(5,206,18,37),(6,178,19,140),(7,208,20,39),(8,180,21,128),(9,210,22,41),(10,182,23,130),(11,198,24,29),(12,170,25,132),(13,200,26,31),(14,172,27,134),(30,104,199,144),(32,106,201,146),(34,108,203,148),(36,110,205,150),(38,112,207,152),(40,100,209,154),(42,102,197,142),(43,221,193,124),(44,84,194,96),(45,223,195,126),(46,72,196,98),(47,211,183,114),(48,74,184,86),(49,213,185,116),(50,76,186,88),(51,215,187,118),(52,78,188,90),(53,217,189,120),(54,80,190,92),(55,219,191,122),(56,82,192,94),(57,81,158,93),(58,220,159,123),(59,83,160,95),(60,222,161,125),(61,71,162,97),(62,224,163,113),(63,73,164,85),(64,212,165,115),(65,75,166,87),(66,214,167,117),(67,77,168,89),(68,216,155,119),(69,79,156,91),(70,218,157,121),(99,179,153,127),(101,181,141,129),(103,169,143,131),(105,171,145,133),(107,173,147,135),(109,175,149,137),(111,177,151,139)], [(1,124,107,95),(2,222,108,84),(3,126,109,97),(4,224,110,72),(5,114,111,85),(6,212,112,74),(7,116,99,87),(8,214,100,76),(9,118,101,89),(10,216,102,78),(11,120,103,91),(12,218,104,80),(13,122,105,93),(14,220,106,82),(15,125,148,96),(16,223,149,71),(17,113,150,98),(18,211,151,73),(19,115,152,86),(20,213,153,75),(21,117,154,88),(22,215,141,77),(23,119,142,90),(24,217,143,79),(25,121,144,92),(26,219,145,81),(27,123,146,94),(28,221,147,83),(29,189,131,156),(30,54,132,70),(31,191,133,158),(32,56,134,58),(33,193,135,160),(34,44,136,60),(35,195,137,162),(36,46,138,62),(37,183,139,164),(38,48,140,64),(39,185,127,166),(40,50,128,66),(41,187,129,168),(42,52,130,68),(43,173,59,202),(45,175,61,204),(47,177,63,206),(49,179,65,208),(51,181,67,210),(53,169,69,198),(55,171,57,200),(155,197,188,182),(157,199,190,170),(159,201,192,172),(161,203,194,174),(163,205,196,176),(165,207,184,178),(167,209,186,180)], [(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)], [(1,159,28,58),(2,57,15,158),(3,157,16,70),(4,69,17,156),(5,155,18,68),(6,67,19,168),(7,167,20,66),(8,65,21,166),(9,165,22,64),(10,63,23,164),(11,163,24,62),(12,61,25,162),(13,161,26,60),(14,59,27,160),(29,72,198,98),(30,97,199,71),(31,84,200,96),(32,95,201,83),(33,82,202,94),(34,93,203,81),(35,80,204,92),(36,91,205,79),(37,78,206,90),(38,89,207,77),(39,76,208,88),(40,87,209,75),(41,74,210,86),(42,85,197,73),(43,146,193,106),(44,105,194,145),(45,144,195,104),(46,103,196,143),(47,142,183,102),(48,101,184,141),(49,154,185,100),(50,99,186,153),(51,152,187,112),(52,111,188,151),(53,150,189,110),(54,109,190,149),(55,148,191,108),(56,107,192,147),(113,131,224,169),(114,182,211,130),(115,129,212,181),(116,180,213,128),(117,127,214,179),(118,178,215,140),(119,139,216,177),(120,176,217,138),(121,137,218,175),(122,174,219,136),(123,135,220,173),(124,172,221,134),(125,133,222,171),(126,170,223,132)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.143D14 | C4×Dic14 | C4×D28 | Dic7⋊4D4 | D14.D4 | Dic7.D4 | C22.D28 | D4×Dic7 | C28⋊D4 | Q8×Dic7 | C28.23D4 | C7×C4.4D4 | C4.4D4 | Dic7 | C28 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 12 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of C42.143D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 28 | 17 |
| 4 | 4 | 0 | 0 | 0 | 0 |
| 25 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 25 | 25 | 0 | 0 | 0 | 0 |
| 11 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 5 |
| 0 | 0 | 0 | 0 | 17 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,1,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,28,0,0,0,0,0,17],[4,25,0,0,0,0,4,18,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,24,28],[25,11,0,0,0,0,25,4,0,0,0,0,0,0,0,12,0,0,0,0,12,0,0,0,0,0,0,0,28,17,0,0,0,0,5,1] >;
C42.143D14 in GAP, Magma, Sage, TeX
C_4^2._{143}D_{14} % in TeX
G:=Group("C4^2.143D14"); // GroupNames label
G:=SmallGroup(448,1134);
// by ID
G=gap.SmallGroup(448,1134);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,297,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=a^2*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations