metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C28)⋊17D4, C28⋊D4⋊33C2, C28.454(C2×D4), Dic7⋊4(C4○D4), (C2×D4).237D14, (C2×Q8).194D14, Dic7⋊D4⋊47C2, Dic7⋊Q8⋊34C2, C28.17D4⋊33C2, C28.23D4⋊34C2, (C2×C14).318C24, (C2×C28).889C23, (C22×C4).288D14, C14.168(C22×D4), D14⋊C4.160C22, (C2×D28).282C22, (D4×C14).277C22, (Q8×C14).244C22, C7⋊7(C22.26C24), C22.327(C23×D7), C23.139(C22×D7), Dic7⋊C4.172C22, (C22×C28).297C22, (C22×C14).244C23, (C2×Dic7).294C23, (C4×Dic7).261C22, (C22×D7).139C23, C23.D7.137C22, (C2×Dic14).311C22, (C22×Dic7).237C22, (C2×C4○D4)⋊10D7, (C4×C7⋊D4)⋊61C2, (C2×C4×Dic7)⋊15C2, (C2×C4○D28)⋊32C2, (C14×C4○D4)⋊10C2, (C2×C4)⋊11(C7⋊D4), C2.106(D7×C4○D4), (C2×C14).83(C2×D4), C4.146(C2×C7⋊D4), C22.1(C2×C7⋊D4), C14.218(C2×C4○D4), (C2×C4×D7).221C22, C2.41(C22×C7⋊D4), (C2×C4).832(C22×D7), (C2×C7⋊D4).142C22, SmallGroup(448,1285)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C28)⋊17D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, dad=ab14, cbc-1=dbd=b13, dcd=c-1 >
Subgroups: 1300 in 310 conjugacy classes, 115 normal (31 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C42, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C22×C14, C22.26C24, C4×Dic7, C4×Dic7, Dic7⋊C4, D14⋊C4, C23.D7, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C22×Dic7, C2×C7⋊D4, C22×C28, C22×C28, D4×C14, D4×C14, Q8×C14, C7×C4○D4, C2×C4×Dic7, C4×C7⋊D4, C28.17D4, Dic7⋊D4, C28⋊D4, Dic7⋊Q8, C28.23D4, C2×C4○D28, C14×C4○D4, (C2×C28)⋊17D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, C7⋊D4, C22×D7, C22.26C24, C2×C7⋊D4, C23×D7, D7×C4○D4, C22×C7⋊D4, (C2×C28)⋊17D4
►On 224 points
Generators in S224
(1 151)(2 152)(3 153)(4 154)(5 155)(6 156)(7 157)(8 158)(9 159)(10 160)(11 161)(12 162)(13 163)(14 164)(15 165)(16 166)(17 167)(18 168)(19 141)(20 142)(21 143)(22 144)(23 145)(24 146)(25 147)(26 148)(27 149)(28 150)(29 68)(30 69)(31 70)(32 71)(33 72)(34 73)(35 74)(36 75)(37 76)(38 77)(39 78)(40 79)(41 80)(42 81)(43 82)(44 83)(45 84)(46 57)(47 58)(48 59)(49 60)(50 61)(51 62)(52 63)(53 64)(54 65)(55 66)(56 67)(85 211)(86 212)(87 213)(88 214)(89 215)(90 216)(91 217)(92 218)(93 219)(94 220)(95 221)(96 222)(97 223)(98 224)(99 197)(100 198)(101 199)(102 200)(103 201)(104 202)(105 203)(106 204)(107 205)(108 206)(109 207)(110 208)(111 209)(112 210)(113 180)(114 181)(115 182)(116 183)(117 184)(118 185)(119 186)(120 187)(121 188)(122 189)(123 190)(124 191)(125 192)(126 193)(127 194)(128 195)(129 196)(130 169)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)
(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 90 151 216)(2 103 152 201)(3 88 153 214)(4 101 154 199)(5 86 155 212)(6 99 156 197)(7 112 157 210)(8 97 158 223)(9 110 159 208)(10 95 160 221)(11 108 161 206)(12 93 162 219)(13 106 163 204)(14 91 164 217)(15 104 165 202)(16 89 166 215)(17 102 167 200)(18 87 168 213)(19 100 141 198)(20 85 142 211)(21 98 143 224)(22 111 144 209)(23 96 145 222)(24 109 146 207)(25 94 147 220)(26 107 148 205)(27 92 149 218)(28 105 150 203)(29 135 82 188)(30 120 83 173)(31 133 84 186)(32 118 57 171)(33 131 58 184)(34 116 59 169)(35 129 60 182)(36 114 61 195)(37 127 62 180)(38 140 63 193)(39 125 64 178)(40 138 65 191)(41 123 66 176)(42 136 67 189)(43 121 68 174)(44 134 69 187)(45 119 70 172)(46 132 71 185)(47 117 72 170)(48 130 73 183)(49 115 74 196)(50 128 75 181)(51 113 76 194)(52 126 77 179)(53 139 78 192)(54 124 79 177)(55 137 80 190)(56 122 81 175)
(1 131)(2 116)(3 129)(4 114)(5 127)(6 140)(7 125)(8 138)(9 123)(10 136)(11 121)(12 134)(13 119)(14 132)(15 117)(16 130)(17 115)(18 128)(19 113)(20 126)(21 139)(22 124)(23 137)(24 122)(25 135)(26 120)(27 133)(28 118)(29 94)(30 107)(31 92)(32 105)(33 90)(34 103)(35 88)(36 101)(37 86)(38 99)(39 112)(40 97)(41 110)(42 95)(43 108)(44 93)(45 106)(46 91)(47 104)(48 89)(49 102)(50 87)(51 100)(52 85)(53 98)(54 111)(55 96)(56 109)(57 203)(58 216)(59 201)(60 214)(61 199)(62 212)(63 197)(64 210)(65 223)(66 208)(67 221)(68 206)(69 219)(70 204)(71 217)(72 202)(73 215)(74 200)(75 213)(76 198)(77 211)(78 224)(79 209)(80 222)(81 207)(82 220)(83 205)(84 218)(141 194)(142 179)(143 192)(144 177)(145 190)(146 175)(147 188)(148 173)(149 186)(150 171)(151 184)(152 169)(153 182)(154 195)(155 180)(156 193)(157 178)(158 191)(159 176)(160 189)(161 174)(162 187)(163 172)(164 185)(165 170)(166 183)(167 196)(168 181)
G:=sub<Sym(224)| (1,151)(2,152)(3,153)(4,154)(5,155)(6,156)(7,157)(8,158)(9,159)(10,160)(11,161)(12,162)(13,163)(14,164)(15,165)(16,166)(17,167)(18,168)(19,141)(20,142)(21,143)(22,144)(23,145)(24,146)(25,147)(26,148)(27,149)(28,150)(29,68)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,84)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,197)(100,198)(101,199)(102,200)(103,201)(104,202)(105,203)(106,204)(107,205)(108,206)(109,207)(110,208)(111,209)(112,210)(113,180)(114,181)(115,182)(116,183)(117,184)(118,185)(119,186)(120,187)(121,188)(122,189)(123,190)(124,191)(125,192)(126,193)(127,194)(128,195)(129,196)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179), (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), (1,90,151,216)(2,103,152,201)(3,88,153,214)(4,101,154,199)(5,86,155,212)(6,99,156,197)(7,112,157,210)(8,97,158,223)(9,110,159,208)(10,95,160,221)(11,108,161,206)(12,93,162,219)(13,106,163,204)(14,91,164,217)(15,104,165,202)(16,89,166,215)(17,102,167,200)(18,87,168,213)(19,100,141,198)(20,85,142,211)(21,98,143,224)(22,111,144,209)(23,96,145,222)(24,109,146,207)(25,94,147,220)(26,107,148,205)(27,92,149,218)(28,105,150,203)(29,135,82,188)(30,120,83,173)(31,133,84,186)(32,118,57,171)(33,131,58,184)(34,116,59,169)(35,129,60,182)(36,114,61,195)(37,127,62,180)(38,140,63,193)(39,125,64,178)(40,138,65,191)(41,123,66,176)(42,136,67,189)(43,121,68,174)(44,134,69,187)(45,119,70,172)(46,132,71,185)(47,117,72,170)(48,130,73,183)(49,115,74,196)(50,128,75,181)(51,113,76,194)(52,126,77,179)(53,139,78,192)(54,124,79,177)(55,137,80,190)(56,122,81,175), (1,131)(2,116)(3,129)(4,114)(5,127)(6,140)(7,125)(8,138)(9,123)(10,136)(11,121)(12,134)(13,119)(14,132)(15,117)(16,130)(17,115)(18,128)(19,113)(20,126)(21,139)(22,124)(23,137)(24,122)(25,135)(26,120)(27,133)(28,118)(29,94)(30,107)(31,92)(32,105)(33,90)(34,103)(35,88)(36,101)(37,86)(38,99)(39,112)(40,97)(41,110)(42,95)(43,108)(44,93)(45,106)(46,91)(47,104)(48,89)(49,102)(50,87)(51,100)(52,85)(53,98)(54,111)(55,96)(56,109)(57,203)(58,216)(59,201)(60,214)(61,199)(62,212)(63,197)(64,210)(65,223)(66,208)(67,221)(68,206)(69,219)(70,204)(71,217)(72,202)(73,215)(74,200)(75,213)(76,198)(77,211)(78,224)(79,209)(80,222)(81,207)(82,220)(83,205)(84,218)(141,194)(142,179)(143,192)(144,177)(145,190)(146,175)(147,188)(148,173)(149,186)(150,171)(151,184)(152,169)(153,182)(154,195)(155,180)(156,193)(157,178)(158,191)(159,176)(160,189)(161,174)(162,187)(163,172)(164,185)(165,170)(166,183)(167,196)(168,181)>;
G:=Group( (1,151)(2,152)(3,153)(4,154)(5,155)(6,156)(7,157)(8,158)(9,159)(10,160)(11,161)(12,162)(13,163)(14,164)(15,165)(16,166)(17,167)(18,168)(19,141)(20,142)(21,143)(22,144)(23,145)(24,146)(25,147)(26,148)(27,149)(28,150)(29,68)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,84)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,197)(100,198)(101,199)(102,200)(103,201)(104,202)(105,203)(106,204)(107,205)(108,206)(109,207)(110,208)(111,209)(112,210)(113,180)(114,181)(115,182)(116,183)(117,184)(118,185)(119,186)(120,187)(121,188)(122,189)(123,190)(124,191)(125,192)(126,193)(127,194)(128,195)(129,196)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179), (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), (1,90,151,216)(2,103,152,201)(3,88,153,214)(4,101,154,199)(5,86,155,212)(6,99,156,197)(7,112,157,210)(8,97,158,223)(9,110,159,208)(10,95,160,221)(11,108,161,206)(12,93,162,219)(13,106,163,204)(14,91,164,217)(15,104,165,202)(16,89,166,215)(17,102,167,200)(18,87,168,213)(19,100,141,198)(20,85,142,211)(21,98,143,224)(22,111,144,209)(23,96,145,222)(24,109,146,207)(25,94,147,220)(26,107,148,205)(27,92,149,218)(28,105,150,203)(29,135,82,188)(30,120,83,173)(31,133,84,186)(32,118,57,171)(33,131,58,184)(34,116,59,169)(35,129,60,182)(36,114,61,195)(37,127,62,180)(38,140,63,193)(39,125,64,178)(40,138,65,191)(41,123,66,176)(42,136,67,189)(43,121,68,174)(44,134,69,187)(45,119,70,172)(46,132,71,185)(47,117,72,170)(48,130,73,183)(49,115,74,196)(50,128,75,181)(51,113,76,194)(52,126,77,179)(53,139,78,192)(54,124,79,177)(55,137,80,190)(56,122,81,175), (1,131)(2,116)(3,129)(4,114)(5,127)(6,140)(7,125)(8,138)(9,123)(10,136)(11,121)(12,134)(13,119)(14,132)(15,117)(16,130)(17,115)(18,128)(19,113)(20,126)(21,139)(22,124)(23,137)(24,122)(25,135)(26,120)(27,133)(28,118)(29,94)(30,107)(31,92)(32,105)(33,90)(34,103)(35,88)(36,101)(37,86)(38,99)(39,112)(40,97)(41,110)(42,95)(43,108)(44,93)(45,106)(46,91)(47,104)(48,89)(49,102)(50,87)(51,100)(52,85)(53,98)(54,111)(55,96)(56,109)(57,203)(58,216)(59,201)(60,214)(61,199)(62,212)(63,197)(64,210)(65,223)(66,208)(67,221)(68,206)(69,219)(70,204)(71,217)(72,202)(73,215)(74,200)(75,213)(76,198)(77,211)(78,224)(79,209)(80,222)(81,207)(82,220)(83,205)(84,218)(141,194)(142,179)(143,192)(144,177)(145,190)(146,175)(147,188)(148,173)(149,186)(150,171)(151,184)(152,169)(153,182)(154,195)(155,180)(156,193)(157,178)(158,191)(159,176)(160,189)(161,174)(162,187)(163,172)(164,185)(165,170)(166,183)(167,196)(168,181) );
G=PermutationGroup([[(1,151),(2,152),(3,153),(4,154),(5,155),(6,156),(7,157),(8,158),(9,159),(10,160),(11,161),(12,162),(13,163),(14,164),(15,165),(16,166),(17,167),(18,168),(19,141),(20,142),(21,143),(22,144),(23,145),(24,146),(25,147),(26,148),(27,149),(28,150),(29,68),(30,69),(31,70),(32,71),(33,72),(34,73),(35,74),(36,75),(37,76),(38,77),(39,78),(40,79),(41,80),(42,81),(43,82),(44,83),(45,84),(46,57),(47,58),(48,59),(49,60),(50,61),(51,62),(52,63),(53,64),(54,65),(55,66),(56,67),(85,211),(86,212),(87,213),(88,214),(89,215),(90,216),(91,217),(92,218),(93,219),(94,220),(95,221),(96,222),(97,223),(98,224),(99,197),(100,198),(101,199),(102,200),(103,201),(104,202),(105,203),(106,204),(107,205),(108,206),(109,207),(110,208),(111,209),(112,210),(113,180),(114,181),(115,182),(116,183),(117,184),(118,185),(119,186),(120,187),(121,188),(122,189),(123,190),(124,191),(125,192),(126,193),(127,194),(128,195),(129,196),(130,169),(131,170),(132,171),(133,172),(134,173),(135,174),(136,175),(137,176),(138,177),(139,178),(140,179)], [(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)], [(1,90,151,216),(2,103,152,201),(3,88,153,214),(4,101,154,199),(5,86,155,212),(6,99,156,197),(7,112,157,210),(8,97,158,223),(9,110,159,208),(10,95,160,221),(11,108,161,206),(12,93,162,219),(13,106,163,204),(14,91,164,217),(15,104,165,202),(16,89,166,215),(17,102,167,200),(18,87,168,213),(19,100,141,198),(20,85,142,211),(21,98,143,224),(22,111,144,209),(23,96,145,222),(24,109,146,207),(25,94,147,220),(26,107,148,205),(27,92,149,218),(28,105,150,203),(29,135,82,188),(30,120,83,173),(31,133,84,186),(32,118,57,171),(33,131,58,184),(34,116,59,169),(35,129,60,182),(36,114,61,195),(37,127,62,180),(38,140,63,193),(39,125,64,178),(40,138,65,191),(41,123,66,176),(42,136,67,189),(43,121,68,174),(44,134,69,187),(45,119,70,172),(46,132,71,185),(47,117,72,170),(48,130,73,183),(49,115,74,196),(50,128,75,181),(51,113,76,194),(52,126,77,179),(53,139,78,192),(54,124,79,177),(55,137,80,190),(56,122,81,175)], [(1,131),(2,116),(3,129),(4,114),(5,127),(6,140),(7,125),(8,138),(9,123),(10,136),(11,121),(12,134),(13,119),(14,132),(15,117),(16,130),(17,115),(18,128),(19,113),(20,126),(21,139),(22,124),(23,137),(24,122),(25,135),(26,120),(27,133),(28,118),(29,94),(30,107),(31,92),(32,105),(33,90),(34,103),(35,88),(36,101),(37,86),(38,99),(39,112),(40,97),(41,110),(42,95),(43,108),(44,93),(45,106),(46,91),(47,104),(48,89),(49,102),(50,87),(51,100),(52,85),(53,98),(54,111),(55,96),(56,109),(57,203),(58,216),(59,201),(60,214),(61,199),(62,212),(63,197),(64,210),(65,223),(66,208),(67,221),(68,206),(69,219),(70,204),(71,217),(72,202),(73,215),(74,200),(75,213),(76,198),(77,211),(78,224),(79,209),(80,222),(81,207),(82,220),(83,205),(84,218),(141,194),(142,179),(143,192),(144,177),(145,190),(146,175),(147,188),(148,173),(149,186),(150,171),(151,184),(152,169),(153,182),(154,195),(155,180),(156,193),(157,178),(158,191),(159,176),(160,189),(161,174),(162,187),(163,172),(164,185),(165,170),(166,183),(167,196),(168,181)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 28A | ··· | 28L | 28M | ··· | 28AD |
| order | 1 | 2 | 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 | 4 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | D7×C4○D4 |
| kernel | (C2×C28)⋊17D4 | C2×C4×Dic7 | C4×C7⋊D4 | C28.17D4 | Dic7⋊D4 | C28⋊D4 | Dic7⋊Q8 | C28.23D4 | C2×C4○D28 | C14×C4○D4 | C2×C28 | C2×C4○D4 | Dic7 | C22×C4 | C2×D4 | C2×Q8 | C2×C4 | C2 |
| # reps | 1 | 1 | 4 | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 8 | 9 | 9 | 3 | 24 | 12 |
Matrix representation of (C2×C28)⋊17D4 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 28 |
| 28 | 3 | 0 | 0 |
| 26 | 8 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 17 | 0 | 0 | 0 |
| 22 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 17 |
| 27 | 11 | 0 | 0 |
| 5 | 2 | 0 | 0 |
| 0 | 0 | 0 | 12 |
| 0 | 0 | 17 | 0 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,1,0,0,0,0,28],[28,26,0,0,3,8,0,0,0,0,12,0,0,0,0,12],[17,22,0,0,0,12,0,0,0,0,12,0,0,0,0,17],[27,5,0,0,11,2,0,0,0,0,0,17,0,0,12,0] >;
(C2×C28)⋊17D4 in GAP, Magma, Sage, TeX
(C_2\times C_{28})\rtimes_{17}D_4 % in TeX
G:=Group("(C2xC28):17D4"); // GroupNames label
G:=SmallGroup(448,1285);
// by ID
G=gap.SmallGroup(448,1285);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,d*a*d=a*b^14,c*b*c^-1=d*b*d=b^13,d*c*d=c^-1>;
// generators/relations