metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.97D14, C14.982+ 1+4, C28⋊Q8⋊12C2, D14⋊D4⋊4C2, C28⋊7D4⋊30C2, C4⋊D28⋊13C2, C4⋊C4.311D14, C4.D28⋊7C2, C42⋊D7⋊4C2, D28⋊C4⋊13C2, C4.97(C4○D28), C42⋊C2⋊16D7, (C2×C14).76C24, (C4×C28).27C22, C28.199(C4○D4), (C2×C28).697C23, D14⋊C4.83C22, C22⋊C4.100D14, Dic7.D4⋊4C2, (C2×D28).24C22, (C22×C4).197D14, C2.10(D4⋊8D14), C23.87(C22×D7), Dic7.18(C4○D4), C4⋊Dic7.196C22, (C2×Dic7).29C23, (C22×D7).24C23, C22.105(C23×D7), C23.D7.98C22, Dic7⋊C4.106C22, (C22×C28).233C22, (C22×C14).146C23, C7⋊1(C22.49C24), (C4×Dic7).198C22, (C2×Dic14).24C22, (C4×C7⋊D4)⋊13C2, C2.15(D7×C4○D4), C4⋊C4⋊7D7⋊12C2, C2.35(C2×C4○D28), C14.32(C2×C4○D4), (C2×C4×D7).194C22, (C7×C42⋊C2)⋊18C2, (C7×C4⋊C4).312C22, (C2×C4).278(C22×D7), (C2×C7⋊D4).105C22, (C7×C22⋊C4).115C22, SmallGroup(448,985)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.97D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=ab2, ad=da, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1172 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, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C42⋊C2, C4×D4, C4⋊D4, C4.4D4, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C22.49C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C2×C7⋊D4, C2×C7⋊D4, C22×C28, C42⋊D7, C4.D28, D14⋊D4, Dic7.D4, C28⋊Q8, C4⋊C4⋊7D7, D28⋊C4, C4⋊D28, C4×C7⋊D4, C28⋊7D4, C7×C42⋊C2, C42.97D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.49C24, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, D4⋊8D14, C42.97D14
►On 224 points
Generators in S224
(1 68 47 129)(2 83 48 116)(3 70 49 131)(4 57 50 118)(5 72 51 133)(6 59 52 120)(7 74 53 135)(8 61 54 122)(9 76 55 137)(10 63 56 124)(11 78 29 139)(12 65 30 126)(13 80 31 113)(14 67 32 128)(15 82 33 115)(16 69 34 130)(17 84 35 117)(18 71 36 132)(19 58 37 119)(20 73 38 134)(21 60 39 121)(22 75 40 136)(23 62 41 123)(24 77 42 138)(25 64 43 125)(26 79 44 140)(27 66 45 127)(28 81 46 114)(85 154 173 215)(86 141 174 202)(87 156 175 217)(88 143 176 204)(89 158 177 219)(90 145 178 206)(91 160 179 221)(92 147 180 208)(93 162 181 223)(94 149 182 210)(95 164 183 197)(96 151 184 212)(97 166 185 199)(98 153 186 214)(99 168 187 201)(100 155 188 216)(101 142 189 203)(102 157 190 218)(103 144 191 205)(104 159 192 220)(105 146 193 207)(106 161 194 222)(107 148 195 209)(108 163 196 224)(109 150 169 211)(110 165 170 198)(111 152 171 213)(112 167 172 200)
(1 187 15 173)(2 188 16 174)(3 189 17 175)(4 190 18 176)(5 191 19 177)(6 192 20 178)(7 193 21 179)(8 194 22 180)(9 195 23 181)(10 196 24 182)(11 169 25 183)(12 170 26 184)(13 171 27 185)(14 172 28 186)(29 109 43 95)(30 110 44 96)(31 111 45 97)(32 112 46 98)(33 85 47 99)(34 86 48 100)(35 87 49 101)(36 88 50 102)(37 89 51 103)(38 90 52 104)(39 91 53 105)(40 92 54 106)(41 93 55 107)(42 94 56 108)(57 218 71 204)(58 219 72 205)(59 220 73 206)(60 221 74 207)(61 222 75 208)(62 223 76 209)(63 224 77 210)(64 197 78 211)(65 198 79 212)(66 199 80 213)(67 200 81 214)(68 201 82 215)(69 202 83 216)(70 203 84 217)(113 152 127 166)(114 153 128 167)(115 154 129 168)(116 155 130 141)(117 156 131 142)(118 157 132 143)(119 158 133 144)(120 159 134 145)(121 160 135 146)(122 161 136 147)(123 162 137 148)(124 163 138 149)(125 164 139 150)(126 165 140 151)
(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)
(1 146 15 160)(2 159 16 145)(3 144 17 158)(4 157 18 143)(5 142 19 156)(6 155 20 141)(7 168 21 154)(8 153 22 167)(9 166 23 152)(10 151 24 165)(11 164 25 150)(12 149 26 163)(13 162 27 148)(14 147 28 161)(29 197 43 211)(30 210 44 224)(31 223 45 209)(32 208 46 222)(33 221 47 207)(34 206 48 220)(35 219 49 205)(36 204 50 218)(37 217 51 203)(38 202 52 216)(39 215 53 201)(40 200 54 214)(41 213 55 199)(42 198 56 212)(57 190 71 176)(58 175 72 189)(59 188 73 174)(60 173 74 187)(61 186 75 172)(62 171 76 185)(63 184 77 170)(64 169 78 183)(65 182 79 196)(66 195 80 181)(67 180 81 194)(68 193 82 179)(69 178 83 192)(70 191 84 177)(85 135 99 121)(86 120 100 134)(87 133 101 119)(88 118 102 132)(89 131 103 117)(90 116 104 130)(91 129 105 115)(92 114 106 128)(93 127 107 113)(94 140 108 126)(95 125 109 139)(96 138 110 124)(97 123 111 137)(98 136 112 122)
G:=sub<Sym(224)| (1,68,47,129)(2,83,48,116)(3,70,49,131)(4,57,50,118)(5,72,51,133)(6,59,52,120)(7,74,53,135)(8,61,54,122)(9,76,55,137)(10,63,56,124)(11,78,29,139)(12,65,30,126)(13,80,31,113)(14,67,32,128)(15,82,33,115)(16,69,34,130)(17,84,35,117)(18,71,36,132)(19,58,37,119)(20,73,38,134)(21,60,39,121)(22,75,40,136)(23,62,41,123)(24,77,42,138)(25,64,43,125)(26,79,44,140)(27,66,45,127)(28,81,46,114)(85,154,173,215)(86,141,174,202)(87,156,175,217)(88,143,176,204)(89,158,177,219)(90,145,178,206)(91,160,179,221)(92,147,180,208)(93,162,181,223)(94,149,182,210)(95,164,183,197)(96,151,184,212)(97,166,185,199)(98,153,186,214)(99,168,187,201)(100,155,188,216)(101,142,189,203)(102,157,190,218)(103,144,191,205)(104,159,192,220)(105,146,193,207)(106,161,194,222)(107,148,195,209)(108,163,196,224)(109,150,169,211)(110,165,170,198)(111,152,171,213)(112,167,172,200), (1,187,15,173)(2,188,16,174)(3,189,17,175)(4,190,18,176)(5,191,19,177)(6,192,20,178)(7,193,21,179)(8,194,22,180)(9,195,23,181)(10,196,24,182)(11,169,25,183)(12,170,26,184)(13,171,27,185)(14,172,28,186)(29,109,43,95)(30,110,44,96)(31,111,45,97)(32,112,46,98)(33,85,47,99)(34,86,48,100)(35,87,49,101)(36,88,50,102)(37,89,51,103)(38,90,52,104)(39,91,53,105)(40,92,54,106)(41,93,55,107)(42,94,56,108)(57,218,71,204)(58,219,72,205)(59,220,73,206)(60,221,74,207)(61,222,75,208)(62,223,76,209)(63,224,77,210)(64,197,78,211)(65,198,79,212)(66,199,80,213)(67,200,81,214)(68,201,82,215)(69,202,83,216)(70,203,84,217)(113,152,127,166)(114,153,128,167)(115,154,129,168)(116,155,130,141)(117,156,131,142)(118,157,132,143)(119,158,133,144)(120,159,134,145)(121,160,135,146)(122,161,136,147)(123,162,137,148)(124,163,138,149)(125,164,139,150)(126,165,140,151), (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), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,197,43,211)(30,210,44,224)(31,223,45,209)(32,208,46,222)(33,221,47,207)(34,206,48,220)(35,219,49,205)(36,204,50,218)(37,217,51,203)(38,202,52,216)(39,215,53,201)(40,200,54,214)(41,213,55,199)(42,198,56,212)(57,190,71,176)(58,175,72,189)(59,188,73,174)(60,173,74,187)(61,186,75,172)(62,171,76,185)(63,184,77,170)(64,169,78,183)(65,182,79,196)(66,195,80,181)(67,180,81,194)(68,193,82,179)(69,178,83,192)(70,191,84,177)(85,135,99,121)(86,120,100,134)(87,133,101,119)(88,118,102,132)(89,131,103,117)(90,116,104,130)(91,129,105,115)(92,114,106,128)(93,127,107,113)(94,140,108,126)(95,125,109,139)(96,138,110,124)(97,123,111,137)(98,136,112,122)>;
G:=Group( (1,68,47,129)(2,83,48,116)(3,70,49,131)(4,57,50,118)(5,72,51,133)(6,59,52,120)(7,74,53,135)(8,61,54,122)(9,76,55,137)(10,63,56,124)(11,78,29,139)(12,65,30,126)(13,80,31,113)(14,67,32,128)(15,82,33,115)(16,69,34,130)(17,84,35,117)(18,71,36,132)(19,58,37,119)(20,73,38,134)(21,60,39,121)(22,75,40,136)(23,62,41,123)(24,77,42,138)(25,64,43,125)(26,79,44,140)(27,66,45,127)(28,81,46,114)(85,154,173,215)(86,141,174,202)(87,156,175,217)(88,143,176,204)(89,158,177,219)(90,145,178,206)(91,160,179,221)(92,147,180,208)(93,162,181,223)(94,149,182,210)(95,164,183,197)(96,151,184,212)(97,166,185,199)(98,153,186,214)(99,168,187,201)(100,155,188,216)(101,142,189,203)(102,157,190,218)(103,144,191,205)(104,159,192,220)(105,146,193,207)(106,161,194,222)(107,148,195,209)(108,163,196,224)(109,150,169,211)(110,165,170,198)(111,152,171,213)(112,167,172,200), (1,187,15,173)(2,188,16,174)(3,189,17,175)(4,190,18,176)(5,191,19,177)(6,192,20,178)(7,193,21,179)(8,194,22,180)(9,195,23,181)(10,196,24,182)(11,169,25,183)(12,170,26,184)(13,171,27,185)(14,172,28,186)(29,109,43,95)(30,110,44,96)(31,111,45,97)(32,112,46,98)(33,85,47,99)(34,86,48,100)(35,87,49,101)(36,88,50,102)(37,89,51,103)(38,90,52,104)(39,91,53,105)(40,92,54,106)(41,93,55,107)(42,94,56,108)(57,218,71,204)(58,219,72,205)(59,220,73,206)(60,221,74,207)(61,222,75,208)(62,223,76,209)(63,224,77,210)(64,197,78,211)(65,198,79,212)(66,199,80,213)(67,200,81,214)(68,201,82,215)(69,202,83,216)(70,203,84,217)(113,152,127,166)(114,153,128,167)(115,154,129,168)(116,155,130,141)(117,156,131,142)(118,157,132,143)(119,158,133,144)(120,159,134,145)(121,160,135,146)(122,161,136,147)(123,162,137,148)(124,163,138,149)(125,164,139,150)(126,165,140,151), (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), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,197,43,211)(30,210,44,224)(31,223,45,209)(32,208,46,222)(33,221,47,207)(34,206,48,220)(35,219,49,205)(36,204,50,218)(37,217,51,203)(38,202,52,216)(39,215,53,201)(40,200,54,214)(41,213,55,199)(42,198,56,212)(57,190,71,176)(58,175,72,189)(59,188,73,174)(60,173,74,187)(61,186,75,172)(62,171,76,185)(63,184,77,170)(64,169,78,183)(65,182,79,196)(66,195,80,181)(67,180,81,194)(68,193,82,179)(69,178,83,192)(70,191,84,177)(85,135,99,121)(86,120,100,134)(87,133,101,119)(88,118,102,132)(89,131,103,117)(90,116,104,130)(91,129,105,115)(92,114,106,128)(93,127,107,113)(94,140,108,126)(95,125,109,139)(96,138,110,124)(97,123,111,137)(98,136,112,122) );
G=PermutationGroup([[(1,68,47,129),(2,83,48,116),(3,70,49,131),(4,57,50,118),(5,72,51,133),(6,59,52,120),(7,74,53,135),(8,61,54,122),(9,76,55,137),(10,63,56,124),(11,78,29,139),(12,65,30,126),(13,80,31,113),(14,67,32,128),(15,82,33,115),(16,69,34,130),(17,84,35,117),(18,71,36,132),(19,58,37,119),(20,73,38,134),(21,60,39,121),(22,75,40,136),(23,62,41,123),(24,77,42,138),(25,64,43,125),(26,79,44,140),(27,66,45,127),(28,81,46,114),(85,154,173,215),(86,141,174,202),(87,156,175,217),(88,143,176,204),(89,158,177,219),(90,145,178,206),(91,160,179,221),(92,147,180,208),(93,162,181,223),(94,149,182,210),(95,164,183,197),(96,151,184,212),(97,166,185,199),(98,153,186,214),(99,168,187,201),(100,155,188,216),(101,142,189,203),(102,157,190,218),(103,144,191,205),(104,159,192,220),(105,146,193,207),(106,161,194,222),(107,148,195,209),(108,163,196,224),(109,150,169,211),(110,165,170,198),(111,152,171,213),(112,167,172,200)], [(1,187,15,173),(2,188,16,174),(3,189,17,175),(4,190,18,176),(5,191,19,177),(6,192,20,178),(7,193,21,179),(8,194,22,180),(9,195,23,181),(10,196,24,182),(11,169,25,183),(12,170,26,184),(13,171,27,185),(14,172,28,186),(29,109,43,95),(30,110,44,96),(31,111,45,97),(32,112,46,98),(33,85,47,99),(34,86,48,100),(35,87,49,101),(36,88,50,102),(37,89,51,103),(38,90,52,104),(39,91,53,105),(40,92,54,106),(41,93,55,107),(42,94,56,108),(57,218,71,204),(58,219,72,205),(59,220,73,206),(60,221,74,207),(61,222,75,208),(62,223,76,209),(63,224,77,210),(64,197,78,211),(65,198,79,212),(66,199,80,213),(67,200,81,214),(68,201,82,215),(69,202,83,216),(70,203,84,217),(113,152,127,166),(114,153,128,167),(115,154,129,168),(116,155,130,141),(117,156,131,142),(118,157,132,143),(119,158,133,144),(120,159,134,145),(121,160,135,146),(122,161,136,147),(123,162,137,148),(124,163,138,149),(125,164,139,150),(126,165,140,151)], [(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)], [(1,146,15,160),(2,159,16,145),(3,144,17,158),(4,157,18,143),(5,142,19,156),(6,155,20,141),(7,168,21,154),(8,153,22,167),(9,166,23,152),(10,151,24,165),(11,164,25,150),(12,149,26,163),(13,162,27,148),(14,147,28,161),(29,197,43,211),(30,210,44,224),(31,223,45,209),(32,208,46,222),(33,221,47,207),(34,206,48,220),(35,219,49,205),(36,204,50,218),(37,217,51,203),(38,202,52,216),(39,215,53,201),(40,200,54,214),(41,213,55,199),(42,198,56,212),(57,190,71,176),(58,175,72,189),(59,188,73,174),(60,173,74,187),(61,186,75,172),(62,171,76,185),(63,184,77,170),(64,169,78,183),(65,182,79,196),(66,195,80,181),(67,180,81,194),(68,193,82,179),(69,178,83,192),(70,191,84,177),(85,135,99,121),(86,120,100,134),(87,133,101,119),(88,118,102,132),(89,131,103,117),(90,116,104,130),(91,129,105,115),(92,114,106,128),(93,127,107,113),(94,140,108,126),(95,125,109,139),(96,138,110,124),(97,123,111,137),(98,136,112,122)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| 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 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | C4○D28 | 2+ 1+4 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.97D14 | C42⋊D7 | C4.D28 | D14⋊D4 | Dic7.D4 | C28⋊Q8 | C4⋊C4⋊7D7 | D28⋊C4 | C4⋊D28 | C4×C7⋊D4 | C28⋊7D4 | C7×C42⋊C2 | C42⋊C2 | Dic7 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 6 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.97D14 ►in GL4(𝔽29) generated by
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 26 | 1 |
| 11 | 16 | 0 | 0 |
| 7 | 18 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 11 | 8 | 0 | 0 |
| 18 | 0 | 0 | 0 |
| 0 | 0 | 14 | 10 |
| 0 | 0 | 18 | 15 |
| 13 | 11 | 0 | 0 |
| 19 | 16 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
G:=sub<GL(4,GF(29))| [17,0,0,0,0,17,0,0,0,0,28,26,0,0,0,1],[11,7,0,0,16,18,0,0,0,0,17,0,0,0,0,17],[11,18,0,0,8,0,0,0,0,0,14,18,0,0,10,15],[13,19,0,0,11,16,0,0,0,0,17,0,0,0,0,17] >;
C42.97D14 in GAP, Magma, Sage, TeX
C_4^2._{97}D_{14} % in TeX
G:=Group("C4^2.97D14"); // GroupNames label
G:=SmallGroup(448,985);
// by ID
G=gap.SmallGroup(448,985);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,100,675,136,18822]);
// 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,a*d=d*a,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations