metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.166D14, C14.752+ 1+4, C4⋊1D4.7D7, (D4×Dic7)⋊33C2, (C4×Dic14)⋊50C2, (C2×D4).114D14, C28.133(C4○D4), C28.17D4⋊25C2, C4.17(D4⋊2D7), (C2×C14).257C24, (C2×C28).634C23, (C4×C28).202C22, C2.79(D4⋊6D14), C23.63(C22×D7), (D4×C14).160C22, C4⋊Dic7.380C22, (C22×C14).71C23, C22.278(C23×D7), C23.D7.71C22, C23.18D14⋊26C2, Dic7⋊C4.163C22, C7⋊5(C22.53C24), (C2×Dic7).133C23, (C4×Dic7).154C22, (C2×Dic14).300C22, (C22×Dic7).156C22, C14.95(C2×C4○D4), (C7×C4⋊1D4).6C2, C2.59(C2×D4⋊2D7), (C2×C4).595(C22×D7), SmallGroup(448,1166)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.166D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=c-1 >
Subgroups: 908 in 236 conjugacy classes, 99 normal (13 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C4×D4, C4×Q8, C22.D4, C4.4D4, C4⋊1D4, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C22.53C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C2×Dic14, C22×Dic7, D4×C14, C4×Dic14, D4×Dic7, C23.18D14, C28.17D4, C7×C4⋊1D4, C42.166D14
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, D4⋊6D14, C42.166D14
►On 224 points
Generators in S224
(1 224 76 182)(2 169 77 211)(3 212 78 170)(4 171 79 213)(5 214 80 172)(6 173 81 215)(7 216 82 174)(8 175 83 217)(9 218 84 176)(10 177 71 219)(11 220 72 178)(12 179 73 221)(13 222 74 180)(14 181 75 223)(15 112 47 61)(16 62 48 99)(17 100 49 63)(18 64 50 101)(19 102 51 65)(20 66 52 103)(21 104 53 67)(22 68 54 105)(23 106 55 69)(24 70 56 107)(25 108 43 57)(26 58 44 109)(27 110 45 59)(28 60 46 111)(29 199 193 153)(30 154 194 200)(31 201 195 141)(32 142 196 202)(33 203 183 143)(34 144 184 204)(35 205 185 145)(36 146 186 206)(37 207 187 147)(38 148 188 208)(39 209 189 149)(40 150 190 210)(41 197 191 151)(42 152 192 198)(85 158 134 121)(86 122 135 159)(87 160 136 123)(88 124 137 161)(89 162 138 125)(90 126 139 163)(91 164 140 113)(92 114 127 165)(93 166 128 115)(94 116 129 167)(95 168 130 117)(96 118 131 155)(97 156 132 119)(98 120 133 157)
(1 122 115 8)(2 9 116 123)(3 124 117 10)(4 11 118 125)(5 126 119 12)(6 13 120 113)(7 114 121 14)(15 54 38 195)(16 196 39 55)(17 56 40 183)(18 184 41 43)(19 44 42 185)(20 186 29 45)(21 46 30 187)(22 188 31 47)(23 48 32 189)(24 190 33 49)(25 50 34 191)(26 192 35 51)(27 52 36 193)(28 194 37 53)(57 64 204 197)(58 198 205 65)(59 66 206 199)(60 200 207 67)(61 68 208 201)(62 202 209 69)(63 70 210 203)(71 78 161 168)(72 155 162 79)(73 80 163 156)(74 157 164 81)(75 82 165 158)(76 159 166 83)(77 84 167 160)(85 181 216 127)(86 128 217 182)(87 169 218 129)(88 130 219 170)(89 171 220 131)(90 132 221 172)(91 173 222 133)(92 134 223 174)(93 175 224 135)(94 136 211 176)(95 177 212 137)(96 138 213 178)(97 179 214 139)(98 140 215 180)(99 142 149 106)(100 107 150 143)(101 144 151 108)(102 109 152 145)(103 146 153 110)(104 111 154 147)(105 148 141 112)
(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 35 115 26)(2 34 116 25)(3 33 117 24)(4 32 118 23)(5 31 119 22)(6 30 120 21)(7 29 121 20)(8 42 122 19)(9 41 123 18)(10 40 124 17)(11 39 125 16)(12 38 126 15)(13 37 113 28)(14 36 114 27)(43 77 184 167)(44 76 185 166)(45 75 186 165)(46 74 187 164)(47 73 188 163)(48 72 189 162)(49 71 190 161)(50 84 191 160)(51 83 192 159)(52 82 193 158)(53 81 194 157)(54 80 195 156)(55 79 196 155)(56 78 183 168)(57 169 204 129)(58 182 205 128)(59 181 206 127)(60 180 207 140)(61 179 208 139)(62 178 209 138)(63 177 210 137)(64 176 197 136)(65 175 198 135)(66 174 199 134)(67 173 200 133)(68 172 201 132)(69 171 202 131)(70 170 203 130)(85 103 216 153)(86 102 217 152)(87 101 218 151)(88 100 219 150)(89 99 220 149)(90 112 221 148)(91 111 222 147)(92 110 223 146)(93 109 224 145)(94 108 211 144)(95 107 212 143)(96 106 213 142)(97 105 214 141)(98 104 215 154)
G:=sub<Sym(224)| (1,224,76,182)(2,169,77,211)(3,212,78,170)(4,171,79,213)(5,214,80,172)(6,173,81,215)(7,216,82,174)(8,175,83,217)(9,218,84,176)(10,177,71,219)(11,220,72,178)(12,179,73,221)(13,222,74,180)(14,181,75,223)(15,112,47,61)(16,62,48,99)(17,100,49,63)(18,64,50,101)(19,102,51,65)(20,66,52,103)(21,104,53,67)(22,68,54,105)(23,106,55,69)(24,70,56,107)(25,108,43,57)(26,58,44,109)(27,110,45,59)(28,60,46,111)(29,199,193,153)(30,154,194,200)(31,201,195,141)(32,142,196,202)(33,203,183,143)(34,144,184,204)(35,205,185,145)(36,146,186,206)(37,207,187,147)(38,148,188,208)(39,209,189,149)(40,150,190,210)(41,197,191,151)(42,152,192,198)(85,158,134,121)(86,122,135,159)(87,160,136,123)(88,124,137,161)(89,162,138,125)(90,126,139,163)(91,164,140,113)(92,114,127,165)(93,166,128,115)(94,116,129,167)(95,168,130,117)(96,118,131,155)(97,156,132,119)(98,120,133,157), (1,122,115,8)(2,9,116,123)(3,124,117,10)(4,11,118,125)(5,126,119,12)(6,13,120,113)(7,114,121,14)(15,54,38,195)(16,196,39,55)(17,56,40,183)(18,184,41,43)(19,44,42,185)(20,186,29,45)(21,46,30,187)(22,188,31,47)(23,48,32,189)(24,190,33,49)(25,50,34,191)(26,192,35,51)(27,52,36,193)(28,194,37,53)(57,64,204,197)(58,198,205,65)(59,66,206,199)(60,200,207,67)(61,68,208,201)(62,202,209,69)(63,70,210,203)(71,78,161,168)(72,155,162,79)(73,80,163,156)(74,157,164,81)(75,82,165,158)(76,159,166,83)(77,84,167,160)(85,181,216,127)(86,128,217,182)(87,169,218,129)(88,130,219,170)(89,171,220,131)(90,132,221,172)(91,173,222,133)(92,134,223,174)(93,175,224,135)(94,136,211,176)(95,177,212,137)(96,138,213,178)(97,179,214,139)(98,140,215,180)(99,142,149,106)(100,107,150,143)(101,144,151,108)(102,109,152,145)(103,146,153,110)(104,111,154,147)(105,148,141,112), (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), (1,35,115,26)(2,34,116,25)(3,33,117,24)(4,32,118,23)(5,31,119,22)(6,30,120,21)(7,29,121,20)(8,42,122,19)(9,41,123,18)(10,40,124,17)(11,39,125,16)(12,38,126,15)(13,37,113,28)(14,36,114,27)(43,77,184,167)(44,76,185,166)(45,75,186,165)(46,74,187,164)(47,73,188,163)(48,72,189,162)(49,71,190,161)(50,84,191,160)(51,83,192,159)(52,82,193,158)(53,81,194,157)(54,80,195,156)(55,79,196,155)(56,78,183,168)(57,169,204,129)(58,182,205,128)(59,181,206,127)(60,180,207,140)(61,179,208,139)(62,178,209,138)(63,177,210,137)(64,176,197,136)(65,175,198,135)(66,174,199,134)(67,173,200,133)(68,172,201,132)(69,171,202,131)(70,170,203,130)(85,103,216,153)(86,102,217,152)(87,101,218,151)(88,100,219,150)(89,99,220,149)(90,112,221,148)(91,111,222,147)(92,110,223,146)(93,109,224,145)(94,108,211,144)(95,107,212,143)(96,106,213,142)(97,105,214,141)(98,104,215,154)>;
G:=Group( (1,224,76,182)(2,169,77,211)(3,212,78,170)(4,171,79,213)(5,214,80,172)(6,173,81,215)(7,216,82,174)(8,175,83,217)(9,218,84,176)(10,177,71,219)(11,220,72,178)(12,179,73,221)(13,222,74,180)(14,181,75,223)(15,112,47,61)(16,62,48,99)(17,100,49,63)(18,64,50,101)(19,102,51,65)(20,66,52,103)(21,104,53,67)(22,68,54,105)(23,106,55,69)(24,70,56,107)(25,108,43,57)(26,58,44,109)(27,110,45,59)(28,60,46,111)(29,199,193,153)(30,154,194,200)(31,201,195,141)(32,142,196,202)(33,203,183,143)(34,144,184,204)(35,205,185,145)(36,146,186,206)(37,207,187,147)(38,148,188,208)(39,209,189,149)(40,150,190,210)(41,197,191,151)(42,152,192,198)(85,158,134,121)(86,122,135,159)(87,160,136,123)(88,124,137,161)(89,162,138,125)(90,126,139,163)(91,164,140,113)(92,114,127,165)(93,166,128,115)(94,116,129,167)(95,168,130,117)(96,118,131,155)(97,156,132,119)(98,120,133,157), (1,122,115,8)(2,9,116,123)(3,124,117,10)(4,11,118,125)(5,126,119,12)(6,13,120,113)(7,114,121,14)(15,54,38,195)(16,196,39,55)(17,56,40,183)(18,184,41,43)(19,44,42,185)(20,186,29,45)(21,46,30,187)(22,188,31,47)(23,48,32,189)(24,190,33,49)(25,50,34,191)(26,192,35,51)(27,52,36,193)(28,194,37,53)(57,64,204,197)(58,198,205,65)(59,66,206,199)(60,200,207,67)(61,68,208,201)(62,202,209,69)(63,70,210,203)(71,78,161,168)(72,155,162,79)(73,80,163,156)(74,157,164,81)(75,82,165,158)(76,159,166,83)(77,84,167,160)(85,181,216,127)(86,128,217,182)(87,169,218,129)(88,130,219,170)(89,171,220,131)(90,132,221,172)(91,173,222,133)(92,134,223,174)(93,175,224,135)(94,136,211,176)(95,177,212,137)(96,138,213,178)(97,179,214,139)(98,140,215,180)(99,142,149,106)(100,107,150,143)(101,144,151,108)(102,109,152,145)(103,146,153,110)(104,111,154,147)(105,148,141,112), (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), (1,35,115,26)(2,34,116,25)(3,33,117,24)(4,32,118,23)(5,31,119,22)(6,30,120,21)(7,29,121,20)(8,42,122,19)(9,41,123,18)(10,40,124,17)(11,39,125,16)(12,38,126,15)(13,37,113,28)(14,36,114,27)(43,77,184,167)(44,76,185,166)(45,75,186,165)(46,74,187,164)(47,73,188,163)(48,72,189,162)(49,71,190,161)(50,84,191,160)(51,83,192,159)(52,82,193,158)(53,81,194,157)(54,80,195,156)(55,79,196,155)(56,78,183,168)(57,169,204,129)(58,182,205,128)(59,181,206,127)(60,180,207,140)(61,179,208,139)(62,178,209,138)(63,177,210,137)(64,176,197,136)(65,175,198,135)(66,174,199,134)(67,173,200,133)(68,172,201,132)(69,171,202,131)(70,170,203,130)(85,103,216,153)(86,102,217,152)(87,101,218,151)(88,100,219,150)(89,99,220,149)(90,112,221,148)(91,111,222,147)(92,110,223,146)(93,109,224,145)(94,108,211,144)(95,107,212,143)(96,106,213,142)(97,105,214,141)(98,104,215,154) );
G=PermutationGroup([[(1,224,76,182),(2,169,77,211),(3,212,78,170),(4,171,79,213),(5,214,80,172),(6,173,81,215),(7,216,82,174),(8,175,83,217),(9,218,84,176),(10,177,71,219),(11,220,72,178),(12,179,73,221),(13,222,74,180),(14,181,75,223),(15,112,47,61),(16,62,48,99),(17,100,49,63),(18,64,50,101),(19,102,51,65),(20,66,52,103),(21,104,53,67),(22,68,54,105),(23,106,55,69),(24,70,56,107),(25,108,43,57),(26,58,44,109),(27,110,45,59),(28,60,46,111),(29,199,193,153),(30,154,194,200),(31,201,195,141),(32,142,196,202),(33,203,183,143),(34,144,184,204),(35,205,185,145),(36,146,186,206),(37,207,187,147),(38,148,188,208),(39,209,189,149),(40,150,190,210),(41,197,191,151),(42,152,192,198),(85,158,134,121),(86,122,135,159),(87,160,136,123),(88,124,137,161),(89,162,138,125),(90,126,139,163),(91,164,140,113),(92,114,127,165),(93,166,128,115),(94,116,129,167),(95,168,130,117),(96,118,131,155),(97,156,132,119),(98,120,133,157)], [(1,122,115,8),(2,9,116,123),(3,124,117,10),(4,11,118,125),(5,126,119,12),(6,13,120,113),(7,114,121,14),(15,54,38,195),(16,196,39,55),(17,56,40,183),(18,184,41,43),(19,44,42,185),(20,186,29,45),(21,46,30,187),(22,188,31,47),(23,48,32,189),(24,190,33,49),(25,50,34,191),(26,192,35,51),(27,52,36,193),(28,194,37,53),(57,64,204,197),(58,198,205,65),(59,66,206,199),(60,200,207,67),(61,68,208,201),(62,202,209,69),(63,70,210,203),(71,78,161,168),(72,155,162,79),(73,80,163,156),(74,157,164,81),(75,82,165,158),(76,159,166,83),(77,84,167,160),(85,181,216,127),(86,128,217,182),(87,169,218,129),(88,130,219,170),(89,171,220,131),(90,132,221,172),(91,173,222,133),(92,134,223,174),(93,175,224,135),(94,136,211,176),(95,177,212,137),(96,138,213,178),(97,179,214,139),(98,140,215,180),(99,142,149,106),(100,107,150,143),(101,144,151,108),(102,109,152,145),(103,146,153,110),(104,111,154,147),(105,148,141,112)], [(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)], [(1,35,115,26),(2,34,116,25),(3,33,117,24),(4,32,118,23),(5,31,119,22),(6,30,120,21),(7,29,121,20),(8,42,122,19),(9,41,123,18),(10,40,124,17),(11,39,125,16),(12,38,126,15),(13,37,113,28),(14,36,114,27),(43,77,184,167),(44,76,185,166),(45,75,186,165),(46,74,187,164),(47,73,188,163),(48,72,189,162),(49,71,190,161),(50,84,191,160),(51,83,192,159),(52,82,193,158),(53,81,194,157),(54,80,195,156),(55,79,196,155),(56,78,183,168),(57,169,204,129),(58,182,205,128),(59,181,206,127),(60,180,207,140),(61,179,208,139),(62,178,209,138),(63,177,210,137),(64,176,197,136),(65,175,198,135),(66,174,199,134),(67,173,200,133),(68,172,201,132),(69,171,202,131),(70,170,203,130),(85,103,216,153),(86,102,217,152),(87,101,218,151),(88,100,219,150),(89,99,220,149),(90,112,221,148),(91,111,222,147),(92,110,223,146),(93,109,224,145),(94,108,211,144),(95,107,212,143),(96,106,213,142),(97,105,214,141),(98,104,215,154)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| 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 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | D4⋊6D14 |
| kernel | C42.166D14 | C4×Dic14 | D4×Dic7 | C23.18D14 | C28.17D4 | C7×C4⋊1D4 | C4⋊1D4 | C28 | C42 | C2×D4 | C14 | C4 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 8 | 3 | 18 | 1 | 12 | 6 |
Matrix representation of C42.166D14 ►in GL6(𝔽29)
| 28 | 18 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 17 | 13 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [28,16,0,0,0,0,18,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,16,0,0,0,0,18,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[28,0,0,0,0,0,18,1,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[17,0,0,0,0,0,13,12,0,0,0,0,0,0,21,8,0,0,0,0,3,8,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C42.166D14 in GAP, Magma, Sage, TeX
C_4^2._{166}D_{14} % in TeX
G:=Group("C4^2.166D14"); // GroupNames label
G:=SmallGroup(448,1166);
// by ID
G=gap.SmallGroup(448,1166);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,219,1571,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations