metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊22D4, C14.192- 1+4, C7⋊4(Q8⋊5D4), C4.114(D4×D7), C22⋊Q8⋊10D7, C4⋊D28⋊26C2, C4⋊C4.191D14, C28.237(C2×D4), D14⋊14(C4○D4), D28⋊C4⋊27C2, D14⋊D4⋊26C2, D14⋊Q8⋊20C2, (C2×C28).56C23, (C2×Q8).128D14, C22⋊C4.17D14, Dic7.25(C2×D4), C14.79(C22×D4), Dic7⋊3Q8⋊26C2, C28.23D4⋊13C2, (C2×C14).177C24, (C22×C4).239D14, D14⋊C4.128C22, Dic7.D4⋊25C2, (C2×D28).265C22, Dic7⋊C4.29C22, (Q8×C14).109C22, C22.198(C23×D7), C23.120(C22×D7), (C22×C28).257C22, (C22×C14).205C23, (C4×Dic7).107C22, (C2×Dic7).236C23, (C22×D7).199C23, C23.D7.118C22, C2.20(Q8.10D14), (C2×Dic14).295C22, (C2×Q8×D7)⋊8C2, C2.52(C2×D4×D7), (C4×C7⋊D4)⋊24C2, C2.50(D7×C4○D4), (C2×C4○D28)⋊25C2, (C7×C22⋊Q8)⋊13C2, (C2×C4×D7).97C22, C14.162(C2×C4○D4), (C7×C4⋊C4).160C22, (C2×C4).592(C22×D7), (C2×C7⋊D4).125C22, (C7×C22⋊C4).32C22, SmallGroup(448,1086)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊22D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, cac-1=dad=a13, cbc-1=a14b, bd=db, dcd=c-1 >
Subgroups: 1404 in 290 conjugacy classes, 105 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, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, Dic14, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22×C14, Q8⋊5D4, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, D14⋊C4, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C4○D28, Q8×D7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, Q8×C14, D14⋊D4, Dic7.D4, Dic7⋊3Q8, D28⋊C4, C4⋊D28, D14⋊Q8, C4×C7⋊D4, C28.23D4, C7×C22⋊Q8, C2×C4○D28, C2×Q8×D7, Dic14⋊22D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, C22×D7, Q8⋊5D4, D4×D7, C23×D7, C2×D4×D7, Q8.10D14, D7×C4○D4, Dic14⋊22D4
►On 224 points
Generators in S224
(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)
(1 147 15 161)(2 146 16 160)(3 145 17 159)(4 144 18 158)(5 143 19 157)(6 142 20 156)(7 141 21 155)(8 168 22 154)(9 167 23 153)(10 166 24 152)(11 165 25 151)(12 164 26 150)(13 163 27 149)(14 162 28 148)(29 98 43 112)(30 97 44 111)(31 96 45 110)(32 95 46 109)(33 94 47 108)(34 93 48 107)(35 92 49 106)(36 91 50 105)(37 90 51 104)(38 89 52 103)(39 88 53 102)(40 87 54 101)(41 86 55 100)(42 85 56 99)(57 121 71 135)(58 120 72 134)(59 119 73 133)(60 118 74 132)(61 117 75 131)(62 116 76 130)(63 115 77 129)(64 114 78 128)(65 113 79 127)(66 140 80 126)(67 139 81 125)(68 138 82 124)(69 137 83 123)(70 136 84 122)(169 208 183 222)(170 207 184 221)(171 206 185 220)(172 205 186 219)(173 204 187 218)(174 203 188 217)(175 202 189 216)(176 201 190 215)(177 200 191 214)(178 199 192 213)(179 198 193 212)(180 197 194 211)(181 224 195 210)(182 223 196 209)
(1 36 134 206)(2 49 135 219)(3 34 136 204)(4 47 137 217)(5 32 138 202)(6 45 139 215)(7 30 140 200)(8 43 113 213)(9 56 114 198)(10 41 115 211)(11 54 116 224)(12 39 117 209)(13 52 118 222)(14 37 119 207)(15 50 120 220)(16 35 121 205)(17 48 122 218)(18 33 123 203)(19 46 124 216)(20 31 125 201)(21 44 126 214)(22 29 127 199)(23 42 128 212)(24 55 129 197)(25 40 130 210)(26 53 131 223)(27 38 132 208)(28 51 133 221)(57 186 146 92)(58 171 147 105)(59 184 148 90)(60 169 149 103)(61 182 150 88)(62 195 151 101)(63 180 152 86)(64 193 153 99)(65 178 154 112)(66 191 155 97)(67 176 156 110)(68 189 157 95)(69 174 158 108)(70 187 159 93)(71 172 160 106)(72 185 161 91)(73 170 162 104)(74 183 163 89)(75 196 164 102)(76 181 165 87)(77 194 166 100)(78 179 167 85)(79 192 168 98)(80 177 141 111)(81 190 142 96)(82 175 143 109)(83 188 144 94)(84 173 145 107)
(1 120)(2 133)(3 118)(4 131)(5 116)(6 129)(7 114)(8 127)(9 140)(10 125)(11 138)(12 123)(13 136)(14 121)(15 134)(16 119)(17 132)(18 117)(19 130)(20 115)(21 128)(22 113)(23 126)(24 139)(25 124)(26 137)(27 122)(28 135)(29 43)(30 56)(31 41)(32 54)(33 39)(34 52)(35 37)(36 50)(38 48)(40 46)(42 44)(45 55)(47 53)(49 51)(57 148)(58 161)(59 146)(60 159)(61 144)(62 157)(63 142)(64 155)(65 168)(66 153)(67 166)(68 151)(69 164)(70 149)(71 162)(72 147)(73 160)(74 145)(75 158)(76 143)(77 156)(78 141)(79 154)(80 167)(81 152)(82 165)(83 150)(84 163)(85 111)(86 96)(87 109)(88 94)(89 107)(90 92)(91 105)(93 103)(95 101)(97 99)(98 112)(100 110)(102 108)(104 106)(169 187)(170 172)(171 185)(173 183)(174 196)(175 181)(176 194)(177 179)(178 192)(180 190)(182 188)(184 186)(189 195)(191 193)(197 215)(198 200)(199 213)(201 211)(202 224)(203 209)(204 222)(205 207)(206 220)(208 218)(210 216)(212 214)(217 223)(219 221)
G:=sub<Sym(224)| (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), (1,147,15,161)(2,146,16,160)(3,145,17,159)(4,144,18,158)(5,143,19,157)(6,142,20,156)(7,141,21,155)(8,168,22,154)(9,167,23,153)(10,166,24,152)(11,165,25,151)(12,164,26,150)(13,163,27,149)(14,162,28,148)(29,98,43,112)(30,97,44,111)(31,96,45,110)(32,95,46,109)(33,94,47,108)(34,93,48,107)(35,92,49,106)(36,91,50,105)(37,90,51,104)(38,89,52,103)(39,88,53,102)(40,87,54,101)(41,86,55,100)(42,85,56,99)(57,121,71,135)(58,120,72,134)(59,119,73,133)(60,118,74,132)(61,117,75,131)(62,116,76,130)(63,115,77,129)(64,114,78,128)(65,113,79,127)(66,140,80,126)(67,139,81,125)(68,138,82,124)(69,137,83,123)(70,136,84,122)(169,208,183,222)(170,207,184,221)(171,206,185,220)(172,205,186,219)(173,204,187,218)(174,203,188,217)(175,202,189,216)(176,201,190,215)(177,200,191,214)(178,199,192,213)(179,198,193,212)(180,197,194,211)(181,224,195,210)(182,223,196,209), (1,36,134,206)(2,49,135,219)(3,34,136,204)(4,47,137,217)(5,32,138,202)(6,45,139,215)(7,30,140,200)(8,43,113,213)(9,56,114,198)(10,41,115,211)(11,54,116,224)(12,39,117,209)(13,52,118,222)(14,37,119,207)(15,50,120,220)(16,35,121,205)(17,48,122,218)(18,33,123,203)(19,46,124,216)(20,31,125,201)(21,44,126,214)(22,29,127,199)(23,42,128,212)(24,55,129,197)(25,40,130,210)(26,53,131,223)(27,38,132,208)(28,51,133,221)(57,186,146,92)(58,171,147,105)(59,184,148,90)(60,169,149,103)(61,182,150,88)(62,195,151,101)(63,180,152,86)(64,193,153,99)(65,178,154,112)(66,191,155,97)(67,176,156,110)(68,189,157,95)(69,174,158,108)(70,187,159,93)(71,172,160,106)(72,185,161,91)(73,170,162,104)(74,183,163,89)(75,196,164,102)(76,181,165,87)(77,194,166,100)(78,179,167,85)(79,192,168,98)(80,177,141,111)(81,190,142,96)(82,175,143,109)(83,188,144,94)(84,173,145,107), (1,120)(2,133)(3,118)(4,131)(5,116)(6,129)(7,114)(8,127)(9,140)(10,125)(11,138)(12,123)(13,136)(14,121)(15,134)(16,119)(17,132)(18,117)(19,130)(20,115)(21,128)(22,113)(23,126)(24,139)(25,124)(26,137)(27,122)(28,135)(29,43)(30,56)(31,41)(32,54)(33,39)(34,52)(35,37)(36,50)(38,48)(40,46)(42,44)(45,55)(47,53)(49,51)(57,148)(58,161)(59,146)(60,159)(61,144)(62,157)(63,142)(64,155)(65,168)(66,153)(67,166)(68,151)(69,164)(70,149)(71,162)(72,147)(73,160)(74,145)(75,158)(76,143)(77,156)(78,141)(79,154)(80,167)(81,152)(82,165)(83,150)(84,163)(85,111)(86,96)(87,109)(88,94)(89,107)(90,92)(91,105)(93,103)(95,101)(97,99)(98,112)(100,110)(102,108)(104,106)(169,187)(170,172)(171,185)(173,183)(174,196)(175,181)(176,194)(177,179)(178,192)(180,190)(182,188)(184,186)(189,195)(191,193)(197,215)(198,200)(199,213)(201,211)(202,224)(203,209)(204,222)(205,207)(206,220)(208,218)(210,216)(212,214)(217,223)(219,221)>;
G:=Group( (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), (1,147,15,161)(2,146,16,160)(3,145,17,159)(4,144,18,158)(5,143,19,157)(6,142,20,156)(7,141,21,155)(8,168,22,154)(9,167,23,153)(10,166,24,152)(11,165,25,151)(12,164,26,150)(13,163,27,149)(14,162,28,148)(29,98,43,112)(30,97,44,111)(31,96,45,110)(32,95,46,109)(33,94,47,108)(34,93,48,107)(35,92,49,106)(36,91,50,105)(37,90,51,104)(38,89,52,103)(39,88,53,102)(40,87,54,101)(41,86,55,100)(42,85,56,99)(57,121,71,135)(58,120,72,134)(59,119,73,133)(60,118,74,132)(61,117,75,131)(62,116,76,130)(63,115,77,129)(64,114,78,128)(65,113,79,127)(66,140,80,126)(67,139,81,125)(68,138,82,124)(69,137,83,123)(70,136,84,122)(169,208,183,222)(170,207,184,221)(171,206,185,220)(172,205,186,219)(173,204,187,218)(174,203,188,217)(175,202,189,216)(176,201,190,215)(177,200,191,214)(178,199,192,213)(179,198,193,212)(180,197,194,211)(181,224,195,210)(182,223,196,209), (1,36,134,206)(2,49,135,219)(3,34,136,204)(4,47,137,217)(5,32,138,202)(6,45,139,215)(7,30,140,200)(8,43,113,213)(9,56,114,198)(10,41,115,211)(11,54,116,224)(12,39,117,209)(13,52,118,222)(14,37,119,207)(15,50,120,220)(16,35,121,205)(17,48,122,218)(18,33,123,203)(19,46,124,216)(20,31,125,201)(21,44,126,214)(22,29,127,199)(23,42,128,212)(24,55,129,197)(25,40,130,210)(26,53,131,223)(27,38,132,208)(28,51,133,221)(57,186,146,92)(58,171,147,105)(59,184,148,90)(60,169,149,103)(61,182,150,88)(62,195,151,101)(63,180,152,86)(64,193,153,99)(65,178,154,112)(66,191,155,97)(67,176,156,110)(68,189,157,95)(69,174,158,108)(70,187,159,93)(71,172,160,106)(72,185,161,91)(73,170,162,104)(74,183,163,89)(75,196,164,102)(76,181,165,87)(77,194,166,100)(78,179,167,85)(79,192,168,98)(80,177,141,111)(81,190,142,96)(82,175,143,109)(83,188,144,94)(84,173,145,107), (1,120)(2,133)(3,118)(4,131)(5,116)(6,129)(7,114)(8,127)(9,140)(10,125)(11,138)(12,123)(13,136)(14,121)(15,134)(16,119)(17,132)(18,117)(19,130)(20,115)(21,128)(22,113)(23,126)(24,139)(25,124)(26,137)(27,122)(28,135)(29,43)(30,56)(31,41)(32,54)(33,39)(34,52)(35,37)(36,50)(38,48)(40,46)(42,44)(45,55)(47,53)(49,51)(57,148)(58,161)(59,146)(60,159)(61,144)(62,157)(63,142)(64,155)(65,168)(66,153)(67,166)(68,151)(69,164)(70,149)(71,162)(72,147)(73,160)(74,145)(75,158)(76,143)(77,156)(78,141)(79,154)(80,167)(81,152)(82,165)(83,150)(84,163)(85,111)(86,96)(87,109)(88,94)(89,107)(90,92)(91,105)(93,103)(95,101)(97,99)(98,112)(100,110)(102,108)(104,106)(169,187)(170,172)(171,185)(173,183)(174,196)(175,181)(176,194)(177,179)(178,192)(180,190)(182,188)(184,186)(189,195)(191,193)(197,215)(198,200)(199,213)(201,211)(202,224)(203,209)(204,222)(205,207)(206,220)(208,218)(210,216)(212,214)(217,223)(219,221) );
G=PermutationGroup([[(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)], [(1,147,15,161),(2,146,16,160),(3,145,17,159),(4,144,18,158),(5,143,19,157),(6,142,20,156),(7,141,21,155),(8,168,22,154),(9,167,23,153),(10,166,24,152),(11,165,25,151),(12,164,26,150),(13,163,27,149),(14,162,28,148),(29,98,43,112),(30,97,44,111),(31,96,45,110),(32,95,46,109),(33,94,47,108),(34,93,48,107),(35,92,49,106),(36,91,50,105),(37,90,51,104),(38,89,52,103),(39,88,53,102),(40,87,54,101),(41,86,55,100),(42,85,56,99),(57,121,71,135),(58,120,72,134),(59,119,73,133),(60,118,74,132),(61,117,75,131),(62,116,76,130),(63,115,77,129),(64,114,78,128),(65,113,79,127),(66,140,80,126),(67,139,81,125),(68,138,82,124),(69,137,83,123),(70,136,84,122),(169,208,183,222),(170,207,184,221),(171,206,185,220),(172,205,186,219),(173,204,187,218),(174,203,188,217),(175,202,189,216),(176,201,190,215),(177,200,191,214),(178,199,192,213),(179,198,193,212),(180,197,194,211),(181,224,195,210),(182,223,196,209)], [(1,36,134,206),(2,49,135,219),(3,34,136,204),(4,47,137,217),(5,32,138,202),(6,45,139,215),(7,30,140,200),(8,43,113,213),(9,56,114,198),(10,41,115,211),(11,54,116,224),(12,39,117,209),(13,52,118,222),(14,37,119,207),(15,50,120,220),(16,35,121,205),(17,48,122,218),(18,33,123,203),(19,46,124,216),(20,31,125,201),(21,44,126,214),(22,29,127,199),(23,42,128,212),(24,55,129,197),(25,40,130,210),(26,53,131,223),(27,38,132,208),(28,51,133,221),(57,186,146,92),(58,171,147,105),(59,184,148,90),(60,169,149,103),(61,182,150,88),(62,195,151,101),(63,180,152,86),(64,193,153,99),(65,178,154,112),(66,191,155,97),(67,176,156,110),(68,189,157,95),(69,174,158,108),(70,187,159,93),(71,172,160,106),(72,185,161,91),(73,170,162,104),(74,183,163,89),(75,196,164,102),(76,181,165,87),(77,194,166,100),(78,179,167,85),(79,192,168,98),(80,177,141,111),(81,190,142,96),(82,175,143,109),(83,188,144,94),(84,173,145,107)], [(1,120),(2,133),(3,118),(4,131),(5,116),(6,129),(7,114),(8,127),(9,140),(10,125),(11,138),(12,123),(13,136),(14,121),(15,134),(16,119),(17,132),(18,117),(19,130),(20,115),(21,128),(22,113),(23,126),(24,139),(25,124),(26,137),(27,122),(28,135),(29,43),(30,56),(31,41),(32,54),(33,39),(34,52),(35,37),(36,50),(38,48),(40,46),(42,44),(45,55),(47,53),(49,51),(57,148),(58,161),(59,146),(60,159),(61,144),(62,157),(63,142),(64,155),(65,168),(66,153),(67,166),(68,151),(69,164),(70,149),(71,162),(72,147),(73,160),(74,145),(75,158),(76,143),(77,156),(78,141),(79,154),(80,167),(81,152),(82,165),(83,150),(84,163),(85,111),(86,96),(87,109),(88,94),(89,107),(90,92),(91,105),(93,103),(95,101),(97,99),(98,112),(100,110),(102,108),(104,106),(169,187),(170,172),(171,185),(173,183),(174,196),(175,181),(176,194),(177,179),(178,192),(180,190),(182,188),(184,186),(189,195),(191,193),(197,215),(198,200),(199,213),(201,211),(202,224),(203,209),(204,222),(205,207),(206,220),(208,218),(210,216),(212,214),(217,223),(219,221)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 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 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 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 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | Q8.10D14 | D7×C4○D4 |
| kernel | Dic14⋊22D4 | D14⋊D4 | Dic7.D4 | Dic7⋊3Q8 | D28⋊C4 | C4⋊D28 | D14⋊Q8 | C4×C7⋊D4 | C28.23D4 | C7×C22⋊Q8 | C2×C4○D28 | C2×Q8×D7 | Dic14 | C22⋊Q8 | D14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 6 | 9 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of Dic14⋊22D4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 2 |
| 0 | 0 | 0 | 0 | 22 | 10 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 3 |
| 0 | 0 | 0 | 0 | 11 | 13 |
| 1 | 27 | 0 | 0 | 0 | 0 |
| 1 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 5 |
| 0 | 0 | 0 | 0 | 26 | 25 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 18 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,28,11,0,0,0,0,0,0,19,22,0,0,0,0,2,10],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,11,0,0,0,0,0,1,0,0,0,0,0,0,16,11,0,0,0,0,3,13],[1,1,0,0,0,0,27,28,0,0,0,0,0,0,28,11,0,0,0,0,0,1,0,0,0,0,0,0,4,26,0,0,0,0,5,25],[28,28,0,0,0,0,0,1,0,0,0,0,0,0,1,18,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;
Dic14⋊22D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{22}D_4 % in TeX
G:=Group("Dic14:22D4"); // GroupNames label
G:=SmallGroup(448,1086);
// by ID
G=gap.SmallGroup(448,1086);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,1571,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,c*a*c^-1=d*a*d=a^13,c*b*c^-1=a^14*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations