metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊23D4, C42.110D14, C14.602- 1+4, (C4×D4)⋊14D7, (D4×C28)⋊16C2, C28⋊7D4⋊8C2, C7⋊1(Q8⋊5D4), C4.141(D4×D7), C4⋊C4.283D14, D14⋊Q8⋊7C2, C28.347(C2×D4), (C4×Dic14)⋊31C2, (C2×D4).215D14, C4.D28⋊17C2, C22⋊1(C4○D28), (C2×C14).96C24, Dic7.17(C2×D4), C14.51(C22×D4), Dic7⋊D4⋊26C2, Dic7⋊4D4⋊47C2, C28.48D4⋊21C2, (C4×C28).153C22, (C2×C28).784C23, D14⋊C4.66C22, C22⋊C4.111D14, Dic7.D4⋊6C2, (C22×Dic14)⋊9C2, (C22×C4).209D14, C23.96(C22×D7), (C2×D28).211C22, (D4×C14).306C22, C4⋊Dic7.298C22, (C22×D7).31C23, C22.121(C23×D7), C23.D7.13C22, Dic7⋊C4.154C22, (C22×C14).166C23, (C22×C28).108C22, (C4×Dic7).204C22, (C2×Dic7).204C23, C2.17(D4.10D14), (C2×Dic14).240C22, (C22×Dic7).96C22, C2.24(C2×D4×D7), (C2×C4○D28)⋊9C2, (C2×C14)⋊3(C4○D4), C2.47(C2×C4○D28), C14.43(C2×C4○D4), (C2×C4×D7).199C22, (C7×C4⋊C4).327C22, (C2×C4).159(C22×D7), (C2×C7⋊D4).114C22, (C7×C22⋊C4).123C22, SmallGroup(448,1005)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊23D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, ad=da, cbc-1=a14b, bd=db, dcd=c-1 >
Subgroups: 1332 in 290 conjugacy classes, 107 normal (51 characteristic)
C1, C2, C2, C4, C4, C22, 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, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C4×D4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, Dic14, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, Q8⋊5D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C4.D28, Dic7⋊4D4, Dic7.D4, D14⋊Q8, C28.48D4, C28⋊7D4, Dic7⋊D4, D4×C28, C22×Dic14, C2×C4○D28, Dic14⋊23D4
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, C4○D28, D4×D7, C23×D7, C2×C4○D28, C2×D4×D7, D4.10D14, Dic14⋊23D4
►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 98 15 112)(2 97 16 111)(3 96 17 110)(4 95 18 109)(5 94 19 108)(6 93 20 107)(7 92 21 106)(8 91 22 105)(9 90 23 104)(10 89 24 103)(11 88 25 102)(12 87 26 101)(13 86 27 100)(14 85 28 99)(29 74 43 60)(30 73 44 59)(31 72 45 58)(32 71 46 57)(33 70 47 84)(34 69 48 83)(35 68 49 82)(36 67 50 81)(37 66 51 80)(38 65 52 79)(39 64 53 78)(40 63 54 77)(41 62 55 76)(42 61 56 75)(113 168 127 154)(114 167 128 153)(115 166 129 152)(116 165 130 151)(117 164 131 150)(118 163 132 149)(119 162 133 148)(120 161 134 147)(121 160 135 146)(122 159 136 145)(123 158 137 144)(124 157 138 143)(125 156 139 142)(126 155 140 141)(169 220 183 206)(170 219 184 205)(171 218 185 204)(172 217 186 203)(173 216 187 202)(174 215 188 201)(175 214 189 200)(176 213 190 199)(177 212 191 198)(178 211 192 197)(179 210 193 224)(180 209 194 223)(181 208 195 222)(182 207 196 221)
(1 218 74 157)(2 219 75 158)(3 220 76 159)(4 221 77 160)(5 222 78 161)(6 223 79 162)(7 224 80 163)(8 197 81 164)(9 198 82 165)(10 199 83 166)(11 200 84 167)(12 201 57 168)(13 202 58 141)(14 203 59 142)(15 204 60 143)(16 205 61 144)(17 206 62 145)(18 207 63 146)(19 208 64 147)(20 209 65 148)(21 210 66 149)(22 211 67 150)(23 212 68 151)(24 213 69 152)(25 214 70 153)(26 215 71 154)(27 216 72 155)(28 217 73 156)(29 138 112 185)(30 139 85 186)(31 140 86 187)(32 113 87 188)(33 114 88 189)(34 115 89 190)(35 116 90 191)(36 117 91 192)(37 118 92 193)(38 119 93 194)(39 120 94 195)(40 121 95 196)(41 122 96 169)(42 123 97 170)(43 124 98 171)(44 125 99 172)(45 126 100 173)(46 127 101 174)(47 128 102 175)(48 129 103 176)(49 130 104 177)(50 131 105 178)(51 132 106 179)(52 133 107 180)(53 134 108 181)(54 135 109 182)(55 136 110 183)(56 137 111 184)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 174)(114 175)(115 176)(116 177)(117 178)(118 179)(119 180)(120 181)(121 182)(122 183)(123 184)(124 185)(125 186)(126 187)(127 188)(128 189)(129 190)(130 191)(131 192)(132 193)(133 194)(134 195)(135 196)(136 169)(137 170)(138 171)(139 172)(140 173)(141 216)(142 217)(143 218)(144 219)(145 220)(146 221)(147 222)(148 223)(149 224)(150 197)(151 198)(152 199)(153 200)(154 201)(155 202)(156 203)(157 204)(158 205)(159 206)(160 207)(161 208)(162 209)(163 210)(164 211)(165 212)(166 213)(167 214)(168 215)
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), (1,98,15,112)(2,97,16,111)(3,96,17,110)(4,95,18,109)(5,94,19,108)(6,93,20,107)(7,92,21,106)(8,91,22,105)(9,90,23,104)(10,89,24,103)(11,88,25,102)(12,87,26,101)(13,86,27,100)(14,85,28,99)(29,74,43,60)(30,73,44,59)(31,72,45,58)(32,71,46,57)(33,70,47,84)(34,69,48,83)(35,68,49,82)(36,67,50,81)(37,66,51,80)(38,65,52,79)(39,64,53,78)(40,63,54,77)(41,62,55,76)(42,61,56,75)(113,168,127,154)(114,167,128,153)(115,166,129,152)(116,165,130,151)(117,164,131,150)(118,163,132,149)(119,162,133,148)(120,161,134,147)(121,160,135,146)(122,159,136,145)(123,158,137,144)(124,157,138,143)(125,156,139,142)(126,155,140,141)(169,220,183,206)(170,219,184,205)(171,218,185,204)(172,217,186,203)(173,216,187,202)(174,215,188,201)(175,214,189,200)(176,213,190,199)(177,212,191,198)(178,211,192,197)(179,210,193,224)(180,209,194,223)(181,208,195,222)(182,207,196,221), (1,218,74,157)(2,219,75,158)(3,220,76,159)(4,221,77,160)(5,222,78,161)(6,223,79,162)(7,224,80,163)(8,197,81,164)(9,198,82,165)(10,199,83,166)(11,200,84,167)(12,201,57,168)(13,202,58,141)(14,203,59,142)(15,204,60,143)(16,205,61,144)(17,206,62,145)(18,207,63,146)(19,208,64,147)(20,209,65,148)(21,210,66,149)(22,211,67,150)(23,212,68,151)(24,213,69,152)(25,214,70,153)(26,215,71,154)(27,216,72,155)(28,217,73,156)(29,138,112,185)(30,139,85,186)(31,140,86,187)(32,113,87,188)(33,114,88,189)(34,115,89,190)(35,116,90,191)(36,117,91,192)(37,118,92,193)(38,119,93,194)(39,120,94,195)(40,121,95,196)(41,122,96,169)(42,123,97,170)(43,124,98,171)(44,125,99,172)(45,126,100,173)(46,127,101,174)(47,128,102,175)(48,129,103,176)(49,130,104,177)(50,131,105,178)(51,132,106,179)(52,133,107,180)(53,134,108,181)(54,135,109,182)(55,136,110,183)(56,137,111,184), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,174)(114,175)(115,176)(116,177)(117,178)(118,179)(119,180)(120,181)(121,182)(122,183)(123,184)(124,185)(125,186)(126,187)(127,188)(128,189)(129,190)(130,191)(131,192)(132,193)(133,194)(134,195)(135,196)(136,169)(137,170)(138,171)(139,172)(140,173)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,197)(151,198)(152,199)(153,200)(154,201)(155,202)(156,203)(157,204)(158,205)(159,206)(160,207)(161,208)(162,209)(163,210)(164,211)(165,212)(166,213)(167,214)(168,215)>;
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), (1,98,15,112)(2,97,16,111)(3,96,17,110)(4,95,18,109)(5,94,19,108)(6,93,20,107)(7,92,21,106)(8,91,22,105)(9,90,23,104)(10,89,24,103)(11,88,25,102)(12,87,26,101)(13,86,27,100)(14,85,28,99)(29,74,43,60)(30,73,44,59)(31,72,45,58)(32,71,46,57)(33,70,47,84)(34,69,48,83)(35,68,49,82)(36,67,50,81)(37,66,51,80)(38,65,52,79)(39,64,53,78)(40,63,54,77)(41,62,55,76)(42,61,56,75)(113,168,127,154)(114,167,128,153)(115,166,129,152)(116,165,130,151)(117,164,131,150)(118,163,132,149)(119,162,133,148)(120,161,134,147)(121,160,135,146)(122,159,136,145)(123,158,137,144)(124,157,138,143)(125,156,139,142)(126,155,140,141)(169,220,183,206)(170,219,184,205)(171,218,185,204)(172,217,186,203)(173,216,187,202)(174,215,188,201)(175,214,189,200)(176,213,190,199)(177,212,191,198)(178,211,192,197)(179,210,193,224)(180,209,194,223)(181,208,195,222)(182,207,196,221), (1,218,74,157)(2,219,75,158)(3,220,76,159)(4,221,77,160)(5,222,78,161)(6,223,79,162)(7,224,80,163)(8,197,81,164)(9,198,82,165)(10,199,83,166)(11,200,84,167)(12,201,57,168)(13,202,58,141)(14,203,59,142)(15,204,60,143)(16,205,61,144)(17,206,62,145)(18,207,63,146)(19,208,64,147)(20,209,65,148)(21,210,66,149)(22,211,67,150)(23,212,68,151)(24,213,69,152)(25,214,70,153)(26,215,71,154)(27,216,72,155)(28,217,73,156)(29,138,112,185)(30,139,85,186)(31,140,86,187)(32,113,87,188)(33,114,88,189)(34,115,89,190)(35,116,90,191)(36,117,91,192)(37,118,92,193)(38,119,93,194)(39,120,94,195)(40,121,95,196)(41,122,96,169)(42,123,97,170)(43,124,98,171)(44,125,99,172)(45,126,100,173)(46,127,101,174)(47,128,102,175)(48,129,103,176)(49,130,104,177)(50,131,105,178)(51,132,106,179)(52,133,107,180)(53,134,108,181)(54,135,109,182)(55,136,110,183)(56,137,111,184), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,174)(114,175)(115,176)(116,177)(117,178)(118,179)(119,180)(120,181)(121,182)(122,183)(123,184)(124,185)(125,186)(126,187)(127,188)(128,189)(129,190)(130,191)(131,192)(132,193)(133,194)(134,195)(135,196)(136,169)(137,170)(138,171)(139,172)(140,173)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,197)(151,198)(152,199)(153,200)(154,201)(155,202)(156,203)(157,204)(158,205)(159,206)(160,207)(161,208)(162,209)(163,210)(164,211)(165,212)(166,213)(167,214)(168,215) );
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)], [(1,98,15,112),(2,97,16,111),(3,96,17,110),(4,95,18,109),(5,94,19,108),(6,93,20,107),(7,92,21,106),(8,91,22,105),(9,90,23,104),(10,89,24,103),(11,88,25,102),(12,87,26,101),(13,86,27,100),(14,85,28,99),(29,74,43,60),(30,73,44,59),(31,72,45,58),(32,71,46,57),(33,70,47,84),(34,69,48,83),(35,68,49,82),(36,67,50,81),(37,66,51,80),(38,65,52,79),(39,64,53,78),(40,63,54,77),(41,62,55,76),(42,61,56,75),(113,168,127,154),(114,167,128,153),(115,166,129,152),(116,165,130,151),(117,164,131,150),(118,163,132,149),(119,162,133,148),(120,161,134,147),(121,160,135,146),(122,159,136,145),(123,158,137,144),(124,157,138,143),(125,156,139,142),(126,155,140,141),(169,220,183,206),(170,219,184,205),(171,218,185,204),(172,217,186,203),(173,216,187,202),(174,215,188,201),(175,214,189,200),(176,213,190,199),(177,212,191,198),(178,211,192,197),(179,210,193,224),(180,209,194,223),(181,208,195,222),(182,207,196,221)], [(1,218,74,157),(2,219,75,158),(3,220,76,159),(4,221,77,160),(5,222,78,161),(6,223,79,162),(7,224,80,163),(8,197,81,164),(9,198,82,165),(10,199,83,166),(11,200,84,167),(12,201,57,168),(13,202,58,141),(14,203,59,142),(15,204,60,143),(16,205,61,144),(17,206,62,145),(18,207,63,146),(19,208,64,147),(20,209,65,148),(21,210,66,149),(22,211,67,150),(23,212,68,151),(24,213,69,152),(25,214,70,153),(26,215,71,154),(27,216,72,155),(28,217,73,156),(29,138,112,185),(30,139,85,186),(31,140,86,187),(32,113,87,188),(33,114,88,189),(34,115,89,190),(35,116,90,191),(36,117,91,192),(37,118,92,193),(38,119,93,194),(39,120,94,195),(40,121,95,196),(41,122,96,169),(42,123,97,170),(43,124,98,171),(44,125,99,172),(45,126,100,173),(46,127,101,174),(47,128,102,175),(48,129,103,176),(49,130,104,177),(50,131,105,178),(51,132,106,179),(52,133,107,180),(53,134,108,181),(54,135,109,182),(55,136,110,183),(56,137,111,184)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,174),(114,175),(115,176),(116,177),(117,178),(118,179),(119,180),(120,181),(121,182),(122,183),(123,184),(124,185),(125,186),(126,187),(127,188),(128,189),(129,190),(130,191),(131,192),(132,193),(133,194),(134,195),(135,196),(136,169),(137,170),(138,171),(139,172),(140,173),(141,216),(142,217),(143,218),(144,219),(145,220),(146,221),(147,222),(148,223),(149,224),(150,197),(151,198),(152,199),(153,200),(154,201),(155,202),(156,203),(157,204),(158,205),(159,206),(160,207),(161,208),(162,209),(163,210),(164,211),(165,212),(166,213),(167,214),(168,215)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| 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 | 2 | 2 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 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 | 2 | 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 | D14 | C4○D28 | 2- 1+4 | D4×D7 | D4.10D14 |
| kernel | Dic14⋊23D4 | C4×Dic14 | C4.D28 | Dic7⋊4D4 | Dic7.D4 | D14⋊Q8 | C28.48D4 | C28⋊7D4 | Dic7⋊D4 | D4×C28 | C22×Dic14 | C2×C4○D28 | Dic14 | C4×D4 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of Dic14⋊23D4 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 9 | 16 |
| 0 | 0 | 28 | 8 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 4 | 17 |
| 0 | 0 | 28 | 25 |
| 0 | 1 | 0 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 0 | 20 | 2 |
| 0 | 0 | 18 | 9 |
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,9,28,0,0,16,8],[28,0,0,0,0,28,0,0,0,0,4,28,0,0,17,25],[0,28,0,0,1,0,0,0,0,0,20,18,0,0,2,9],[28,0,0,0,0,1,0,0,0,0,28,0,0,0,0,28] >;
Dic14⋊23D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{23}D_4 % in TeX
G:=Group("Dic14:23D4"); // GroupNames label
G:=SmallGroup(448,1005);
// by ID
G=gap.SmallGroup(448,1005);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,100,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^14*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations