metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊22D4, C14.192- (1+4), C7⋊4(Q8⋊5D4), C4.114(D4×D7), C22⋊Q8⋊10D7, C28⋊1D4⋊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
Subgroups: 1404 in 290 conjugacy classes, 105 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×12], C22, C22 [×13], C7, C2×C4 [×2], C2×C4 [×4], C2×C4 [×17], D4 [×12], Q8 [×10], C23, C23 [×3], D7 [×4], C14 [×3], C14, C42 [×3], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×3], C22×C4, C22×C4 [×5], C2×D4 [×6], C2×Q8, C2×Q8 [×7], C4○D4 [×4], Dic7 [×4], Dic7 [×3], C28 [×2], C28 [×5], D14 [×2], D14 [×8], C2×C14, C2×C14 [×3], C4×D4 [×3], C4×Q8, C4⋊D4 [×3], C22⋊Q8, C22⋊Q8 [×2], C4.4D4 [×3], C22×Q8, C2×C4○D4, Dic14 [×4], Dic14 [×4], C4×D7 [×10], D28 [×6], C2×Dic7 [×3], C2×Dic7 [×2], C7⋊D4 [×6], C2×C28 [×2], C2×C28 [×4], C2×C28 [×2], C7×Q8 [×2], C22×D7, C22×D7 [×2], C22×C14, Q8⋊5D4, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4, Dic7⋊C4 [×2], D14⋊C4, D14⋊C4 [×6], C23.D7, C7×C22⋊C4 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14, C2×Dic14 [×2], C2×C4×D7, C2×C4×D7 [×4], C2×D28, C2×D28 [×2], C4○D28 [×4], Q8×D7 [×4], C2×C7⋊D4, C2×C7⋊D4 [×2], C22×C28, Q8×C14, D14⋊D4 [×2], Dic7.D4 [×2], Dic7⋊3Q8, D28⋊C4 [×2], C28⋊1D4, D14⋊Q8 [×2], C4×C7⋊D4, C28.23D4, C7×C22⋊Q8, C2×C4○D28, C2×Q8×D7, Dic14⋊22D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×2], C24, D14 [×7], C22×D4, C2×C4○D4, 2- (1+4), C22×D7 [×7], Q8⋊5D4, D4×D7 [×2], C23×D7, C2×D4×D7, Q8.10D14, D7×C4○D4, Dic14⋊22D4
Generators and relations
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 >
►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)
(1 157 15 143)(2 156 16 142)(3 155 17 141)(4 154 18 168)(5 153 19 167)(6 152 20 166)(7 151 21 165)(8 150 22 164)(9 149 23 163)(10 148 24 162)(11 147 25 161)(12 146 26 160)(13 145 27 159)(14 144 28 158)(29 58 43 72)(30 57 44 71)(31 84 45 70)(32 83 46 69)(33 82 47 68)(34 81 48 67)(35 80 49 66)(36 79 50 65)(37 78 51 64)(38 77 52 63)(39 76 53 62)(40 75 54 61)(41 74 55 60)(42 73 56 59)(85 223 99 209)(86 222 100 208)(87 221 101 207)(88 220 102 206)(89 219 103 205)(90 218 104 204)(91 217 105 203)(92 216 106 202)(93 215 107 201)(94 214 108 200)(95 213 109 199)(96 212 110 198)(97 211 111 197)(98 210 112 224)(113 177 127 191)(114 176 128 190)(115 175 129 189)(116 174 130 188)(117 173 131 187)(118 172 132 186)(119 171 133 185)(120 170 134 184)(121 169 135 183)(122 196 136 182)(123 195 137 181)(124 194 138 180)(125 193 139 179)(126 192 140 178)
(1 195 34 220)(2 180 35 205)(3 193 36 218)(4 178 37 203)(5 191 38 216)(6 176 39 201)(7 189 40 214)(8 174 41 199)(9 187 42 212)(10 172 43 197)(11 185 44 210)(12 170 45 223)(13 183 46 208)(14 196 47 221)(15 181 48 206)(16 194 49 219)(17 179 50 204)(18 192 51 217)(19 177 52 202)(20 190 53 215)(21 175 54 200)(22 188 55 213)(23 173 56 198)(24 186 29 211)(25 171 30 224)(26 184 31 209)(27 169 32 222)(28 182 33 207)(57 112 161 119)(58 97 162 132)(59 110 163 117)(60 95 164 130)(61 108 165 115)(62 93 166 128)(63 106 167 113)(64 91 168 126)(65 104 141 139)(66 89 142 124)(67 102 143 137)(68 87 144 122)(69 100 145 135)(70 85 146 120)(71 98 147 133)(72 111 148 118)(73 96 149 131)(74 109 150 116)(75 94 151 129)(76 107 152 114)(77 92 153 127)(78 105 154 140)(79 90 155 125)(80 103 156 138)(81 88 157 123)(82 101 158 136)(83 86 159 121)(84 99 160 134)
(1 48)(2 33)(3 46)(4 31)(5 44)(6 29)(7 42)(8 55)(9 40)(10 53)(11 38)(12 51)(13 36)(14 49)(15 34)(16 47)(17 32)(18 45)(19 30)(20 43)(21 56)(22 41)(23 54)(24 39)(25 52)(26 37)(27 50)(28 35)(57 167)(58 152)(59 165)(60 150)(61 163)(62 148)(63 161)(64 146)(65 159)(66 144)(67 157)(68 142)(69 155)(70 168)(71 153)(72 166)(73 151)(74 164)(75 149)(76 162)(77 147)(78 160)(79 145)(80 158)(81 143)(82 156)(83 141)(84 154)(85 91)(86 104)(87 89)(88 102)(90 100)(92 98)(93 111)(94 96)(95 109)(97 107)(99 105)(101 103)(106 112)(108 110)(113 119)(114 132)(115 117)(116 130)(118 128)(120 126)(121 139)(122 124)(123 137)(125 135)(127 133)(129 131)(134 140)(136 138)(169 179)(170 192)(171 177)(172 190)(173 175)(174 188)(176 186)(178 184)(180 182)(181 195)(183 193)(185 191)(187 189)(194 196)(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), (1,157,15,143)(2,156,16,142)(3,155,17,141)(4,154,18,168)(5,153,19,167)(6,152,20,166)(7,151,21,165)(8,150,22,164)(9,149,23,163)(10,148,24,162)(11,147,25,161)(12,146,26,160)(13,145,27,159)(14,144,28,158)(29,58,43,72)(30,57,44,71)(31,84,45,70)(32,83,46,69)(33,82,47,68)(34,81,48,67)(35,80,49,66)(36,79,50,65)(37,78,51,64)(38,77,52,63)(39,76,53,62)(40,75,54,61)(41,74,55,60)(42,73,56,59)(85,223,99,209)(86,222,100,208)(87,221,101,207)(88,220,102,206)(89,219,103,205)(90,218,104,204)(91,217,105,203)(92,216,106,202)(93,215,107,201)(94,214,108,200)(95,213,109,199)(96,212,110,198)(97,211,111,197)(98,210,112,224)(113,177,127,191)(114,176,128,190)(115,175,129,189)(116,174,130,188)(117,173,131,187)(118,172,132,186)(119,171,133,185)(120,170,134,184)(121,169,135,183)(122,196,136,182)(123,195,137,181)(124,194,138,180)(125,193,139,179)(126,192,140,178), (1,195,34,220)(2,180,35,205)(3,193,36,218)(4,178,37,203)(5,191,38,216)(6,176,39,201)(7,189,40,214)(8,174,41,199)(9,187,42,212)(10,172,43,197)(11,185,44,210)(12,170,45,223)(13,183,46,208)(14,196,47,221)(15,181,48,206)(16,194,49,219)(17,179,50,204)(18,192,51,217)(19,177,52,202)(20,190,53,215)(21,175,54,200)(22,188,55,213)(23,173,56,198)(24,186,29,211)(25,171,30,224)(26,184,31,209)(27,169,32,222)(28,182,33,207)(57,112,161,119)(58,97,162,132)(59,110,163,117)(60,95,164,130)(61,108,165,115)(62,93,166,128)(63,106,167,113)(64,91,168,126)(65,104,141,139)(66,89,142,124)(67,102,143,137)(68,87,144,122)(69,100,145,135)(70,85,146,120)(71,98,147,133)(72,111,148,118)(73,96,149,131)(74,109,150,116)(75,94,151,129)(76,107,152,114)(77,92,153,127)(78,105,154,140)(79,90,155,125)(80,103,156,138)(81,88,157,123)(82,101,158,136)(83,86,159,121)(84,99,160,134), (1,48)(2,33)(3,46)(4,31)(5,44)(6,29)(7,42)(8,55)(9,40)(10,53)(11,38)(12,51)(13,36)(14,49)(15,34)(16,47)(17,32)(18,45)(19,30)(20,43)(21,56)(22,41)(23,54)(24,39)(25,52)(26,37)(27,50)(28,35)(57,167)(58,152)(59,165)(60,150)(61,163)(62,148)(63,161)(64,146)(65,159)(66,144)(67,157)(68,142)(69,155)(70,168)(71,153)(72,166)(73,151)(74,164)(75,149)(76,162)(77,147)(78,160)(79,145)(80,158)(81,143)(82,156)(83,141)(84,154)(85,91)(86,104)(87,89)(88,102)(90,100)(92,98)(93,111)(94,96)(95,109)(97,107)(99,105)(101,103)(106,112)(108,110)(113,119)(114,132)(115,117)(116,130)(118,128)(120,126)(121,139)(122,124)(123,137)(125,135)(127,133)(129,131)(134,140)(136,138)(169,179)(170,192)(171,177)(172,190)(173,175)(174,188)(176,186)(178,184)(180,182)(181,195)(183,193)(185,191)(187,189)(194,196)(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), (1,157,15,143)(2,156,16,142)(3,155,17,141)(4,154,18,168)(5,153,19,167)(6,152,20,166)(7,151,21,165)(8,150,22,164)(9,149,23,163)(10,148,24,162)(11,147,25,161)(12,146,26,160)(13,145,27,159)(14,144,28,158)(29,58,43,72)(30,57,44,71)(31,84,45,70)(32,83,46,69)(33,82,47,68)(34,81,48,67)(35,80,49,66)(36,79,50,65)(37,78,51,64)(38,77,52,63)(39,76,53,62)(40,75,54,61)(41,74,55,60)(42,73,56,59)(85,223,99,209)(86,222,100,208)(87,221,101,207)(88,220,102,206)(89,219,103,205)(90,218,104,204)(91,217,105,203)(92,216,106,202)(93,215,107,201)(94,214,108,200)(95,213,109,199)(96,212,110,198)(97,211,111,197)(98,210,112,224)(113,177,127,191)(114,176,128,190)(115,175,129,189)(116,174,130,188)(117,173,131,187)(118,172,132,186)(119,171,133,185)(120,170,134,184)(121,169,135,183)(122,196,136,182)(123,195,137,181)(124,194,138,180)(125,193,139,179)(126,192,140,178), (1,195,34,220)(2,180,35,205)(3,193,36,218)(4,178,37,203)(5,191,38,216)(6,176,39,201)(7,189,40,214)(8,174,41,199)(9,187,42,212)(10,172,43,197)(11,185,44,210)(12,170,45,223)(13,183,46,208)(14,196,47,221)(15,181,48,206)(16,194,49,219)(17,179,50,204)(18,192,51,217)(19,177,52,202)(20,190,53,215)(21,175,54,200)(22,188,55,213)(23,173,56,198)(24,186,29,211)(25,171,30,224)(26,184,31,209)(27,169,32,222)(28,182,33,207)(57,112,161,119)(58,97,162,132)(59,110,163,117)(60,95,164,130)(61,108,165,115)(62,93,166,128)(63,106,167,113)(64,91,168,126)(65,104,141,139)(66,89,142,124)(67,102,143,137)(68,87,144,122)(69,100,145,135)(70,85,146,120)(71,98,147,133)(72,111,148,118)(73,96,149,131)(74,109,150,116)(75,94,151,129)(76,107,152,114)(77,92,153,127)(78,105,154,140)(79,90,155,125)(80,103,156,138)(81,88,157,123)(82,101,158,136)(83,86,159,121)(84,99,160,134), (1,48)(2,33)(3,46)(4,31)(5,44)(6,29)(7,42)(8,55)(9,40)(10,53)(11,38)(12,51)(13,36)(14,49)(15,34)(16,47)(17,32)(18,45)(19,30)(20,43)(21,56)(22,41)(23,54)(24,39)(25,52)(26,37)(27,50)(28,35)(57,167)(58,152)(59,165)(60,150)(61,163)(62,148)(63,161)(64,146)(65,159)(66,144)(67,157)(68,142)(69,155)(70,168)(71,153)(72,166)(73,151)(74,164)(75,149)(76,162)(77,147)(78,160)(79,145)(80,158)(81,143)(82,156)(83,141)(84,154)(85,91)(86,104)(87,89)(88,102)(90,100)(92,98)(93,111)(94,96)(95,109)(97,107)(99,105)(101,103)(106,112)(108,110)(113,119)(114,132)(115,117)(116,130)(118,128)(120,126)(121,139)(122,124)(123,137)(125,135)(127,133)(129,131)(134,140)(136,138)(169,179)(170,192)(171,177)(172,190)(173,175)(174,188)(176,186)(178,184)(180,182)(181,195)(183,193)(185,191)(187,189)(194,196)(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)], [(1,157,15,143),(2,156,16,142),(3,155,17,141),(4,154,18,168),(5,153,19,167),(6,152,20,166),(7,151,21,165),(8,150,22,164),(9,149,23,163),(10,148,24,162),(11,147,25,161),(12,146,26,160),(13,145,27,159),(14,144,28,158),(29,58,43,72),(30,57,44,71),(31,84,45,70),(32,83,46,69),(33,82,47,68),(34,81,48,67),(35,80,49,66),(36,79,50,65),(37,78,51,64),(38,77,52,63),(39,76,53,62),(40,75,54,61),(41,74,55,60),(42,73,56,59),(85,223,99,209),(86,222,100,208),(87,221,101,207),(88,220,102,206),(89,219,103,205),(90,218,104,204),(91,217,105,203),(92,216,106,202),(93,215,107,201),(94,214,108,200),(95,213,109,199),(96,212,110,198),(97,211,111,197),(98,210,112,224),(113,177,127,191),(114,176,128,190),(115,175,129,189),(116,174,130,188),(117,173,131,187),(118,172,132,186),(119,171,133,185),(120,170,134,184),(121,169,135,183),(122,196,136,182),(123,195,137,181),(124,194,138,180),(125,193,139,179),(126,192,140,178)], [(1,195,34,220),(2,180,35,205),(3,193,36,218),(4,178,37,203),(5,191,38,216),(6,176,39,201),(7,189,40,214),(8,174,41,199),(9,187,42,212),(10,172,43,197),(11,185,44,210),(12,170,45,223),(13,183,46,208),(14,196,47,221),(15,181,48,206),(16,194,49,219),(17,179,50,204),(18,192,51,217),(19,177,52,202),(20,190,53,215),(21,175,54,200),(22,188,55,213),(23,173,56,198),(24,186,29,211),(25,171,30,224),(26,184,31,209),(27,169,32,222),(28,182,33,207),(57,112,161,119),(58,97,162,132),(59,110,163,117),(60,95,164,130),(61,108,165,115),(62,93,166,128),(63,106,167,113),(64,91,168,126),(65,104,141,139),(66,89,142,124),(67,102,143,137),(68,87,144,122),(69,100,145,135),(70,85,146,120),(71,98,147,133),(72,111,148,118),(73,96,149,131),(74,109,150,116),(75,94,151,129),(76,107,152,114),(77,92,153,127),(78,105,154,140),(79,90,155,125),(80,103,156,138),(81,88,157,123),(82,101,158,136),(83,86,159,121),(84,99,160,134)], [(1,48),(2,33),(3,46),(4,31),(5,44),(6,29),(7,42),(8,55),(9,40),(10,53),(11,38),(12,51),(13,36),(14,49),(15,34),(16,47),(17,32),(18,45),(19,30),(20,43),(21,56),(22,41),(23,54),(24,39),(25,52),(26,37),(27,50),(28,35),(57,167),(58,152),(59,165),(60,150),(61,163),(62,148),(63,161),(64,146),(65,159),(66,144),(67,157),(68,142),(69,155),(70,168),(71,153),(72,166),(73,151),(74,164),(75,149),(76,162),(77,147),(78,160),(79,145),(80,158),(81,143),(82,156),(83,141),(84,154),(85,91),(86,104),(87,89),(88,102),(90,100),(92,98),(93,111),(94,96),(95,109),(97,107),(99,105),(101,103),(106,112),(108,110),(113,119),(114,132),(115,117),(116,130),(118,128),(120,126),(121,139),(122,124),(123,137),(125,135),(127,133),(129,131),(134,140),(136,138),(169,179),(170,192),(171,177),(172,190),(173,175),(174,188),(176,186),(178,184),(180,182),(181,195),(183,193),(185,191),(187,189),(194,196),(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)])
Matrix representation ►G ⊆ 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] >;
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 | C28⋊1D4 | 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 |
In GAP, Magma, Sage, TeX
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
×
⋊
ℤ
𝔽
○
≀