direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C4○D4×C28, D4⋊6(C2×C28), Q8⋊6(C2×C28), (C4×D4)⋊23C14, (D4×C28)⋊52C2, (C2×C42)⋊8C14, (Q8×C28)⋊38C2, (C4×Q8)⋊18C14, C2.6(C23×C28), C4.18(C22×C28), C14.58(C23×C4), C42.87(C2×C14), C42⋊C2⋊19C14, (C4×C28).371C22, (C2×C28).959C23, C28.163(C22×C4), (C2×C14).337C24, C22.1(C22×C28), (D4×C14).331C22, C23.29(C22×C14), C22.10(C23×C14), (Q8×C14).283C22, (C22×C28).595C22, (C22×C14).253C23, (C2×C4×C28)⋊21C2, (C2×C4)⋊8(C2×C28), (C2×C28)⋊33(C2×C4), (C7×D4)⋊26(C2×C4), (C7×Q8)⋊24(C2×C4), C2.4(C14×C4○D4), C4⋊C4.81(C2×C14), (C14×C4○D4).27C2, (C2×C4○D4).13C14, (C2×D4).77(C2×C14), C14.223(C2×C4○D4), (C2×Q8).71(C2×C14), (C7×C42⋊C2)⋊40C2, C22⋊C4.28(C2×C14), (C7×C4⋊C4).406C22, (C22×C4).99(C2×C14), (C2×C14).32(C22×C4), (C2×C4).134(C22×C14), (C7×C22⋊C4).159C22, SmallGroup(448,1300)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4○D4×C28
G = < a,b,c,d | a28=b4=d2=1, c2=b2, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b2c >
Subgroups: 370 in 310 conjugacy classes, 250 normal (16 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C2×C4○D4, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C4×C4○D4, C4×C28, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, D4×C14, Q8×C14, C7×C4○D4, C2×C4×C28, C7×C42⋊C2, D4×C28, Q8×C28, C14×C4○D4, C4○D4×C28
Quotients: C1, C2, C4, C22, C7, C2×C4, C23, C14, C22×C4, C4○D4, C24, C28, C2×C14, C23×C4, C2×C4○D4, C2×C28, C22×C14, C4×C4○D4, C22×C28, C7×C4○D4, C23×C14, C23×C28, C14×C4○D4, C4○D4×C28
►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 39 78 221)(2 40 79 222)(3 41 80 223)(4 42 81 224)(5 43 82 197)(6 44 83 198)(7 45 84 199)(8 46 57 200)(9 47 58 201)(10 48 59 202)(11 49 60 203)(12 50 61 204)(13 51 62 205)(14 52 63 206)(15 53 64 207)(16 54 65 208)(17 55 66 209)(18 56 67 210)(19 29 68 211)(20 30 69 212)(21 31 70 213)(22 32 71 214)(23 33 72 215)(24 34 73 216)(25 35 74 217)(26 36 75 218)(27 37 76 219)(28 38 77 220)(85 128 173 150)(86 129 174 151)(87 130 175 152)(88 131 176 153)(89 132 177 154)(90 133 178 155)(91 134 179 156)(92 135 180 157)(93 136 181 158)(94 137 182 159)(95 138 183 160)(96 139 184 161)(97 140 185 162)(98 113 186 163)(99 114 187 164)(100 115 188 165)(101 116 189 166)(102 117 190 167)(103 118 191 168)(104 119 192 141)(105 120 193 142)(106 121 194 143)(107 122 195 144)(108 123 196 145)(109 124 169 146)(110 125 170 147)(111 126 171 148)(112 127 172 149)
(1 221 78 39)(2 222 79 40)(3 223 80 41)(4 224 81 42)(5 197 82 43)(6 198 83 44)(7 199 84 45)(8 200 57 46)(9 201 58 47)(10 202 59 48)(11 203 60 49)(12 204 61 50)(13 205 62 51)(14 206 63 52)(15 207 64 53)(16 208 65 54)(17 209 66 55)(18 210 67 56)(19 211 68 29)(20 212 69 30)(21 213 70 31)(22 214 71 32)(23 215 72 33)(24 216 73 34)(25 217 74 35)(26 218 75 36)(27 219 76 37)(28 220 77 38)(85 128 173 150)(86 129 174 151)(87 130 175 152)(88 131 176 153)(89 132 177 154)(90 133 178 155)(91 134 179 156)(92 135 180 157)(93 136 181 158)(94 137 182 159)(95 138 183 160)(96 139 184 161)(97 140 185 162)(98 113 186 163)(99 114 187 164)(100 115 188 165)(101 116 189 166)(102 117 190 167)(103 118 191 168)(104 119 192 141)(105 120 193 142)(106 121 194 143)(107 122 195 144)(108 123 196 145)(109 124 169 146)(110 125 170 147)(111 126 171 148)(112 127 172 149)
(1 157)(2 158)(3 159)(4 160)(5 161)(6 162)(7 163)(8 164)(9 165)(10 166)(11 167)(12 168)(13 141)(14 142)(15 143)(16 144)(17 145)(18 146)(19 147)(20 148)(21 149)(22 150)(23 151)(24 152)(25 153)(26 154)(27 155)(28 156)(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)(57 114)(58 115)(59 116)(60 117)(61 118)(62 119)(63 120)(64 121)(65 122)(66 123)(67 124)(68 125)(69 126)(70 127)(71 128)(72 129)(73 130)(74 131)(75 132)(76 133)(77 134)(78 135)(79 136)(80 137)(81 138)(82 139)(83 140)(84 113)(169 210)(170 211)(171 212)(172 213)(173 214)(174 215)(175 216)(176 217)(177 218)(178 219)(179 220)(180 221)(181 222)(182 223)(183 224)(184 197)(185 198)(186 199)(187 200)(188 201)(189 202)(190 203)(191 204)(192 205)(193 206)(194 207)(195 208)(196 209)
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), (1,39,78,221)(2,40,79,222)(3,41,80,223)(4,42,81,224)(5,43,82,197)(6,44,83,198)(7,45,84,199)(8,46,57,200)(9,47,58,201)(10,48,59,202)(11,49,60,203)(12,50,61,204)(13,51,62,205)(14,52,63,206)(15,53,64,207)(16,54,65,208)(17,55,66,209)(18,56,67,210)(19,29,68,211)(20,30,69,212)(21,31,70,213)(22,32,71,214)(23,33,72,215)(24,34,73,216)(25,35,74,217)(26,36,75,218)(27,37,76,219)(28,38,77,220)(85,128,173,150)(86,129,174,151)(87,130,175,152)(88,131,176,153)(89,132,177,154)(90,133,178,155)(91,134,179,156)(92,135,180,157)(93,136,181,158)(94,137,182,159)(95,138,183,160)(96,139,184,161)(97,140,185,162)(98,113,186,163)(99,114,187,164)(100,115,188,165)(101,116,189,166)(102,117,190,167)(103,118,191,168)(104,119,192,141)(105,120,193,142)(106,121,194,143)(107,122,195,144)(108,123,196,145)(109,124,169,146)(110,125,170,147)(111,126,171,148)(112,127,172,149), (1,221,78,39)(2,222,79,40)(3,223,80,41)(4,224,81,42)(5,197,82,43)(6,198,83,44)(7,199,84,45)(8,200,57,46)(9,201,58,47)(10,202,59,48)(11,203,60,49)(12,204,61,50)(13,205,62,51)(14,206,63,52)(15,207,64,53)(16,208,65,54)(17,209,66,55)(18,210,67,56)(19,211,68,29)(20,212,69,30)(21,213,70,31)(22,214,71,32)(23,215,72,33)(24,216,73,34)(25,217,74,35)(26,218,75,36)(27,219,76,37)(28,220,77,38)(85,128,173,150)(86,129,174,151)(87,130,175,152)(88,131,176,153)(89,132,177,154)(90,133,178,155)(91,134,179,156)(92,135,180,157)(93,136,181,158)(94,137,182,159)(95,138,183,160)(96,139,184,161)(97,140,185,162)(98,113,186,163)(99,114,187,164)(100,115,188,165)(101,116,189,166)(102,117,190,167)(103,118,191,168)(104,119,192,141)(105,120,193,142)(106,121,194,143)(107,122,195,144)(108,123,196,145)(109,124,169,146)(110,125,170,147)(111,126,171,148)(112,127,172,149), (1,157)(2,158)(3,159)(4,160)(5,161)(6,162)(7,163)(8,164)(9,165)(10,166)(11,167)(12,168)(13,141)(14,142)(15,143)(16,144)(17,145)(18,146)(19,147)(20,148)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(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)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,113)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)(179,220)(180,221)(181,222)(182,223)(183,224)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)(192,205)(193,206)(194,207)(195,208)(196,209)>;
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), (1,39,78,221)(2,40,79,222)(3,41,80,223)(4,42,81,224)(5,43,82,197)(6,44,83,198)(7,45,84,199)(8,46,57,200)(9,47,58,201)(10,48,59,202)(11,49,60,203)(12,50,61,204)(13,51,62,205)(14,52,63,206)(15,53,64,207)(16,54,65,208)(17,55,66,209)(18,56,67,210)(19,29,68,211)(20,30,69,212)(21,31,70,213)(22,32,71,214)(23,33,72,215)(24,34,73,216)(25,35,74,217)(26,36,75,218)(27,37,76,219)(28,38,77,220)(85,128,173,150)(86,129,174,151)(87,130,175,152)(88,131,176,153)(89,132,177,154)(90,133,178,155)(91,134,179,156)(92,135,180,157)(93,136,181,158)(94,137,182,159)(95,138,183,160)(96,139,184,161)(97,140,185,162)(98,113,186,163)(99,114,187,164)(100,115,188,165)(101,116,189,166)(102,117,190,167)(103,118,191,168)(104,119,192,141)(105,120,193,142)(106,121,194,143)(107,122,195,144)(108,123,196,145)(109,124,169,146)(110,125,170,147)(111,126,171,148)(112,127,172,149), (1,221,78,39)(2,222,79,40)(3,223,80,41)(4,224,81,42)(5,197,82,43)(6,198,83,44)(7,199,84,45)(8,200,57,46)(9,201,58,47)(10,202,59,48)(11,203,60,49)(12,204,61,50)(13,205,62,51)(14,206,63,52)(15,207,64,53)(16,208,65,54)(17,209,66,55)(18,210,67,56)(19,211,68,29)(20,212,69,30)(21,213,70,31)(22,214,71,32)(23,215,72,33)(24,216,73,34)(25,217,74,35)(26,218,75,36)(27,219,76,37)(28,220,77,38)(85,128,173,150)(86,129,174,151)(87,130,175,152)(88,131,176,153)(89,132,177,154)(90,133,178,155)(91,134,179,156)(92,135,180,157)(93,136,181,158)(94,137,182,159)(95,138,183,160)(96,139,184,161)(97,140,185,162)(98,113,186,163)(99,114,187,164)(100,115,188,165)(101,116,189,166)(102,117,190,167)(103,118,191,168)(104,119,192,141)(105,120,193,142)(106,121,194,143)(107,122,195,144)(108,123,196,145)(109,124,169,146)(110,125,170,147)(111,126,171,148)(112,127,172,149), (1,157)(2,158)(3,159)(4,160)(5,161)(6,162)(7,163)(8,164)(9,165)(10,166)(11,167)(12,168)(13,141)(14,142)(15,143)(16,144)(17,145)(18,146)(19,147)(20,148)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(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)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,113)(169,210)(170,211)(171,212)(172,213)(173,214)(174,215)(175,216)(176,217)(177,218)(178,219)(179,220)(180,221)(181,222)(182,223)(183,224)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)(192,205)(193,206)(194,207)(195,208)(196,209) );
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)], [(1,39,78,221),(2,40,79,222),(3,41,80,223),(4,42,81,224),(5,43,82,197),(6,44,83,198),(7,45,84,199),(8,46,57,200),(9,47,58,201),(10,48,59,202),(11,49,60,203),(12,50,61,204),(13,51,62,205),(14,52,63,206),(15,53,64,207),(16,54,65,208),(17,55,66,209),(18,56,67,210),(19,29,68,211),(20,30,69,212),(21,31,70,213),(22,32,71,214),(23,33,72,215),(24,34,73,216),(25,35,74,217),(26,36,75,218),(27,37,76,219),(28,38,77,220),(85,128,173,150),(86,129,174,151),(87,130,175,152),(88,131,176,153),(89,132,177,154),(90,133,178,155),(91,134,179,156),(92,135,180,157),(93,136,181,158),(94,137,182,159),(95,138,183,160),(96,139,184,161),(97,140,185,162),(98,113,186,163),(99,114,187,164),(100,115,188,165),(101,116,189,166),(102,117,190,167),(103,118,191,168),(104,119,192,141),(105,120,193,142),(106,121,194,143),(107,122,195,144),(108,123,196,145),(109,124,169,146),(110,125,170,147),(111,126,171,148),(112,127,172,149)], [(1,221,78,39),(2,222,79,40),(3,223,80,41),(4,224,81,42),(5,197,82,43),(6,198,83,44),(7,199,84,45),(8,200,57,46),(9,201,58,47),(10,202,59,48),(11,203,60,49),(12,204,61,50),(13,205,62,51),(14,206,63,52),(15,207,64,53),(16,208,65,54),(17,209,66,55),(18,210,67,56),(19,211,68,29),(20,212,69,30),(21,213,70,31),(22,214,71,32),(23,215,72,33),(24,216,73,34),(25,217,74,35),(26,218,75,36),(27,219,76,37),(28,220,77,38),(85,128,173,150),(86,129,174,151),(87,130,175,152),(88,131,176,153),(89,132,177,154),(90,133,178,155),(91,134,179,156),(92,135,180,157),(93,136,181,158),(94,137,182,159),(95,138,183,160),(96,139,184,161),(97,140,185,162),(98,113,186,163),(99,114,187,164),(100,115,188,165),(101,116,189,166),(102,117,190,167),(103,118,191,168),(104,119,192,141),(105,120,193,142),(106,121,194,143),(107,122,195,144),(108,123,196,145),(109,124,169,146),(110,125,170,147),(111,126,171,148),(112,127,172,149)], [(1,157),(2,158),(3,159),(4,160),(5,161),(6,162),(7,163),(8,164),(9,165),(10,166),(11,167),(12,168),(13,141),(14,142),(15,143),(16,144),(17,145),(18,146),(19,147),(20,148),(21,149),(22,150),(23,151),(24,152),(25,153),(26,154),(27,155),(28,156),(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),(57,114),(58,115),(59,116),(60,117),(61,118),(62,119),(63,120),(64,121),(65,122),(66,123),(67,124),(68,125),(69,126),(70,127),(71,128),(72,129),(73,130),(74,131),(75,132),(76,133),(77,134),(78,135),(79,136),(80,137),(81,138),(82,139),(83,140),(84,113),(169,210),(170,211),(171,212),(172,213),(173,214),(174,215),(175,216),(176,217),(177,218),(178,219),(179,220),(180,221),(181,222),(182,223),(183,224),(184,197),(185,198),(186,199),(187,200),(188,201),(189,202),(190,203),(191,204),(192,205),(193,206),(194,207),(195,208),(196,209)]])
280 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | ··· | 4L | 4M | ··· | 4AD | 7A | ··· | 7F | 14A | ··· | 14R | 14S | ··· | 14BB | 28A | ··· | 28BT | 28BU | ··· | 28FX |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 |
280 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C7 | C14 | C14 | C14 | C14 | C14 | C28 | C4○D4 | C7×C4○D4 |
| kernel | C4○D4×C28 | C2×C4×C28 | C7×C42⋊C2 | D4×C28 | Q8×C28 | C14×C4○D4 | C7×C4○D4 | C4×C4○D4 | C2×C42 | C42⋊C2 | C4×D4 | C4×Q8 | C2×C4○D4 | C4○D4 | C28 | C4 |
| # reps | 1 | 3 | 3 | 6 | 2 | 1 | 16 | 6 | 18 | 18 | 36 | 12 | 6 | 96 | 8 | 48 |
Matrix representation of C4○D4×C28 ►in GL3(𝔽29) generated by
| 17 | 0 | 0 |
| 0 | 15 | 0 |
| 0 | 0 | 15 |
| 28 | 0 | 0 |
| 0 | 12 | 0 |
| 0 | 0 | 12 |
| 1 | 0 | 0 |
| 0 | 17 | 0 |
| 0 | 26 | 12 |
| 1 | 0 | 0 |
| 0 | 26 | 24 |
| 0 | 19 | 3 |
G:=sub<GL(3,GF(29))| [17,0,0,0,15,0,0,0,15],[28,0,0,0,12,0,0,0,12],[1,0,0,0,17,26,0,0,12],[1,0,0,0,26,19,0,24,3] >;
C4○D4×C28 in GAP, Magma, Sage, TeX
C_4\circ D_4\times C_{28} % in TeX
G:=Group("C4oD4xC28"); // GroupNames label
G:=SmallGroup(448,1300);
// by ID
G=gap.SmallGroup(448,1300);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1568,1597,1192,416]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^4=d^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^2*c>;
// generators/relations