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×C28).889C23, (C2×C14).318C24, C14.168(C22×D4), (C22×C4).288D14, 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, (C14×C4○D4)⋊10C2, (C2×C4○D28)⋊32C2, (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
Subgroups: 1300 in 310 conjugacy classes, 115 normal (31 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×4], C4 [×10], C22, C22 [×2], C22 [×14], C7, C2×C4 [×2], C2×C4 [×6], C2×C4 [×18], D4 [×20], Q8 [×4], C23, C23 [×2], C23 [×2], D7 [×2], C14, C14 [×2], C14 [×4], C42 [×4], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4, C22×C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×2], C2×D4 [×7], C2×Q8, C2×Q8, C4○D4 [×8], Dic7 [×4], Dic7 [×4], C28 [×4], C28 [×2], D14 [×6], C2×C14, C2×C14 [×2], C2×C14 [×8], C2×C42, C4×D4 [×4], C4⋊D4 [×4], C4.4D4 [×2], C4⋊1D4, C4⋊Q8, C2×C4○D4, C2×C4○D4, Dic14 [×2], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C2×Dic7 [×4], C7⋊D4 [×12], C2×C28 [×2], C2×C28 [×6], C2×C28 [×4], C7×D4 [×6], C7×Q8 [×2], C22×D7 [×2], C22×C14, C22×C14 [×2], C22.26C24, C4×Dic7 [×2], C4×Dic7 [×2], Dic7⋊C4 [×4], D14⋊C4 [×4], C23.D7 [×4], C2×Dic14, C2×C4×D7 [×2], C2×D28, C4○D28 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×6], C22×C28, C22×C28 [×2], D4×C14, D4×C14 [×2], Q8×C14, C7×C4○D4 [×4], C2×C4×Dic7, C4×C7⋊D4 [×4], C28.17D4, Dic7⋊D4 [×4], C28⋊D4, Dic7⋊Q8, C28.23D4, C2×C4○D28, C14×C4○D4, (C2×C28)⋊17D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C22×D4, C2×C4○D4 [×2], C7⋊D4 [×4], C22×D7 [×7], C22.26C24, C2×C7⋊D4 [×6], C23×D7, D7×C4○D4 [×2], C22×C7⋊D4, (C2×C28)⋊17D4
Generators and relations
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, dad=ab14, cbc-1=dbd=b13, dcd=c-1 >
►On 224 points
Generators in S224
(1 93)(2 94)(3 95)(4 96)(5 97)(6 98)(7 99)(8 100)(9 101)(10 102)(11 103)(12 104)(13 105)(14 106)(15 107)(16 108)(17 109)(18 110)(19 111)(20 112)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 91)(28 92)(29 144)(30 145)(31 146)(32 147)(33 148)(34 149)(35 150)(36 151)(37 152)(38 153)(39 154)(40 155)(41 156)(42 157)(43 158)(44 159)(45 160)(46 161)(47 162)(48 163)(49 164)(50 165)(51 166)(52 167)(53 168)(54 141)(55 142)(56 143)(57 201)(58 202)(59 203)(60 204)(61 205)(62 206)(63 207)(64 208)(65 209)(66 210)(67 211)(68 212)(69 213)(70 214)(71 215)(72 216)(73 217)(74 218)(75 219)(76 220)(77 221)(78 222)(79 223)(80 224)(81 197)(82 198)(83 199)(84 200)(113 181)(114 182)(115 183)(116 184)(117 185)(118 186)(119 187)(120 188)(121 189)(122 190)(123 191)(124 192)(125 193)(126 194)(127 195)(128 196)(129 169)(130 170)(131 171)(132 172)(133 173)(134 174)(135 175)(136 176)(137 177)(138 178)(139 179)(140 180)
(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)
(1 218 93 74)(2 203 94 59)(3 216 95 72)(4 201 96 57)(5 214 97 70)(6 199 98 83)(7 212 99 68)(8 197 100 81)(9 210 101 66)(10 223 102 79)(11 208 103 64)(12 221 104 77)(13 206 105 62)(14 219 106 75)(15 204 107 60)(16 217 108 73)(17 202 109 58)(18 215 110 71)(19 200 111 84)(20 213 112 69)(21 198 85 82)(22 211 86 67)(23 224 87 80)(24 209 88 65)(25 222 89 78)(26 207 90 63)(27 220 91 76)(28 205 92 61)(29 192 158 138)(30 177 159 123)(31 190 160 136)(32 175 161 121)(33 188 162 134)(34 173 163 119)(35 186 164 132)(36 171 165 117)(37 184 166 130)(38 169 167 115)(39 182 168 128)(40 195 141 113)(41 180 142 126)(42 193 143 139)(43 178 144 124)(44 191 145 137)(45 176 146 122)(46 189 147 135)(47 174 148 120)(48 187 149 133)(49 172 150 118)(50 185 151 131)(51 170 152 116)(52 183 153 129)(53 196 154 114)(54 181 155 127)(55 194 156 140)(56 179 157 125)
(1 138)(2 123)(3 136)(4 121)(5 134)(6 119)(7 132)(8 117)(9 130)(10 115)(11 128)(12 113)(13 126)(14 139)(15 124)(16 137)(17 122)(18 135)(19 120)(20 133)(21 118)(22 131)(23 116)(24 129)(25 114)(26 127)(27 140)(28 125)(29 74)(30 59)(31 72)(32 57)(33 70)(34 83)(35 68)(36 81)(37 66)(38 79)(39 64)(40 77)(41 62)(42 75)(43 60)(44 73)(45 58)(46 71)(47 84)(48 69)(49 82)(50 67)(51 80)(52 65)(53 78)(54 63)(55 76)(56 61)(85 172)(86 185)(87 170)(88 183)(89 196)(90 181)(91 194)(92 179)(93 192)(94 177)(95 190)(96 175)(97 188)(98 173)(99 186)(100 171)(101 184)(102 169)(103 182)(104 195)(105 180)(106 193)(107 178)(108 191)(109 176)(110 189)(111 174)(112 187)(141 221)(142 206)(143 219)(144 204)(145 217)(146 202)(147 215)(148 200)(149 213)(150 198)(151 211)(152 224)(153 209)(154 222)(155 207)(156 220)(157 205)(158 218)(159 203)(160 216)(161 201)(162 214)(163 199)(164 212)(165 197)(166 210)(167 223)(168 208)
G:=sub<Sym(224)| (1,93)(2,94)(3,95)(4,96)(5,97)(6,98)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,107)(16,108)(17,109)(18,110)(19,111)(20,112)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,144)(30,145)(31,146)(32,147)(33,148)(34,149)(35,150)(36,151)(37,152)(38,153)(39,154)(40,155)(41,156)(42,157)(43,158)(44,159)(45,160)(46,161)(47,162)(48,163)(49,164)(50,165)(51,166)(52,167)(53,168)(54,141)(55,142)(56,143)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(113,181)(114,182)(115,183)(116,184)(117,185)(118,186)(119,187)(120,188)(121,189)(122,190)(123,191)(124,192)(125,193)(126,194)(127,195)(128,196)(129,169)(130,170)(131,171)(132,172)(133,173)(134,174)(135,175)(136,176)(137,177)(138,178)(139,179)(140,180), (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), (1,218,93,74)(2,203,94,59)(3,216,95,72)(4,201,96,57)(5,214,97,70)(6,199,98,83)(7,212,99,68)(8,197,100,81)(9,210,101,66)(10,223,102,79)(11,208,103,64)(12,221,104,77)(13,206,105,62)(14,219,106,75)(15,204,107,60)(16,217,108,73)(17,202,109,58)(18,215,110,71)(19,200,111,84)(20,213,112,69)(21,198,85,82)(22,211,86,67)(23,224,87,80)(24,209,88,65)(25,222,89,78)(26,207,90,63)(27,220,91,76)(28,205,92,61)(29,192,158,138)(30,177,159,123)(31,190,160,136)(32,175,161,121)(33,188,162,134)(34,173,163,119)(35,186,164,132)(36,171,165,117)(37,184,166,130)(38,169,167,115)(39,182,168,128)(40,195,141,113)(41,180,142,126)(42,193,143,139)(43,178,144,124)(44,191,145,137)(45,176,146,122)(46,189,147,135)(47,174,148,120)(48,187,149,133)(49,172,150,118)(50,185,151,131)(51,170,152,116)(52,183,153,129)(53,196,154,114)(54,181,155,127)(55,194,156,140)(56,179,157,125), (1,138)(2,123)(3,136)(4,121)(5,134)(6,119)(7,132)(8,117)(9,130)(10,115)(11,128)(12,113)(13,126)(14,139)(15,124)(16,137)(17,122)(18,135)(19,120)(20,133)(21,118)(22,131)(23,116)(24,129)(25,114)(26,127)(27,140)(28,125)(29,74)(30,59)(31,72)(32,57)(33,70)(34,83)(35,68)(36,81)(37,66)(38,79)(39,64)(40,77)(41,62)(42,75)(43,60)(44,73)(45,58)(46,71)(47,84)(48,69)(49,82)(50,67)(51,80)(52,65)(53,78)(54,63)(55,76)(56,61)(85,172)(86,185)(87,170)(88,183)(89,196)(90,181)(91,194)(92,179)(93,192)(94,177)(95,190)(96,175)(97,188)(98,173)(99,186)(100,171)(101,184)(102,169)(103,182)(104,195)(105,180)(106,193)(107,178)(108,191)(109,176)(110,189)(111,174)(112,187)(141,221)(142,206)(143,219)(144,204)(145,217)(146,202)(147,215)(148,200)(149,213)(150,198)(151,211)(152,224)(153,209)(154,222)(155,207)(156,220)(157,205)(158,218)(159,203)(160,216)(161,201)(162,214)(163,199)(164,212)(165,197)(166,210)(167,223)(168,208)>;
G:=Group( (1,93)(2,94)(3,95)(4,96)(5,97)(6,98)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,107)(16,108)(17,109)(18,110)(19,111)(20,112)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,144)(30,145)(31,146)(32,147)(33,148)(34,149)(35,150)(36,151)(37,152)(38,153)(39,154)(40,155)(41,156)(42,157)(43,158)(44,159)(45,160)(46,161)(47,162)(48,163)(49,164)(50,165)(51,166)(52,167)(53,168)(54,141)(55,142)(56,143)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(113,181)(114,182)(115,183)(116,184)(117,185)(118,186)(119,187)(120,188)(121,189)(122,190)(123,191)(124,192)(125,193)(126,194)(127,195)(128,196)(129,169)(130,170)(131,171)(132,172)(133,173)(134,174)(135,175)(136,176)(137,177)(138,178)(139,179)(140,180), (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), (1,218,93,74)(2,203,94,59)(3,216,95,72)(4,201,96,57)(5,214,97,70)(6,199,98,83)(7,212,99,68)(8,197,100,81)(9,210,101,66)(10,223,102,79)(11,208,103,64)(12,221,104,77)(13,206,105,62)(14,219,106,75)(15,204,107,60)(16,217,108,73)(17,202,109,58)(18,215,110,71)(19,200,111,84)(20,213,112,69)(21,198,85,82)(22,211,86,67)(23,224,87,80)(24,209,88,65)(25,222,89,78)(26,207,90,63)(27,220,91,76)(28,205,92,61)(29,192,158,138)(30,177,159,123)(31,190,160,136)(32,175,161,121)(33,188,162,134)(34,173,163,119)(35,186,164,132)(36,171,165,117)(37,184,166,130)(38,169,167,115)(39,182,168,128)(40,195,141,113)(41,180,142,126)(42,193,143,139)(43,178,144,124)(44,191,145,137)(45,176,146,122)(46,189,147,135)(47,174,148,120)(48,187,149,133)(49,172,150,118)(50,185,151,131)(51,170,152,116)(52,183,153,129)(53,196,154,114)(54,181,155,127)(55,194,156,140)(56,179,157,125), (1,138)(2,123)(3,136)(4,121)(5,134)(6,119)(7,132)(8,117)(9,130)(10,115)(11,128)(12,113)(13,126)(14,139)(15,124)(16,137)(17,122)(18,135)(19,120)(20,133)(21,118)(22,131)(23,116)(24,129)(25,114)(26,127)(27,140)(28,125)(29,74)(30,59)(31,72)(32,57)(33,70)(34,83)(35,68)(36,81)(37,66)(38,79)(39,64)(40,77)(41,62)(42,75)(43,60)(44,73)(45,58)(46,71)(47,84)(48,69)(49,82)(50,67)(51,80)(52,65)(53,78)(54,63)(55,76)(56,61)(85,172)(86,185)(87,170)(88,183)(89,196)(90,181)(91,194)(92,179)(93,192)(94,177)(95,190)(96,175)(97,188)(98,173)(99,186)(100,171)(101,184)(102,169)(103,182)(104,195)(105,180)(106,193)(107,178)(108,191)(109,176)(110,189)(111,174)(112,187)(141,221)(142,206)(143,219)(144,204)(145,217)(146,202)(147,215)(148,200)(149,213)(150,198)(151,211)(152,224)(153,209)(154,222)(155,207)(156,220)(157,205)(158,218)(159,203)(160,216)(161,201)(162,214)(163,199)(164,212)(165,197)(166,210)(167,223)(168,208) );
G=PermutationGroup([(1,93),(2,94),(3,95),(4,96),(5,97),(6,98),(7,99),(8,100),(9,101),(10,102),(11,103),(12,104),(13,105),(14,106),(15,107),(16,108),(17,109),(18,110),(19,111),(20,112),(21,85),(22,86),(23,87),(24,88),(25,89),(26,90),(27,91),(28,92),(29,144),(30,145),(31,146),(32,147),(33,148),(34,149),(35,150),(36,151),(37,152),(38,153),(39,154),(40,155),(41,156),(42,157),(43,158),(44,159),(45,160),(46,161),(47,162),(48,163),(49,164),(50,165),(51,166),(52,167),(53,168),(54,141),(55,142),(56,143),(57,201),(58,202),(59,203),(60,204),(61,205),(62,206),(63,207),(64,208),(65,209),(66,210),(67,211),(68,212),(69,213),(70,214),(71,215),(72,216),(73,217),(74,218),(75,219),(76,220),(77,221),(78,222),(79,223),(80,224),(81,197),(82,198),(83,199),(84,200),(113,181),(114,182),(115,183),(116,184),(117,185),(118,186),(119,187),(120,188),(121,189),(122,190),(123,191),(124,192),(125,193),(126,194),(127,195),(128,196),(129,169),(130,170),(131,171),(132,172),(133,173),(134,174),(135,175),(136,176),(137,177),(138,178),(139,179),(140,180)], [(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)], [(1,218,93,74),(2,203,94,59),(3,216,95,72),(4,201,96,57),(5,214,97,70),(6,199,98,83),(7,212,99,68),(8,197,100,81),(9,210,101,66),(10,223,102,79),(11,208,103,64),(12,221,104,77),(13,206,105,62),(14,219,106,75),(15,204,107,60),(16,217,108,73),(17,202,109,58),(18,215,110,71),(19,200,111,84),(20,213,112,69),(21,198,85,82),(22,211,86,67),(23,224,87,80),(24,209,88,65),(25,222,89,78),(26,207,90,63),(27,220,91,76),(28,205,92,61),(29,192,158,138),(30,177,159,123),(31,190,160,136),(32,175,161,121),(33,188,162,134),(34,173,163,119),(35,186,164,132),(36,171,165,117),(37,184,166,130),(38,169,167,115),(39,182,168,128),(40,195,141,113),(41,180,142,126),(42,193,143,139),(43,178,144,124),(44,191,145,137),(45,176,146,122),(46,189,147,135),(47,174,148,120),(48,187,149,133),(49,172,150,118),(50,185,151,131),(51,170,152,116),(52,183,153,129),(53,196,154,114),(54,181,155,127),(55,194,156,140),(56,179,157,125)], [(1,138),(2,123),(3,136),(4,121),(5,134),(6,119),(7,132),(8,117),(9,130),(10,115),(11,128),(12,113),(13,126),(14,139),(15,124),(16,137),(17,122),(18,135),(19,120),(20,133),(21,118),(22,131),(23,116),(24,129),(25,114),(26,127),(27,140),(28,125),(29,74),(30,59),(31,72),(32,57),(33,70),(34,83),(35,68),(36,81),(37,66),(38,79),(39,64),(40,77),(41,62),(42,75),(43,60),(44,73),(45,58),(46,71),(47,84),(48,69),(49,82),(50,67),(51,80),(52,65),(53,78),(54,63),(55,76),(56,61),(85,172),(86,185),(87,170),(88,183),(89,196),(90,181),(91,194),(92,179),(93,192),(94,177),(95,190),(96,175),(97,188),(98,173),(99,186),(100,171),(101,184),(102,169),(103,182),(104,195),(105,180),(106,193),(107,178),(108,191),(109,176),(110,189),(111,174),(112,187),(141,221),(142,206),(143,219),(144,204),(145,217),(146,202),(147,215),(148,200),(149,213),(150,198),(151,211),(152,224),(153,209),(154,222),(155,207),(156,220),(157,205),(158,218),(159,203),(160,216),(161,201),(162,214),(163,199),(164,212),(165,197),(166,210),(167,223),(168,208)])
Matrix representation ►G ⊆ 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] >;
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 |
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
×
⋊
ℤ
𝔽
○
≀