metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊20D4, C14.332+ (1+4), C4⋊D4⋊7D7, C7⋊3(Q8⋊6D4), C4.109(D4×D7), C28⋊D4⋊15C2, C28⋊1D4⋊19C2, C4⋊C4.177D14, (C2×D4).90D14, C28.225(C2×D4), D14⋊D4⋊17C2, Dic7⋊8(C4○D4), Dic7⋊4D4⋊6C2, (C2×C28).35C23, C22⋊C4.46D14, Dic7.21(C2×D4), C14.62(C22×D4), Dic7⋊3Q8⋊20C2, Dic7⋊D4⋊10C2, (C2×C14).143C24, D14⋊C4.12C22, (C22×C4).219D14, C2.35(D4⋊6D14), C23.10(C22×D7), (D4×C14).117C22, (C2×D28).142C22, Dic7⋊C4.14C22, (C22×C14).14C23, (C4×Dic7).90C22, (C22×D7).62C23, C22.164(C23×D7), (C22×C28).237C22, (C2×Dic7).225C23, C23.D7.110C22, (C2×Dic14).293C22, (C22×Dic7).104C22, C2.35(C2×D4×D7), (C7×C4⋊D4)⋊8C2, (C4×C7⋊D4)⋊15C2, C2.34(D7×C4○D4), (C2×C4○D28)⋊19C2, (C2×D4⋊2D7)⋊11C2, (C2×C4×D7).82C22, C14.148(C2×C4○D4), (C7×C4⋊C4).139C22, (C2×C4).585(C22×D7), (C2×C7⋊D4).25C22, (C7×C22⋊C4).8C22, SmallGroup(448,1052)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1580 in 312 conjugacy classes, 105 normal (43 characteristic)
C1, C2 [×3], C2 [×6], C4 [×2], C4 [×11], C22, C22 [×18], C7, C2×C4 [×2], C2×C4 [×2], C2×C4 [×17], D4 [×24], Q8 [×4], C23, C23 [×2], C23 [×3], D7 [×3], C14 [×3], C14 [×3], C42 [×3], C22⋊C4 [×2], C22⋊C4 [×4], C4⋊C4, C4⋊C4 [×3], C22×C4, C22×C4 [×5], C2×D4, C2×D4 [×2], C2×D4 [×12], C2×Q8, C4○D4 [×8], Dic7 [×6], Dic7 [×2], C28 [×2], C28 [×3], D14 [×9], C2×C14, C2×C14 [×9], C4×D4 [×3], C4×Q8, C4⋊D4, C4⋊D4 [×5], C4⋊1D4 [×3], C2×C4○D4 [×2], Dic14 [×4], C4×D7 [×6], D28 [×4], C2×Dic7 [×3], C2×Dic7 [×2], C2×Dic7 [×4], C7⋊D4 [×16], C2×C28 [×2], C2×C28 [×2], C2×C28 [×2], C7×D4 [×4], C22×D7, C22×D7 [×2], C22×C14, C22×C14 [×2], Q8⋊6D4, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4, Dic7⋊C4 [×2], D14⋊C4, D14⋊C4 [×2], C23.D7, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7 [×2], C2×D28, C2×D28 [×2], C4○D28 [×4], D4⋊2D7 [×4], C22×Dic7 [×2], C2×C7⋊D4, C2×C7⋊D4 [×8], C22×C28, D4×C14, D4×C14 [×2], Dic7⋊4D4 [×2], D14⋊D4 [×2], Dic7⋊3Q8, C28⋊1D4, C4×C7⋊D4, Dic7⋊D4 [×2], C28⋊D4, C28⋊D4 [×2], C7×C4⋊D4, C2×C4○D28, C2×D4⋊2D7, Dic14⋊20D4
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⋊6D4, D4×D7 [×2], C23×D7, C2×D4×D7, D4⋊6D14, D7×C4○D4, Dic14⋊20D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, cac-1=a15, ad=da, cbc-1=dbd=a14b, 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)
(1 122 15 136)(2 121 16 135)(3 120 17 134)(4 119 18 133)(5 118 19 132)(6 117 20 131)(7 116 21 130)(8 115 22 129)(9 114 23 128)(10 113 24 127)(11 140 25 126)(12 139 26 125)(13 138 27 124)(14 137 28 123)(29 165 43 151)(30 164 44 150)(31 163 45 149)(32 162 46 148)(33 161 47 147)(34 160 48 146)(35 159 49 145)(36 158 50 144)(37 157 51 143)(38 156 52 142)(39 155 53 141)(40 154 54 168)(41 153 55 167)(42 152 56 166)(57 217 71 203)(58 216 72 202)(59 215 73 201)(60 214 74 200)(61 213 75 199)(62 212 76 198)(63 211 77 197)(64 210 78 224)(65 209 79 223)(66 208 80 222)(67 207 81 221)(68 206 82 220)(69 205 83 219)(70 204 84 218)(85 175 99 189)(86 174 100 188)(87 173 101 187)(88 172 102 186)(89 171 103 185)(90 170 104 184)(91 169 105 183)(92 196 106 182)(93 195 107 181)(94 194 108 180)(95 193 109 179)(96 192 110 178)(97 191 111 177)(98 190 112 176)
(1 35 170 58)(2 50 171 73)(3 37 172 60)(4 52 173 75)(5 39 174 62)(6 54 175 77)(7 41 176 64)(8 56 177 79)(9 43 178 66)(10 30 179 81)(11 45 180 68)(12 32 181 83)(13 47 182 70)(14 34 183 57)(15 49 184 72)(16 36 185 59)(17 51 186 74)(18 38 187 61)(19 53 188 76)(20 40 189 63)(21 55 190 78)(22 42 191 65)(23 29 192 80)(24 44 193 67)(25 31 194 82)(26 46 195 69)(27 33 196 84)(28 48 169 71)(85 197 131 168)(86 212 132 155)(87 199 133 142)(88 214 134 157)(89 201 135 144)(90 216 136 159)(91 203 137 146)(92 218 138 161)(93 205 139 148)(94 220 140 163)(95 207 113 150)(96 222 114 165)(97 209 115 152)(98 224 116 167)(99 211 117 154)(100 198 118 141)(101 213 119 156)(102 200 120 143)(103 215 121 158)(104 202 122 145)(105 217 123 160)(106 204 124 147)(107 219 125 162)(108 206 126 149)(109 221 127 164)(110 208 128 151)(111 223 129 166)(112 210 130 153)
(1 129)(2 130)(3 131)(4 132)(5 133)(6 134)(7 135)(8 136)(9 137)(10 138)(11 139)(12 140)(13 113)(14 114)(15 115)(16 116)(17 117)(18 118)(19 119)(20 120)(21 121)(22 122)(23 123)(24 124)(25 125)(26 126)(27 127)(28 128)(29 217)(30 218)(31 219)(32 220)(33 221)(34 222)(35 223)(36 224)(37 197)(38 198)(39 199)(40 200)(41 201)(42 202)(43 203)(44 204)(45 205)(46 206)(47 207)(48 208)(49 209)(50 210)(51 211)(52 212)(53 213)(54 214)(55 215)(56 216)(57 165)(58 166)(59 167)(60 168)(61 141)(62 142)(63 143)(64 144)(65 145)(66 146)(67 147)(68 148)(69 149)(70 150)(71 151)(72 152)(73 153)(74 154)(75 155)(76 156)(77 157)(78 158)(79 159)(80 160)(81 161)(82 162)(83 163)(84 164)(85 172)(86 173)(87 174)(88 175)(89 176)(90 177)(91 178)(92 179)(93 180)(94 181)(95 182)(96 183)(97 184)(98 185)(99 186)(100 187)(101 188)(102 189)(103 190)(104 191)(105 192)(106 193)(107 194)(108 195)(109 196)(110 169)(111 170)(112 171)
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), (1,122,15,136)(2,121,16,135)(3,120,17,134)(4,119,18,133)(5,118,19,132)(6,117,20,131)(7,116,21,130)(8,115,22,129)(9,114,23,128)(10,113,24,127)(11,140,25,126)(12,139,26,125)(13,138,27,124)(14,137,28,123)(29,165,43,151)(30,164,44,150)(31,163,45,149)(32,162,46,148)(33,161,47,147)(34,160,48,146)(35,159,49,145)(36,158,50,144)(37,157,51,143)(38,156,52,142)(39,155,53,141)(40,154,54,168)(41,153,55,167)(42,152,56,166)(57,217,71,203)(58,216,72,202)(59,215,73,201)(60,214,74,200)(61,213,75,199)(62,212,76,198)(63,211,77,197)(64,210,78,224)(65,209,79,223)(66,208,80,222)(67,207,81,221)(68,206,82,220)(69,205,83,219)(70,204,84,218)(85,175,99,189)(86,174,100,188)(87,173,101,187)(88,172,102,186)(89,171,103,185)(90,170,104,184)(91,169,105,183)(92,196,106,182)(93,195,107,181)(94,194,108,180)(95,193,109,179)(96,192,110,178)(97,191,111,177)(98,190,112,176), (1,35,170,58)(2,50,171,73)(3,37,172,60)(4,52,173,75)(5,39,174,62)(6,54,175,77)(7,41,176,64)(8,56,177,79)(9,43,178,66)(10,30,179,81)(11,45,180,68)(12,32,181,83)(13,47,182,70)(14,34,183,57)(15,49,184,72)(16,36,185,59)(17,51,186,74)(18,38,187,61)(19,53,188,76)(20,40,189,63)(21,55,190,78)(22,42,191,65)(23,29,192,80)(24,44,193,67)(25,31,194,82)(26,46,195,69)(27,33,196,84)(28,48,169,71)(85,197,131,168)(86,212,132,155)(87,199,133,142)(88,214,134,157)(89,201,135,144)(90,216,136,159)(91,203,137,146)(92,218,138,161)(93,205,139,148)(94,220,140,163)(95,207,113,150)(96,222,114,165)(97,209,115,152)(98,224,116,167)(99,211,117,154)(100,198,118,141)(101,213,119,156)(102,200,120,143)(103,215,121,158)(104,202,122,145)(105,217,123,160)(106,204,124,147)(107,219,125,162)(108,206,126,149)(109,221,127,164)(110,208,128,151)(111,223,129,166)(112,210,130,153), (1,129)(2,130)(3,131)(4,132)(5,133)(6,134)(7,135)(8,136)(9,137)(10,138)(11,139)(12,140)(13,113)(14,114)(15,115)(16,116)(17,117)(18,118)(19,119)(20,120)(21,121)(22,122)(23,123)(24,124)(25,125)(26,126)(27,127)(28,128)(29,217)(30,218)(31,219)(32,220)(33,221)(34,222)(35,223)(36,224)(37,197)(38,198)(39,199)(40,200)(41,201)(42,202)(43,203)(44,204)(45,205)(46,206)(47,207)(48,208)(49,209)(50,210)(51,211)(52,212)(53,213)(54,214)(55,215)(56,216)(57,165)(58,166)(59,167)(60,168)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160)(81,161)(82,162)(83,163)(84,164)(85,172)(86,173)(87,174)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,181)(95,182)(96,183)(97,184)(98,185)(99,186)(100,187)(101,188)(102,189)(103,190)(104,191)(105,192)(106,193)(107,194)(108,195)(109,196)(110,169)(111,170)(112,171)>;
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), (1,122,15,136)(2,121,16,135)(3,120,17,134)(4,119,18,133)(5,118,19,132)(6,117,20,131)(7,116,21,130)(8,115,22,129)(9,114,23,128)(10,113,24,127)(11,140,25,126)(12,139,26,125)(13,138,27,124)(14,137,28,123)(29,165,43,151)(30,164,44,150)(31,163,45,149)(32,162,46,148)(33,161,47,147)(34,160,48,146)(35,159,49,145)(36,158,50,144)(37,157,51,143)(38,156,52,142)(39,155,53,141)(40,154,54,168)(41,153,55,167)(42,152,56,166)(57,217,71,203)(58,216,72,202)(59,215,73,201)(60,214,74,200)(61,213,75,199)(62,212,76,198)(63,211,77,197)(64,210,78,224)(65,209,79,223)(66,208,80,222)(67,207,81,221)(68,206,82,220)(69,205,83,219)(70,204,84,218)(85,175,99,189)(86,174,100,188)(87,173,101,187)(88,172,102,186)(89,171,103,185)(90,170,104,184)(91,169,105,183)(92,196,106,182)(93,195,107,181)(94,194,108,180)(95,193,109,179)(96,192,110,178)(97,191,111,177)(98,190,112,176), (1,35,170,58)(2,50,171,73)(3,37,172,60)(4,52,173,75)(5,39,174,62)(6,54,175,77)(7,41,176,64)(8,56,177,79)(9,43,178,66)(10,30,179,81)(11,45,180,68)(12,32,181,83)(13,47,182,70)(14,34,183,57)(15,49,184,72)(16,36,185,59)(17,51,186,74)(18,38,187,61)(19,53,188,76)(20,40,189,63)(21,55,190,78)(22,42,191,65)(23,29,192,80)(24,44,193,67)(25,31,194,82)(26,46,195,69)(27,33,196,84)(28,48,169,71)(85,197,131,168)(86,212,132,155)(87,199,133,142)(88,214,134,157)(89,201,135,144)(90,216,136,159)(91,203,137,146)(92,218,138,161)(93,205,139,148)(94,220,140,163)(95,207,113,150)(96,222,114,165)(97,209,115,152)(98,224,116,167)(99,211,117,154)(100,198,118,141)(101,213,119,156)(102,200,120,143)(103,215,121,158)(104,202,122,145)(105,217,123,160)(106,204,124,147)(107,219,125,162)(108,206,126,149)(109,221,127,164)(110,208,128,151)(111,223,129,166)(112,210,130,153), (1,129)(2,130)(3,131)(4,132)(5,133)(6,134)(7,135)(8,136)(9,137)(10,138)(11,139)(12,140)(13,113)(14,114)(15,115)(16,116)(17,117)(18,118)(19,119)(20,120)(21,121)(22,122)(23,123)(24,124)(25,125)(26,126)(27,127)(28,128)(29,217)(30,218)(31,219)(32,220)(33,221)(34,222)(35,223)(36,224)(37,197)(38,198)(39,199)(40,200)(41,201)(42,202)(43,203)(44,204)(45,205)(46,206)(47,207)(48,208)(49,209)(50,210)(51,211)(52,212)(53,213)(54,214)(55,215)(56,216)(57,165)(58,166)(59,167)(60,168)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160)(81,161)(82,162)(83,163)(84,164)(85,172)(86,173)(87,174)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,181)(95,182)(96,183)(97,184)(98,185)(99,186)(100,187)(101,188)(102,189)(103,190)(104,191)(105,192)(106,193)(107,194)(108,195)(109,196)(110,169)(111,170)(112,171) );
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)], [(1,122,15,136),(2,121,16,135),(3,120,17,134),(4,119,18,133),(5,118,19,132),(6,117,20,131),(7,116,21,130),(8,115,22,129),(9,114,23,128),(10,113,24,127),(11,140,25,126),(12,139,26,125),(13,138,27,124),(14,137,28,123),(29,165,43,151),(30,164,44,150),(31,163,45,149),(32,162,46,148),(33,161,47,147),(34,160,48,146),(35,159,49,145),(36,158,50,144),(37,157,51,143),(38,156,52,142),(39,155,53,141),(40,154,54,168),(41,153,55,167),(42,152,56,166),(57,217,71,203),(58,216,72,202),(59,215,73,201),(60,214,74,200),(61,213,75,199),(62,212,76,198),(63,211,77,197),(64,210,78,224),(65,209,79,223),(66,208,80,222),(67,207,81,221),(68,206,82,220),(69,205,83,219),(70,204,84,218),(85,175,99,189),(86,174,100,188),(87,173,101,187),(88,172,102,186),(89,171,103,185),(90,170,104,184),(91,169,105,183),(92,196,106,182),(93,195,107,181),(94,194,108,180),(95,193,109,179),(96,192,110,178),(97,191,111,177),(98,190,112,176)], [(1,35,170,58),(2,50,171,73),(3,37,172,60),(4,52,173,75),(5,39,174,62),(6,54,175,77),(7,41,176,64),(8,56,177,79),(9,43,178,66),(10,30,179,81),(11,45,180,68),(12,32,181,83),(13,47,182,70),(14,34,183,57),(15,49,184,72),(16,36,185,59),(17,51,186,74),(18,38,187,61),(19,53,188,76),(20,40,189,63),(21,55,190,78),(22,42,191,65),(23,29,192,80),(24,44,193,67),(25,31,194,82),(26,46,195,69),(27,33,196,84),(28,48,169,71),(85,197,131,168),(86,212,132,155),(87,199,133,142),(88,214,134,157),(89,201,135,144),(90,216,136,159),(91,203,137,146),(92,218,138,161),(93,205,139,148),(94,220,140,163),(95,207,113,150),(96,222,114,165),(97,209,115,152),(98,224,116,167),(99,211,117,154),(100,198,118,141),(101,213,119,156),(102,200,120,143),(103,215,121,158),(104,202,122,145),(105,217,123,160),(106,204,124,147),(107,219,125,162),(108,206,126,149),(109,221,127,164),(110,208,128,151),(111,223,129,166),(112,210,130,153)], [(1,129),(2,130),(3,131),(4,132),(5,133),(6,134),(7,135),(8,136),(9,137),(10,138),(11,139),(12,140),(13,113),(14,114),(15,115),(16,116),(17,117),(18,118),(19,119),(20,120),(21,121),(22,122),(23,123),(24,124),(25,125),(26,126),(27,127),(28,128),(29,217),(30,218),(31,219),(32,220),(33,221),(34,222),(35,223),(36,224),(37,197),(38,198),(39,199),(40,200),(41,201),(42,202),(43,203),(44,204),(45,205),(46,206),(47,207),(48,208),(49,209),(50,210),(51,211),(52,212),(53,213),(54,214),(55,215),(56,216),(57,165),(58,166),(59,167),(60,168),(61,141),(62,142),(63,143),(64,144),(65,145),(66,146),(67,147),(68,148),(69,149),(70,150),(71,151),(72,152),(73,153),(74,154),(75,155),(76,156),(77,157),(78,158),(79,159),(80,160),(81,161),(82,162),(83,163),(84,164),(85,172),(86,173),(87,174),(88,175),(89,176),(90,177),(91,178),(92,179),(93,180),(94,181),(95,182),(96,183),(97,184),(98,185),(99,186),(100,187),(101,188),(102,189),(103,190),(104,191),(105,192),(106,193),(107,194),(108,195),(109,196),(110,169),(111,170),(112,171)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 2 | 7 | 0 | 0 | 0 | 0 |
| 20 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 18 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 5 | 3 | 0 | 0 | 0 | 0 |
| 1 | 24 | 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 |
| 5 | 3 | 0 | 0 | 0 | 0 |
| 21 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(29))| [2,20,0,0,0,0,7,27,0,0,0,0,0,0,0,1,0,0,0,0,28,22,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[12,18,0,0,0,0,0,17,0,0,0,0,0,0,1,7,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[5,1,0,0,0,0,3,24,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[5,21,0,0,0,0,3,24,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | ··· | 14 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 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 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ (1+4) | D4×D7 | D4⋊6D14 | D7×C4○D4 |
| kernel | Dic14⋊20D4 | Dic7⋊4D4 | D14⋊D4 | Dic7⋊3Q8 | C28⋊1D4 | C4×C7⋊D4 | Dic7⋊D4 | C28⋊D4 | C7×C4⋊D4 | C2×C4○D28 | C2×D4⋊2D7 | Dic14 | C4⋊D4 | Dic7 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 4 | 3 | 4 | 6 | 3 | 3 | 9 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{20}D_4 % in TeX
G:=Group("Dic14:20D4"); // GroupNames label
G:=SmallGroup(448,1052);
// by ID
G=gap.SmallGroup(448,1052);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,477,232,184,570,185,18822]);
// 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=a^15,a*d=d*a,c*b*c^-1=d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀