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## G = Dic14⋊20D4order 448 = 26·7

### 8th semidirect product of Dic14 and D4 acting via D4/C22=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — Dic14⋊20D4
 Chief series C1 — C7 — C14 — C2×C14 — C2×Dic7 — C2×Dic14 — C2×C4○D28 — Dic14⋊20D4
 Lower central C7 — C2×C14 — Dic14⋊20D4
 Upper central C1 — C22 — C4⋊D4

Generators and relations for Dic1420D4
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 >

Subgroups: 1580 in 312 conjugacy classes, 105 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C41D4, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22×C14, Q86D4, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, D14⋊C4, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C4○D28, D42D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, Dic74D4, D14⋊D4, Dic73Q8, C4⋊D28, C4×C7⋊D4, Dic7⋊D4, C28⋊D4, C28⋊D4, C7×C4⋊D4, C2×C4○D28, C2×D42D7, Dic1420D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, C22×D7, Q86D4, D4×D7, C23×D7, C2×D4×D7, D46D14, D7×C4○D4, Dic1420D4

Smallest permutation representation of Dic1420D4
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)
(1 171 15 185)(2 170 16 184)(3 169 17 183)(4 196 18 182)(5 195 19 181)(6 194 20 180)(7 193 21 179)(8 192 22 178)(9 191 23 177)(10 190 24 176)(11 189 25 175)(12 188 26 174)(13 187 27 173)(14 186 28 172)(29 158 43 144)(30 157 44 143)(31 156 45 142)(32 155 46 141)(33 154 47 168)(34 153 48 167)(35 152 49 166)(36 151 50 165)(37 150 51 164)(38 149 52 163)(39 148 53 162)(40 147 54 161)(41 146 55 160)(42 145 56 159)(57 132 71 118)(58 131 72 117)(59 130 73 116)(60 129 74 115)(61 128 75 114)(62 127 76 113)(63 126 77 140)(64 125 78 139)(65 124 79 138)(66 123 80 137)(67 122 81 136)(68 121 82 135)(69 120 83 134)(70 119 84 133)(85 205 99 219)(86 204 100 218)(87 203 101 217)(88 202 102 216)(89 201 103 215)(90 200 104 214)(91 199 105 213)(92 198 106 212)(93 197 107 211)(94 224 108 210)(95 223 109 209)(96 222 110 208)(97 221 111 207)(98 220 112 206)
(1 208 124 50)(2 223 125 37)(3 210 126 52)(4 197 127 39)(5 212 128 54)(6 199 129 41)(7 214 130 56)(8 201 131 43)(9 216 132 30)(10 203 133 45)(11 218 134 32)(12 205 135 47)(13 220 136 34)(14 207 137 49)(15 222 138 36)(16 209 139 51)(17 224 140 38)(18 211 113 53)(19 198 114 40)(20 213 115 55)(21 200 116 42)(22 215 117 29)(23 202 118 44)(24 217 119 31)(25 204 120 46)(26 219 121 33)(27 206 122 48)(28 221 123 35)(57 157 177 88)(58 144 178 103)(59 159 179 90)(60 146 180 105)(61 161 181 92)(62 148 182 107)(63 163 183 94)(64 150 184 109)(65 165 185 96)(66 152 186 111)(67 167 187 98)(68 154 188 85)(69 141 189 100)(70 156 190 87)(71 143 191 102)(72 158 192 89)(73 145 193 104)(74 160 194 91)(75 147 195 106)(76 162 196 93)(77 149 169 108)(78 164 170 95)(79 151 171 110)(80 166 172 97)(81 153 173 112)(82 168 174 99)(83 155 175 86)(84 142 176 101)
(1 178)(2 179)(3 180)(4 181)(5 182)(6 183)(7 184)(8 185)(9 186)(10 187)(11 188)(12 189)(13 190)(14 191)(15 192)(16 193)(17 194)(18 195)(19 196)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 110)(30 111)(31 112)(32 85)(33 86)(34 87)(35 88)(36 89)(37 90)(38 91)(39 92)(40 93)(41 94)(42 95)(43 96)(44 97)(45 98)(46 99)(47 100)(48 101)(49 102)(50 103)(51 104)(52 105)(53 106)(54 107)(55 108)(56 109)(57 123)(58 124)(59 125)(60 126)(61 127)(62 128)(63 129)(64 130)(65 131)(66 132)(67 133)(68 134)(69 135)(70 136)(71 137)(72 138)(73 139)(74 140)(75 113)(76 114)(77 115)(78 116)(79 117)(80 118)(81 119)(82 120)(83 121)(84 122)(141 205)(142 206)(143 207)(144 208)(145 209)(146 210)(147 211)(148 212)(149 213)(150 214)(151 215)(152 216)(153 217)(154 218)(155 219)(156 220)(157 221)(158 222)(159 223)(160 224)(161 197)(162 198)(163 199)(164 200)(165 201)(166 202)(167 203)(168 204)

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

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), (1,171,15,185)(2,170,16,184)(3,169,17,183)(4,196,18,182)(5,195,19,181)(6,194,20,180)(7,193,21,179)(8,192,22,178)(9,191,23,177)(10,190,24,176)(11,189,25,175)(12,188,26,174)(13,187,27,173)(14,186,28,172)(29,158,43,144)(30,157,44,143)(31,156,45,142)(32,155,46,141)(33,154,47,168)(34,153,48,167)(35,152,49,166)(36,151,50,165)(37,150,51,164)(38,149,52,163)(39,148,53,162)(40,147,54,161)(41,146,55,160)(42,145,56,159)(57,132,71,118)(58,131,72,117)(59,130,73,116)(60,129,74,115)(61,128,75,114)(62,127,76,113)(63,126,77,140)(64,125,78,139)(65,124,79,138)(66,123,80,137)(67,122,81,136)(68,121,82,135)(69,120,83,134)(70,119,84,133)(85,205,99,219)(86,204,100,218)(87,203,101,217)(88,202,102,216)(89,201,103,215)(90,200,104,214)(91,199,105,213)(92,198,106,212)(93,197,107,211)(94,224,108,210)(95,223,109,209)(96,222,110,208)(97,221,111,207)(98,220,112,206), (1,208,124,50)(2,223,125,37)(3,210,126,52)(4,197,127,39)(5,212,128,54)(6,199,129,41)(7,214,130,56)(8,201,131,43)(9,216,132,30)(10,203,133,45)(11,218,134,32)(12,205,135,47)(13,220,136,34)(14,207,137,49)(15,222,138,36)(16,209,139,51)(17,224,140,38)(18,211,113,53)(19,198,114,40)(20,213,115,55)(21,200,116,42)(22,215,117,29)(23,202,118,44)(24,217,119,31)(25,204,120,46)(26,219,121,33)(27,206,122,48)(28,221,123,35)(57,157,177,88)(58,144,178,103)(59,159,179,90)(60,146,180,105)(61,161,181,92)(62,148,182,107)(63,163,183,94)(64,150,184,109)(65,165,185,96)(66,152,186,111)(67,167,187,98)(68,154,188,85)(69,141,189,100)(70,156,190,87)(71,143,191,102)(72,158,192,89)(73,145,193,104)(74,160,194,91)(75,147,195,106)(76,162,196,93)(77,149,169,108)(78,164,170,95)(79,151,171,110)(80,166,172,97)(81,153,173,112)(82,168,174,99)(83,155,175,86)(84,142,176,101), (1,178)(2,179)(3,180)(4,181)(5,182)(6,183)(7,184)(8,185)(9,186)(10,187)(11,188)(12,189)(13,190)(14,191)(15,192)(16,193)(17,194)(18,195)(19,196)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,110)(30,111)(31,112)(32,85)(33,86)(34,87)(35,88)(36,89)(37,90)(38,91)(39,92)(40,93)(41,94)(42,95)(43,96)(44,97)(45,98)(46,99)(47,100)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,108)(56,109)(57,123)(58,124)(59,125)(60,126)(61,127)(62,128)(63,129)(64,130)(65,131)(66,132)(67,133)(68,134)(69,135)(70,136)(71,137)(72,138)(73,139)(74,140)(75,113)(76,114)(77,115)(78,116)(79,117)(80,118)(81,119)(82,120)(83,121)(84,122)(141,205)(142,206)(143,207)(144,208)(145,209)(146,210)(147,211)(148,212)(149,213)(150,214)(151,215)(152,216)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)(161,197)(162,198)(163,199)(164,200)(165,201)(166,202)(167,203)(168,204) );

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

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 C4⋊D28 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

Matrix representation of Dic1420D4 in 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] >;

Dic1420D4 in GAP, Magma, Sage, TeX

{\rm 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

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