metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.98D14, C14.532- 1+4, C28⋊Q8⋊13C2, C4⋊C4.312D14, C42⋊2D7⋊6C2, D14⋊2Q8⋊13C2, (C4×Dic14)⋊11C2, C4.98(C4○D28), C42⋊C2⋊17D7, (C2×C14).77C24, (C4×C28).28C22, Dic7⋊3Q8⋊13C2, C28.200(C4○D4), C28.48D4⋊30C2, (C2×C28).698C23, D14⋊C4.84C22, C22⋊C4.101D14, (C22×C4).198D14, C23.D14⋊4C2, Dic7⋊C4.3C22, C23.88(C22×D7), Dic7.34(C4○D4), C4⋊Dic7.293C22, Dic7.D4.1C2, (C2×Dic7).30C23, (C22×D7).25C23, C22.106(C23×D7), C23.D7.99C22, (C22×C28).234C22, (C22×C14).147C23, C7⋊1(C22.50C24), (C4×Dic7).199C22, C2.11(D4.10D14), (C2×Dic14).232C22, C2.16(D7×C4○D4), (C4×C7⋊D4).6C2, C4⋊C4⋊7D7⋊13C2, C14.33(C2×C4○D4), C2.36(C2×C4○D28), (C2×C4×D7).62C22, (C7×C42⋊C2)⋊19C2, (C7×C4⋊C4).313C22, (C2×C4).279(C22×D7), (C2×C7⋊D4).106C22, (C7×C22⋊C4).116C22, SmallGroup(448,986)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.98D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=ab2, ad=da, bc=cb, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 852 in 212 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×Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C22.50C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C22×C28, C4×Dic14, C42⋊2D7, C23.D14, Dic7.D4, Dic7⋊3Q8, C28⋊Q8, C4⋊C4⋊7D7, D14⋊2Q8, C28.48D4, C4×C7⋊D4, C7×C42⋊C2, C42.98D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, D4.10D14, C42.98D14
►On 224 points
Generators in S224
(1 174 71 135)(2 189 72 122)(3 176 73 137)(4 191 74 124)(5 178 75 139)(6 193 76 126)(7 180 77 113)(8 195 78 128)(9 182 79 115)(10 169 80 130)(11 184 81 117)(12 171 82 132)(13 186 83 119)(14 173 84 134)(15 188 57 121)(16 175 58 136)(17 190 59 123)(18 177 60 138)(19 192 61 125)(20 179 62 140)(21 194 63 127)(22 181 64 114)(23 196 65 129)(24 183 66 116)(25 170 67 131)(26 185 68 118)(27 172 69 133)(28 187 70 120)(29 167 222 86)(30 154 223 101)(31 141 224 88)(32 156 197 103)(33 143 198 90)(34 158 199 105)(35 145 200 92)(36 160 201 107)(37 147 202 94)(38 162 203 109)(39 149 204 96)(40 164 205 111)(41 151 206 98)(42 166 207 85)(43 153 208 100)(44 168 209 87)(45 155 210 102)(46 142 211 89)(47 157 212 104)(48 144 213 91)(49 159 214 106)(50 146 215 93)(51 161 216 108)(52 148 217 95)(53 163 218 110)(54 150 219 97)(55 165 220 112)(56 152 221 99)
(1 215 15 201)(2 216 16 202)(3 217 17 203)(4 218 18 204)(5 219 19 205)(6 220 20 206)(7 221 21 207)(8 222 22 208)(9 223 23 209)(10 224 24 210)(11 197 25 211)(12 198 26 212)(13 199 27 213)(14 200 28 214)(29 64 43 78)(30 65 44 79)(31 66 45 80)(32 67 46 81)(33 68 47 82)(34 69 48 83)(35 70 49 84)(36 71 50 57)(37 72 51 58)(38 73 52 59)(39 74 53 60)(40 75 54 61)(41 76 55 62)(42 77 56 63)(85 180 99 194)(86 181 100 195)(87 182 101 196)(88 183 102 169)(89 184 103 170)(90 185 104 171)(91 186 105 172)(92 187 106 173)(93 188 107 174)(94 189 108 175)(95 190 109 176)(96 191 110 177)(97 192 111 178)(98 193 112 179)(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 221 43 207)(30 206 44 220)(31 219 45 205)(32 204 46 218)(33 217 47 203)(34 202 48 216)(35 215 49 201)(36 200 50 214)(37 213 51 199)(38 198 52 212)(39 211 53 197)(40 224 54 210)(41 209 55 223)(42 222 56 208)(57 70 71 84)(58 83 72 69)(59 68 73 82)(60 81 74 67)(61 66 75 80)(62 79 76 65)(63 64 77 78)(85 167 99 153)(86 152 100 166)(87 165 101 151)(88 150 102 164)(89 163 103 149)(90 148 104 162)(91 161 105 147)(92 146 106 160)(93 159 107 145)(94 144 108 158)(95 157 109 143)(96 142 110 156)(97 155 111 141)(98 168 112 154)(113 128 127 114)(115 126 129 140)(116 139 130 125)(117 124 131 138)(118 137 132 123)(119 122 133 136)(120 135 134 121)(169 192 183 178)(170 177 184 191)(171 190 185 176)(172 175 186 189)(173 188 187 174)(179 182 193 196)(180 195 194 181)
G:=sub<Sym(224)| (1,174,71,135)(2,189,72,122)(3,176,73,137)(4,191,74,124)(5,178,75,139)(6,193,76,126)(7,180,77,113)(8,195,78,128)(9,182,79,115)(10,169,80,130)(11,184,81,117)(12,171,82,132)(13,186,83,119)(14,173,84,134)(15,188,57,121)(16,175,58,136)(17,190,59,123)(18,177,60,138)(19,192,61,125)(20,179,62,140)(21,194,63,127)(22,181,64,114)(23,196,65,129)(24,183,66,116)(25,170,67,131)(26,185,68,118)(27,172,69,133)(28,187,70,120)(29,167,222,86)(30,154,223,101)(31,141,224,88)(32,156,197,103)(33,143,198,90)(34,158,199,105)(35,145,200,92)(36,160,201,107)(37,147,202,94)(38,162,203,109)(39,149,204,96)(40,164,205,111)(41,151,206,98)(42,166,207,85)(43,153,208,100)(44,168,209,87)(45,155,210,102)(46,142,211,89)(47,157,212,104)(48,144,213,91)(49,159,214,106)(50,146,215,93)(51,161,216,108)(52,148,217,95)(53,163,218,110)(54,150,219,97)(55,165,220,112)(56,152,221,99), (1,215,15,201)(2,216,16,202)(3,217,17,203)(4,218,18,204)(5,219,19,205)(6,220,20,206)(7,221,21,207)(8,222,22,208)(9,223,23,209)(10,224,24,210)(11,197,25,211)(12,198,26,212)(13,199,27,213)(14,200,28,214)(29,64,43,78)(30,65,44,79)(31,66,45,80)(32,67,46,81)(33,68,47,82)(34,69,48,83)(35,70,49,84)(36,71,50,57)(37,72,51,58)(38,73,52,59)(39,74,53,60)(40,75,54,61)(41,76,55,62)(42,77,56,63)(85,180,99,194)(86,181,100,195)(87,182,101,196)(88,183,102,169)(89,184,103,170)(90,185,104,171)(91,186,105,172)(92,187,106,173)(93,188,107,174)(94,189,108,175)(95,190,109,176)(96,191,110,177)(97,192,111,178)(98,193,112,179)(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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,221,43,207)(30,206,44,220)(31,219,45,205)(32,204,46,218)(33,217,47,203)(34,202,48,216)(35,215,49,201)(36,200,50,214)(37,213,51,199)(38,198,52,212)(39,211,53,197)(40,224,54,210)(41,209,55,223)(42,222,56,208)(57,70,71,84)(58,83,72,69)(59,68,73,82)(60,81,74,67)(61,66,75,80)(62,79,76,65)(63,64,77,78)(85,167,99,153)(86,152,100,166)(87,165,101,151)(88,150,102,164)(89,163,103,149)(90,148,104,162)(91,161,105,147)(92,146,106,160)(93,159,107,145)(94,144,108,158)(95,157,109,143)(96,142,110,156)(97,155,111,141)(98,168,112,154)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181)>;
G:=Group( (1,174,71,135)(2,189,72,122)(3,176,73,137)(4,191,74,124)(5,178,75,139)(6,193,76,126)(7,180,77,113)(8,195,78,128)(9,182,79,115)(10,169,80,130)(11,184,81,117)(12,171,82,132)(13,186,83,119)(14,173,84,134)(15,188,57,121)(16,175,58,136)(17,190,59,123)(18,177,60,138)(19,192,61,125)(20,179,62,140)(21,194,63,127)(22,181,64,114)(23,196,65,129)(24,183,66,116)(25,170,67,131)(26,185,68,118)(27,172,69,133)(28,187,70,120)(29,167,222,86)(30,154,223,101)(31,141,224,88)(32,156,197,103)(33,143,198,90)(34,158,199,105)(35,145,200,92)(36,160,201,107)(37,147,202,94)(38,162,203,109)(39,149,204,96)(40,164,205,111)(41,151,206,98)(42,166,207,85)(43,153,208,100)(44,168,209,87)(45,155,210,102)(46,142,211,89)(47,157,212,104)(48,144,213,91)(49,159,214,106)(50,146,215,93)(51,161,216,108)(52,148,217,95)(53,163,218,110)(54,150,219,97)(55,165,220,112)(56,152,221,99), (1,215,15,201)(2,216,16,202)(3,217,17,203)(4,218,18,204)(5,219,19,205)(6,220,20,206)(7,221,21,207)(8,222,22,208)(9,223,23,209)(10,224,24,210)(11,197,25,211)(12,198,26,212)(13,199,27,213)(14,200,28,214)(29,64,43,78)(30,65,44,79)(31,66,45,80)(32,67,46,81)(33,68,47,82)(34,69,48,83)(35,70,49,84)(36,71,50,57)(37,72,51,58)(38,73,52,59)(39,74,53,60)(40,75,54,61)(41,76,55,62)(42,77,56,63)(85,180,99,194)(86,181,100,195)(87,182,101,196)(88,183,102,169)(89,184,103,170)(90,185,104,171)(91,186,105,172)(92,187,106,173)(93,188,107,174)(94,189,108,175)(95,190,109,176)(96,191,110,177)(97,192,111,178)(98,193,112,179)(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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,221,43,207)(30,206,44,220)(31,219,45,205)(32,204,46,218)(33,217,47,203)(34,202,48,216)(35,215,49,201)(36,200,50,214)(37,213,51,199)(38,198,52,212)(39,211,53,197)(40,224,54,210)(41,209,55,223)(42,222,56,208)(57,70,71,84)(58,83,72,69)(59,68,73,82)(60,81,74,67)(61,66,75,80)(62,79,76,65)(63,64,77,78)(85,167,99,153)(86,152,100,166)(87,165,101,151)(88,150,102,164)(89,163,103,149)(90,148,104,162)(91,161,105,147)(92,146,106,160)(93,159,107,145)(94,144,108,158)(95,157,109,143)(96,142,110,156)(97,155,111,141)(98,168,112,154)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181) );
G=PermutationGroup([[(1,174,71,135),(2,189,72,122),(3,176,73,137),(4,191,74,124),(5,178,75,139),(6,193,76,126),(7,180,77,113),(8,195,78,128),(9,182,79,115),(10,169,80,130),(11,184,81,117),(12,171,82,132),(13,186,83,119),(14,173,84,134),(15,188,57,121),(16,175,58,136),(17,190,59,123),(18,177,60,138),(19,192,61,125),(20,179,62,140),(21,194,63,127),(22,181,64,114),(23,196,65,129),(24,183,66,116),(25,170,67,131),(26,185,68,118),(27,172,69,133),(28,187,70,120),(29,167,222,86),(30,154,223,101),(31,141,224,88),(32,156,197,103),(33,143,198,90),(34,158,199,105),(35,145,200,92),(36,160,201,107),(37,147,202,94),(38,162,203,109),(39,149,204,96),(40,164,205,111),(41,151,206,98),(42,166,207,85),(43,153,208,100),(44,168,209,87),(45,155,210,102),(46,142,211,89),(47,157,212,104),(48,144,213,91),(49,159,214,106),(50,146,215,93),(51,161,216,108),(52,148,217,95),(53,163,218,110),(54,150,219,97),(55,165,220,112),(56,152,221,99)], [(1,215,15,201),(2,216,16,202),(3,217,17,203),(4,218,18,204),(5,219,19,205),(6,220,20,206),(7,221,21,207),(8,222,22,208),(9,223,23,209),(10,224,24,210),(11,197,25,211),(12,198,26,212),(13,199,27,213),(14,200,28,214),(29,64,43,78),(30,65,44,79),(31,66,45,80),(32,67,46,81),(33,68,47,82),(34,69,48,83),(35,70,49,84),(36,71,50,57),(37,72,51,58),(38,73,52,59),(39,74,53,60),(40,75,54,61),(41,76,55,62),(42,77,56,63),(85,180,99,194),(86,181,100,195),(87,182,101,196),(88,183,102,169),(89,184,103,170),(90,185,104,171),(91,186,105,172),(92,187,106,173),(93,188,107,174),(94,189,108,175),(95,190,109,176),(96,191,110,177),(97,192,111,178),(98,193,112,179),(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,221,43,207),(30,206,44,220),(31,219,45,205),(32,204,46,218),(33,217,47,203),(34,202,48,216),(35,215,49,201),(36,200,50,214),(37,213,51,199),(38,198,52,212),(39,211,53,197),(40,224,54,210),(41,209,55,223),(42,222,56,208),(57,70,71,84),(58,83,72,69),(59,68,73,82),(60,81,74,67),(61,66,75,80),(62,79,76,65),(63,64,77,78),(85,167,99,153),(86,152,100,166),(87,165,101,151),(88,150,102,164),(89,163,103,149),(90,148,104,162),(91,161,105,147),(92,146,106,160),(93,159,107,145),(94,144,108,158),(95,157,109,143),(96,142,110,156),(97,155,111,141),(98,168,112,154),(113,128,127,114),(115,126,129,140),(116,139,130,125),(117,124,131,138),(118,137,132,123),(119,122,133,136),(120,135,134,121),(169,192,183,178),(170,177,184,191),(171,190,185,176),(172,175,186,189),(173,188,187,174),(179,182,193,196),(180,195,194,181)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | ··· | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 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 | D4.10D14 |
| kernel | C42.98D14 | C4×Dic14 | C42⋊2D7 | C23.D14 | Dic7.D4 | Dic7⋊3Q8 | C28⋊Q8 | C4⋊C4⋊7D7 | D14⋊2Q8 | C28.48D4 | C4×C7⋊D4 | 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 C42.98D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 8 | 13 | 0 | 0 | 0 | 0 |
| 13 | 21 | 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 | 0 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 7 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[8,13,0,0,0,0,13,21,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,19,10,0,0,0,0,19,7,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[28,28,0,0,0,0,0,1,0,0,0,0,0,0,19,7,0,0,0,0,19,10,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C42.98D14 in GAP, Magma, Sage, TeX
C_4^2._{98}D_{14} % in TeX
G:=Group("C4^2.98D14"); // GroupNames label
G:=SmallGroup(448,986);
// by ID
G=gap.SmallGroup(448,986);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,100,1571,136,18822]);
// 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^-1,d*c*d^-1=c^13>;
// generators/relations