metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.189D14, C4⋊C4.212D14, (D7×C42)⋊20C2, D28⋊C4⋊41C2, D14⋊Q8⋊42C2, D14⋊D4.3C2, C42⋊2C2⋊10D7, C42⋊2D7⋊14C2, Dic7.Q8⋊37C2, (C2×C28).95C23, C22⋊C4.78D14, Dic7⋊3Q8⋊41C2, D14.13(C4○D4), Dic7⋊4D4⋊35C2, D14.5D4⋊40C2, D14.D4⋊50C2, (C2×C14).250C24, (C4×C28).234C22, D14⋊C4.45C22, C23.56(C22×D7), Dic7.15(C4○D4), Dic7.D4⋊46C2, (C2×D28).168C22, Dic7⋊C4.72C22, C4⋊Dic7.246C22, (C22×C14).64C23, C22.271(C23×D7), C23.D7.66C22, C23.11D14⋊21C2, (C2×Dic7).313C23, (C4×Dic7).150C22, (C22×D7).224C23, C7⋊11(C23.36C23), (C2×Dic14).183C22, (C22×Dic7).150C22, C2.97(D7×C4○D4), C4⋊C4⋊7D7⋊40C2, (C7×C42⋊2C2)⋊5C2, C14.208(C2×C4○D4), (C2×C4×D7).300C22, (C2×C4).87(C22×D7), (C7×C4⋊C4).202C22, (C2×C7⋊D4).70C22, (C7×C22⋊C4).75C22, SmallGroup(448,1159)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.189D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=dbd-1=a2b, dcd-1=a2c-1 >
Subgroups: 1036 in 234 conjugacy classes, 97 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C22×D7, C22×C14, C23.36C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, D7×C42, C42⋊2D7, C23.11D14, Dic7⋊4D4, D14.D4, D14⋊D4, Dic7.D4, Dic7⋊3Q8, Dic7.Q8, C4⋊C4⋊7D7, D28⋊C4, D14.5D4, D14⋊Q8, C7×C42⋊2C2, C42.189D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C23×D7, D7×C4○D4, C42.189D14
►On 224 points
Generators in S224
(1 151 104 114)(2 157 105 49)(3 153 106 116)(4 159 107 51)(5 141 108 118)(6 161 109 53)(7 143 110 120)(8 163 111 55)(9 145 112 122)(10 165 99 43)(11 147 100 124)(12 167 101 45)(13 149 102 126)(14 155 103 47)(15 33 132 194)(16 91 133 65)(17 35 134 196)(18 93 135 67)(19 37 136 184)(20 95 137 69)(21 39 138 186)(22 97 139 57)(23 41 140 188)(24 85 127 59)(25 29 128 190)(26 87 129 61)(27 31 130 192)(28 89 131 63)(30 82 191 198)(32 84 193 200)(34 72 195 202)(36 74 183 204)(38 76 185 206)(40 78 187 208)(42 80 189 210)(44 180 166 222)(46 182 168 224)(48 170 156 212)(50 172 158 214)(52 174 160 216)(54 176 162 218)(56 178 164 220)(58 209 98 79)(60 197 86 81)(62 199 88 83)(64 201 90 71)(66 203 92 73)(68 205 94 75)(70 207 96 77)(113 169 150 211)(115 171 152 213)(117 173 154 215)(119 175 142 217)(121 177 144 219)(123 179 146 221)(125 181 148 223)
(1 184 212 94)(2 38 213 69)(3 186 214 96)(4 40 215 57)(5 188 216 98)(6 42 217 59)(7 190 218 86)(8 30 219 61)(9 192 220 88)(10 32 221 63)(11 194 222 90)(12 34 223 65)(13 196 224 92)(14 36 211 67)(15 44 71 147)(16 167 72 125)(17 46 73 149)(18 155 74 113)(19 48 75 151)(20 157 76 115)(21 50 77 153)(22 159 78 117)(23 52 79 141)(24 161 80 119)(25 54 81 143)(26 163 82 121)(27 56 83 145)(28 165 84 123)(29 176 60 110)(31 178 62 112)(33 180 64 100)(35 182 66 102)(37 170 68 104)(39 172 70 106)(41 174 58 108)(43 200 146 131)(45 202 148 133)(47 204 150 135)(49 206 152 137)(51 208 154 139)(53 210 142 127)(55 198 144 129)(85 109 189 175)(87 111 191 177)(89 99 193 179)(91 101 195 181)(93 103 183 169)(95 105 185 171)(97 107 187 173)(114 136 156 205)(116 138 158 207)(118 140 160 209)(120 128 162 197)(122 130 164 199)(124 132 166 201)(126 134 168 203)
(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)
(1 211 104 169)(2 182 105 224)(3 223 106 181)(4 180 107 222)(5 221 108 179)(6 178 109 220)(7 219 110 177)(8 176 111 218)(9 217 112 175)(10 174 99 216)(11 215 100 173)(12 172 101 214)(13 213 102 171)(14 170 103 212)(15 78 132 208)(16 207 133 77)(17 76 134 206)(18 205 135 75)(19 74 136 204)(20 203 137 73)(21 72 138 202)(22 201 139 71)(23 84 140 200)(24 199 127 83)(25 82 128 198)(26 197 129 81)(27 80 130 210)(28 209 131 79)(29 61 190 87)(30 86 191 60)(31 59 192 85)(32 98 193 58)(33 57 194 97)(34 96 195 70)(35 69 196 95)(36 94 183 68)(37 67 184 93)(38 92 185 66)(39 65 186 91)(40 90 187 64)(41 63 188 89)(42 88 189 62)(43 118 165 141)(44 154 166 117)(45 116 167 153)(46 152 168 115)(47 114 155 151)(48 150 156 113)(49 126 157 149)(50 148 158 125)(51 124 159 147)(52 146 160 123)(53 122 161 145)(54 144 162 121)(55 120 163 143)(56 142 164 119)
G:=sub<Sym(224)| (1,151,104,114)(2,157,105,49)(3,153,106,116)(4,159,107,51)(5,141,108,118)(6,161,109,53)(7,143,110,120)(8,163,111,55)(9,145,112,122)(10,165,99,43)(11,147,100,124)(12,167,101,45)(13,149,102,126)(14,155,103,47)(15,33,132,194)(16,91,133,65)(17,35,134,196)(18,93,135,67)(19,37,136,184)(20,95,137,69)(21,39,138,186)(22,97,139,57)(23,41,140,188)(24,85,127,59)(25,29,128,190)(26,87,129,61)(27,31,130,192)(28,89,131,63)(30,82,191,198)(32,84,193,200)(34,72,195,202)(36,74,183,204)(38,76,185,206)(40,78,187,208)(42,80,189,210)(44,180,166,222)(46,182,168,224)(48,170,156,212)(50,172,158,214)(52,174,160,216)(54,176,162,218)(56,178,164,220)(58,209,98,79)(60,197,86,81)(62,199,88,83)(64,201,90,71)(66,203,92,73)(68,205,94,75)(70,207,96,77)(113,169,150,211)(115,171,152,213)(117,173,154,215)(119,175,142,217)(121,177,144,219)(123,179,146,221)(125,181,148,223), (1,184,212,94)(2,38,213,69)(3,186,214,96)(4,40,215,57)(5,188,216,98)(6,42,217,59)(7,190,218,86)(8,30,219,61)(9,192,220,88)(10,32,221,63)(11,194,222,90)(12,34,223,65)(13,196,224,92)(14,36,211,67)(15,44,71,147)(16,167,72,125)(17,46,73,149)(18,155,74,113)(19,48,75,151)(20,157,76,115)(21,50,77,153)(22,159,78,117)(23,52,79,141)(24,161,80,119)(25,54,81,143)(26,163,82,121)(27,56,83,145)(28,165,84,123)(29,176,60,110)(31,178,62,112)(33,180,64,100)(35,182,66,102)(37,170,68,104)(39,172,70,106)(41,174,58,108)(43,200,146,131)(45,202,148,133)(47,204,150,135)(49,206,152,137)(51,208,154,139)(53,210,142,127)(55,198,144,129)(85,109,189,175)(87,111,191,177)(89,99,193,179)(91,101,195,181)(93,103,183,169)(95,105,185,171)(97,107,187,173)(114,136,156,205)(116,138,158,207)(118,140,160,209)(120,128,162,197)(122,130,164,199)(124,132,166,201)(126,134,168,203), (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), (1,211,104,169)(2,182,105,224)(3,223,106,181)(4,180,107,222)(5,221,108,179)(6,178,109,220)(7,219,110,177)(8,176,111,218)(9,217,112,175)(10,174,99,216)(11,215,100,173)(12,172,101,214)(13,213,102,171)(14,170,103,212)(15,78,132,208)(16,207,133,77)(17,76,134,206)(18,205,135,75)(19,74,136,204)(20,203,137,73)(21,72,138,202)(22,201,139,71)(23,84,140,200)(24,199,127,83)(25,82,128,198)(26,197,129,81)(27,80,130,210)(28,209,131,79)(29,61,190,87)(30,86,191,60)(31,59,192,85)(32,98,193,58)(33,57,194,97)(34,96,195,70)(35,69,196,95)(36,94,183,68)(37,67,184,93)(38,92,185,66)(39,65,186,91)(40,90,187,64)(41,63,188,89)(42,88,189,62)(43,118,165,141)(44,154,166,117)(45,116,167,153)(46,152,168,115)(47,114,155,151)(48,150,156,113)(49,126,157,149)(50,148,158,125)(51,124,159,147)(52,146,160,123)(53,122,161,145)(54,144,162,121)(55,120,163,143)(56,142,164,119)>;
G:=Group( (1,151,104,114)(2,157,105,49)(3,153,106,116)(4,159,107,51)(5,141,108,118)(6,161,109,53)(7,143,110,120)(8,163,111,55)(9,145,112,122)(10,165,99,43)(11,147,100,124)(12,167,101,45)(13,149,102,126)(14,155,103,47)(15,33,132,194)(16,91,133,65)(17,35,134,196)(18,93,135,67)(19,37,136,184)(20,95,137,69)(21,39,138,186)(22,97,139,57)(23,41,140,188)(24,85,127,59)(25,29,128,190)(26,87,129,61)(27,31,130,192)(28,89,131,63)(30,82,191,198)(32,84,193,200)(34,72,195,202)(36,74,183,204)(38,76,185,206)(40,78,187,208)(42,80,189,210)(44,180,166,222)(46,182,168,224)(48,170,156,212)(50,172,158,214)(52,174,160,216)(54,176,162,218)(56,178,164,220)(58,209,98,79)(60,197,86,81)(62,199,88,83)(64,201,90,71)(66,203,92,73)(68,205,94,75)(70,207,96,77)(113,169,150,211)(115,171,152,213)(117,173,154,215)(119,175,142,217)(121,177,144,219)(123,179,146,221)(125,181,148,223), (1,184,212,94)(2,38,213,69)(3,186,214,96)(4,40,215,57)(5,188,216,98)(6,42,217,59)(7,190,218,86)(8,30,219,61)(9,192,220,88)(10,32,221,63)(11,194,222,90)(12,34,223,65)(13,196,224,92)(14,36,211,67)(15,44,71,147)(16,167,72,125)(17,46,73,149)(18,155,74,113)(19,48,75,151)(20,157,76,115)(21,50,77,153)(22,159,78,117)(23,52,79,141)(24,161,80,119)(25,54,81,143)(26,163,82,121)(27,56,83,145)(28,165,84,123)(29,176,60,110)(31,178,62,112)(33,180,64,100)(35,182,66,102)(37,170,68,104)(39,172,70,106)(41,174,58,108)(43,200,146,131)(45,202,148,133)(47,204,150,135)(49,206,152,137)(51,208,154,139)(53,210,142,127)(55,198,144,129)(85,109,189,175)(87,111,191,177)(89,99,193,179)(91,101,195,181)(93,103,183,169)(95,105,185,171)(97,107,187,173)(114,136,156,205)(116,138,158,207)(118,140,160,209)(120,128,162,197)(122,130,164,199)(124,132,166,201)(126,134,168,203), (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), (1,211,104,169)(2,182,105,224)(3,223,106,181)(4,180,107,222)(5,221,108,179)(6,178,109,220)(7,219,110,177)(8,176,111,218)(9,217,112,175)(10,174,99,216)(11,215,100,173)(12,172,101,214)(13,213,102,171)(14,170,103,212)(15,78,132,208)(16,207,133,77)(17,76,134,206)(18,205,135,75)(19,74,136,204)(20,203,137,73)(21,72,138,202)(22,201,139,71)(23,84,140,200)(24,199,127,83)(25,82,128,198)(26,197,129,81)(27,80,130,210)(28,209,131,79)(29,61,190,87)(30,86,191,60)(31,59,192,85)(32,98,193,58)(33,57,194,97)(34,96,195,70)(35,69,196,95)(36,94,183,68)(37,67,184,93)(38,92,185,66)(39,65,186,91)(40,90,187,64)(41,63,188,89)(42,88,189,62)(43,118,165,141)(44,154,166,117)(45,116,167,153)(46,152,168,115)(47,114,155,151)(48,150,156,113)(49,126,157,149)(50,148,158,125)(51,124,159,147)(52,146,160,123)(53,122,161,145)(54,144,162,121)(55,120,163,143)(56,142,164,119) );
G=PermutationGroup([[(1,151,104,114),(2,157,105,49),(3,153,106,116),(4,159,107,51),(5,141,108,118),(6,161,109,53),(7,143,110,120),(8,163,111,55),(9,145,112,122),(10,165,99,43),(11,147,100,124),(12,167,101,45),(13,149,102,126),(14,155,103,47),(15,33,132,194),(16,91,133,65),(17,35,134,196),(18,93,135,67),(19,37,136,184),(20,95,137,69),(21,39,138,186),(22,97,139,57),(23,41,140,188),(24,85,127,59),(25,29,128,190),(26,87,129,61),(27,31,130,192),(28,89,131,63),(30,82,191,198),(32,84,193,200),(34,72,195,202),(36,74,183,204),(38,76,185,206),(40,78,187,208),(42,80,189,210),(44,180,166,222),(46,182,168,224),(48,170,156,212),(50,172,158,214),(52,174,160,216),(54,176,162,218),(56,178,164,220),(58,209,98,79),(60,197,86,81),(62,199,88,83),(64,201,90,71),(66,203,92,73),(68,205,94,75),(70,207,96,77),(113,169,150,211),(115,171,152,213),(117,173,154,215),(119,175,142,217),(121,177,144,219),(123,179,146,221),(125,181,148,223)], [(1,184,212,94),(2,38,213,69),(3,186,214,96),(4,40,215,57),(5,188,216,98),(6,42,217,59),(7,190,218,86),(8,30,219,61),(9,192,220,88),(10,32,221,63),(11,194,222,90),(12,34,223,65),(13,196,224,92),(14,36,211,67),(15,44,71,147),(16,167,72,125),(17,46,73,149),(18,155,74,113),(19,48,75,151),(20,157,76,115),(21,50,77,153),(22,159,78,117),(23,52,79,141),(24,161,80,119),(25,54,81,143),(26,163,82,121),(27,56,83,145),(28,165,84,123),(29,176,60,110),(31,178,62,112),(33,180,64,100),(35,182,66,102),(37,170,68,104),(39,172,70,106),(41,174,58,108),(43,200,146,131),(45,202,148,133),(47,204,150,135),(49,206,152,137),(51,208,154,139),(53,210,142,127),(55,198,144,129),(85,109,189,175),(87,111,191,177),(89,99,193,179),(91,101,195,181),(93,103,183,169),(95,105,185,171),(97,107,187,173),(114,136,156,205),(116,138,158,207),(118,140,160,209),(120,128,162,197),(122,130,164,199),(124,132,166,201),(126,134,168,203)], [(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)], [(1,211,104,169),(2,182,105,224),(3,223,106,181),(4,180,107,222),(5,221,108,179),(6,178,109,220),(7,219,110,177),(8,176,111,218),(9,217,112,175),(10,174,99,216),(11,215,100,173),(12,172,101,214),(13,213,102,171),(14,170,103,212),(15,78,132,208),(16,207,133,77),(17,76,134,206),(18,205,135,75),(19,74,136,204),(20,203,137,73),(21,72,138,202),(22,201,139,71),(23,84,140,200),(24,199,127,83),(25,82,128,198),(26,197,129,81),(27,80,130,210),(28,209,131,79),(29,61,190,87),(30,86,191,60),(31,59,192,85),(32,98,193,58),(33,57,194,97),(34,96,195,70),(35,69,196,95),(36,94,183,68),(37,67,184,93),(38,92,185,66),(39,65,186,91),(40,90,187,64),(41,63,188,89),(42,88,189,62),(43,118,165,141),(44,154,166,117),(45,116,167,153),(46,152,168,115),(47,114,155,151),(48,150,156,113),(49,126,157,149),(50,148,158,125),(51,124,159,147),(52,146,160,123),(53,122,161,145),(54,144,162,121),(55,120,163,143),(56,142,164,119)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 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 | 14 | 14 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D7×C4○D4 |
| kernel | C42.189D14 | D7×C42 | C42⋊2D7 | C23.11D14 | Dic7⋊4D4 | D14.D4 | D14⋊D4 | Dic7.D4 | Dic7⋊3Q8 | Dic7.Q8 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | D14⋊Q8 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | D14 | C42 | C22⋊C4 | C4⋊C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 4 | 3 | 9 | 9 | 18 |
Matrix representation of C42.189D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 12 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 28 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 25 | 0 | 0 |
| 0 | 0 | 8 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 27 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 18 | 0 | 0 |
| 0 | 0 | 3 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 28 | 28 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,12,0,0,0,0,0,12],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,28,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,24,8,0,0,0,0,25,12,0,0,0,0,0,0,28,0,0,0,0,0,27,1],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,18,3,0,0,0,0,18,11,0,0,0,0,0,0,1,28,0,0,0,0,2,28] >;
C42.189D14 in GAP, Magma, Sage, TeX
C_4^2._{189}D_{14} % in TeX
G:=Group("C4^2.189D14"); // GroupNames label
G:=SmallGroup(448,1159);
// by ID
G=gap.SmallGroup(448,1159);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,794,297,18822]);
// 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^-1*b^2,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=a^2*c^-1>;
// generators/relations