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), C14.58(C23×C4), C42.87(C2×C14), C4.18(C22×C28), C42⋊C2⋊19C14, (C2×C14).337C24, (C2×C28).959C23, C28.163(C22×C4), (C4×C28).371C22, 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), (C2×C4○D4).13C14, (C14×C4○D4).27C2, (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, (C2×C14).32(C22×C4), (C22×C4).99(C2×C14), (C2×C4).134(C22×C14), (C7×C22⋊C4).159C22, SmallGroup(448,1300)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 370 in 310 conjugacy classes, 250 normal (16 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×12], C4 [×6], C22, C22 [×6], C22 [×6], C7, C2×C4, C2×C4 [×23], C2×C4 [×12], D4 [×12], Q8 [×4], C23 [×3], C14, C14 [×2], C14 [×6], C42, C42 [×9], C22⋊C4 [×6], C4⋊C4 [×6], C22×C4 [×9], C2×D4 [×3], C2×Q8, C4○D4 [×8], C28 [×12], C28 [×6], C2×C14, C2×C14 [×6], C2×C14 [×6], C2×C42 [×3], C42⋊C2 [×3], C4×D4 [×6], C4×Q8 [×2], C2×C4○D4, C2×C28, C2×C28 [×23], C2×C28 [×12], C7×D4 [×12], C7×Q8 [×4], C22×C14 [×3], C4×C4○D4, C4×C28, C4×C28 [×9], C7×C22⋊C4 [×6], C7×C4⋊C4 [×6], C22×C28 [×9], D4×C14 [×3], Q8×C14, C7×C4○D4 [×8], C2×C4×C28 [×3], C7×C42⋊C2 [×3], D4×C28 [×6], Q8×C28 [×2], C14×C4○D4, C4○D4×C28
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C7, C2×C4 [×28], C23 [×15], C14 [×15], C22×C4 [×14], C4○D4 [×4], C24, C28 [×8], C2×C14 [×35], C23×C4, C2×C4○D4 [×2], C2×C28 [×28], C22×C14 [×15], C4×C4○D4, C22×C28 [×14], C7×C4○D4 [×4], C23×C14, C23×C28, C14×C4○D4 [×2], C4○D4×C28
Generators and relations
G = < a,b,c,d | a28=b4=d2=1, c2=b2, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b2c >
►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)
(1 161 69 105)(2 162 70 106)(3 163 71 107)(4 164 72 108)(5 165 73 109)(6 166 74 110)(7 167 75 111)(8 168 76 112)(9 141 77 85)(10 142 78 86)(11 143 79 87)(12 144 80 88)(13 145 81 89)(14 146 82 90)(15 147 83 91)(16 148 84 92)(17 149 57 93)(18 150 58 94)(19 151 59 95)(20 152 60 96)(21 153 61 97)(22 154 62 98)(23 155 63 99)(24 156 64 100)(25 157 65 101)(26 158 66 102)(27 159 67 103)(28 160 68 104)(29 207 179 138)(30 208 180 139)(31 209 181 140)(32 210 182 113)(33 211 183 114)(34 212 184 115)(35 213 185 116)(36 214 186 117)(37 215 187 118)(38 216 188 119)(39 217 189 120)(40 218 190 121)(41 219 191 122)(42 220 192 123)(43 221 193 124)(44 222 194 125)(45 223 195 126)(46 224 196 127)(47 197 169 128)(48 198 170 129)(49 199 171 130)(50 200 172 131)(51 201 173 132)(52 202 174 133)(53 203 175 134)(54 204 176 135)(55 205 177 136)(56 206 178 137)
(1 105 69 161)(2 106 70 162)(3 107 71 163)(4 108 72 164)(5 109 73 165)(6 110 74 166)(7 111 75 167)(8 112 76 168)(9 85 77 141)(10 86 78 142)(11 87 79 143)(12 88 80 144)(13 89 81 145)(14 90 82 146)(15 91 83 147)(16 92 84 148)(17 93 57 149)(18 94 58 150)(19 95 59 151)(20 96 60 152)(21 97 61 153)(22 98 62 154)(23 99 63 155)(24 100 64 156)(25 101 65 157)(26 102 66 158)(27 103 67 159)(28 104 68 160)(29 207 179 138)(30 208 180 139)(31 209 181 140)(32 210 182 113)(33 211 183 114)(34 212 184 115)(35 213 185 116)(36 214 186 117)(37 215 187 118)(38 216 188 119)(39 217 189 120)(40 218 190 121)(41 219 191 122)(42 220 192 123)(43 221 193 124)(44 222 194 125)(45 223 195 126)(46 224 196 127)(47 197 169 128)(48 198 170 129)(49 199 171 130)(50 200 172 131)(51 201 173 132)(52 202 174 133)(53 203 175 134)(54 204 176 135)(55 205 177 136)(56 206 178 137)
(1 195)(2 196)(3 169)(4 170)(5 171)(6 172)(7 173)(8 174)(9 175)(10 176)(11 177)(12 178)(13 179)(14 180)(15 181)(16 182)(17 183)(18 184)(19 185)(20 186)(21 187)(22 188)(23 189)(24 190)(25 191)(26 192)(27 193)(28 194)(29 81)(30 82)(31 83)(32 84)(33 57)(34 58)(35 59)(36 60)(37 61)(38 62)(39 63)(40 64)(41 65)(42 66)(43 67)(44 68)(45 69)(46 70)(47 71)(48 72)(49 73)(50 74)(51 75)(52 76)(53 77)(54 78)(55 79)(56 80)(85 203)(86 204)(87 205)(88 206)(89 207)(90 208)(91 209)(92 210)(93 211)(94 212)(95 213)(96 214)(97 215)(98 216)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 197)(108 198)(109 199)(110 200)(111 201)(112 202)(113 148)(114 149)(115 150)(116 151)(117 152)(118 153)(119 154)(120 155)(121 156)(122 157)(123 158)(124 159)(125 160)(126 161)(127 162)(128 163)(129 164)(130 165)(131 166)(132 167)(133 168)(134 141)(135 142)(136 143)(137 144)(138 145)(139 146)(140 147)
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), (1,161,69,105)(2,162,70,106)(3,163,71,107)(4,164,72,108)(5,165,73,109)(6,166,74,110)(7,167,75,111)(8,168,76,112)(9,141,77,85)(10,142,78,86)(11,143,79,87)(12,144,80,88)(13,145,81,89)(14,146,82,90)(15,147,83,91)(16,148,84,92)(17,149,57,93)(18,150,58,94)(19,151,59,95)(20,152,60,96)(21,153,61,97)(22,154,62,98)(23,155,63,99)(24,156,64,100)(25,157,65,101)(26,158,66,102)(27,159,67,103)(28,160,68,104)(29,207,179,138)(30,208,180,139)(31,209,181,140)(32,210,182,113)(33,211,183,114)(34,212,184,115)(35,213,185,116)(36,214,186,117)(37,215,187,118)(38,216,188,119)(39,217,189,120)(40,218,190,121)(41,219,191,122)(42,220,192,123)(43,221,193,124)(44,222,194,125)(45,223,195,126)(46,224,196,127)(47,197,169,128)(48,198,170,129)(49,199,171,130)(50,200,172,131)(51,201,173,132)(52,202,174,133)(53,203,175,134)(54,204,176,135)(55,205,177,136)(56,206,178,137), (1,105,69,161)(2,106,70,162)(3,107,71,163)(4,108,72,164)(5,109,73,165)(6,110,74,166)(7,111,75,167)(8,112,76,168)(9,85,77,141)(10,86,78,142)(11,87,79,143)(12,88,80,144)(13,89,81,145)(14,90,82,146)(15,91,83,147)(16,92,84,148)(17,93,57,149)(18,94,58,150)(19,95,59,151)(20,96,60,152)(21,97,61,153)(22,98,62,154)(23,99,63,155)(24,100,64,156)(25,101,65,157)(26,102,66,158)(27,103,67,159)(28,104,68,160)(29,207,179,138)(30,208,180,139)(31,209,181,140)(32,210,182,113)(33,211,183,114)(34,212,184,115)(35,213,185,116)(36,214,186,117)(37,215,187,118)(38,216,188,119)(39,217,189,120)(40,218,190,121)(41,219,191,122)(42,220,192,123)(43,221,193,124)(44,222,194,125)(45,223,195,126)(46,224,196,127)(47,197,169,128)(48,198,170,129)(49,199,171,130)(50,200,172,131)(51,201,173,132)(52,202,174,133)(53,203,175,134)(54,204,176,135)(55,205,177,136)(56,206,178,137), (1,195)(2,196)(3,169)(4,170)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,177)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,81)(30,82)(31,83)(32,84)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)(48,72)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(85,203)(86,204)(87,205)(88,206)(89,207)(90,208)(91,209)(92,210)(93,211)(94,212)(95,213)(96,214)(97,215)(98,216)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,155)(121,156)(122,157)(123,158)(124,159)(125,160)(126,161)(127,162)(128,163)(129,164)(130,165)(131,166)(132,167)(133,168)(134,141)(135,142)(136,143)(137,144)(138,145)(139,146)(140,147)>;
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), (1,161,69,105)(2,162,70,106)(3,163,71,107)(4,164,72,108)(5,165,73,109)(6,166,74,110)(7,167,75,111)(8,168,76,112)(9,141,77,85)(10,142,78,86)(11,143,79,87)(12,144,80,88)(13,145,81,89)(14,146,82,90)(15,147,83,91)(16,148,84,92)(17,149,57,93)(18,150,58,94)(19,151,59,95)(20,152,60,96)(21,153,61,97)(22,154,62,98)(23,155,63,99)(24,156,64,100)(25,157,65,101)(26,158,66,102)(27,159,67,103)(28,160,68,104)(29,207,179,138)(30,208,180,139)(31,209,181,140)(32,210,182,113)(33,211,183,114)(34,212,184,115)(35,213,185,116)(36,214,186,117)(37,215,187,118)(38,216,188,119)(39,217,189,120)(40,218,190,121)(41,219,191,122)(42,220,192,123)(43,221,193,124)(44,222,194,125)(45,223,195,126)(46,224,196,127)(47,197,169,128)(48,198,170,129)(49,199,171,130)(50,200,172,131)(51,201,173,132)(52,202,174,133)(53,203,175,134)(54,204,176,135)(55,205,177,136)(56,206,178,137), (1,105,69,161)(2,106,70,162)(3,107,71,163)(4,108,72,164)(5,109,73,165)(6,110,74,166)(7,111,75,167)(8,112,76,168)(9,85,77,141)(10,86,78,142)(11,87,79,143)(12,88,80,144)(13,89,81,145)(14,90,82,146)(15,91,83,147)(16,92,84,148)(17,93,57,149)(18,94,58,150)(19,95,59,151)(20,96,60,152)(21,97,61,153)(22,98,62,154)(23,99,63,155)(24,100,64,156)(25,101,65,157)(26,102,66,158)(27,103,67,159)(28,104,68,160)(29,207,179,138)(30,208,180,139)(31,209,181,140)(32,210,182,113)(33,211,183,114)(34,212,184,115)(35,213,185,116)(36,214,186,117)(37,215,187,118)(38,216,188,119)(39,217,189,120)(40,218,190,121)(41,219,191,122)(42,220,192,123)(43,221,193,124)(44,222,194,125)(45,223,195,126)(46,224,196,127)(47,197,169,128)(48,198,170,129)(49,199,171,130)(50,200,172,131)(51,201,173,132)(52,202,174,133)(53,203,175,134)(54,204,176,135)(55,205,177,136)(56,206,178,137), (1,195)(2,196)(3,169)(4,170)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,177)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,81)(30,82)(31,83)(32,84)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)(48,72)(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(85,203)(86,204)(87,205)(88,206)(89,207)(90,208)(91,209)(92,210)(93,211)(94,212)(95,213)(96,214)(97,215)(98,216)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,155)(121,156)(122,157)(123,158)(124,159)(125,160)(126,161)(127,162)(128,163)(129,164)(130,165)(131,166)(132,167)(133,168)(134,141)(135,142)(136,143)(137,144)(138,145)(139,146)(140,147) );
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)], [(1,161,69,105),(2,162,70,106),(3,163,71,107),(4,164,72,108),(5,165,73,109),(6,166,74,110),(7,167,75,111),(8,168,76,112),(9,141,77,85),(10,142,78,86),(11,143,79,87),(12,144,80,88),(13,145,81,89),(14,146,82,90),(15,147,83,91),(16,148,84,92),(17,149,57,93),(18,150,58,94),(19,151,59,95),(20,152,60,96),(21,153,61,97),(22,154,62,98),(23,155,63,99),(24,156,64,100),(25,157,65,101),(26,158,66,102),(27,159,67,103),(28,160,68,104),(29,207,179,138),(30,208,180,139),(31,209,181,140),(32,210,182,113),(33,211,183,114),(34,212,184,115),(35,213,185,116),(36,214,186,117),(37,215,187,118),(38,216,188,119),(39,217,189,120),(40,218,190,121),(41,219,191,122),(42,220,192,123),(43,221,193,124),(44,222,194,125),(45,223,195,126),(46,224,196,127),(47,197,169,128),(48,198,170,129),(49,199,171,130),(50,200,172,131),(51,201,173,132),(52,202,174,133),(53,203,175,134),(54,204,176,135),(55,205,177,136),(56,206,178,137)], [(1,105,69,161),(2,106,70,162),(3,107,71,163),(4,108,72,164),(5,109,73,165),(6,110,74,166),(7,111,75,167),(8,112,76,168),(9,85,77,141),(10,86,78,142),(11,87,79,143),(12,88,80,144),(13,89,81,145),(14,90,82,146),(15,91,83,147),(16,92,84,148),(17,93,57,149),(18,94,58,150),(19,95,59,151),(20,96,60,152),(21,97,61,153),(22,98,62,154),(23,99,63,155),(24,100,64,156),(25,101,65,157),(26,102,66,158),(27,103,67,159),(28,104,68,160),(29,207,179,138),(30,208,180,139),(31,209,181,140),(32,210,182,113),(33,211,183,114),(34,212,184,115),(35,213,185,116),(36,214,186,117),(37,215,187,118),(38,216,188,119),(39,217,189,120),(40,218,190,121),(41,219,191,122),(42,220,192,123),(43,221,193,124),(44,222,194,125),(45,223,195,126),(46,224,196,127),(47,197,169,128),(48,198,170,129),(49,199,171,130),(50,200,172,131),(51,201,173,132),(52,202,174,133),(53,203,175,134),(54,204,176,135),(55,205,177,136),(56,206,178,137)], [(1,195),(2,196),(3,169),(4,170),(5,171),(6,172),(7,173),(8,174),(9,175),(10,176),(11,177),(12,178),(13,179),(14,180),(15,181),(16,182),(17,183),(18,184),(19,185),(20,186),(21,187),(22,188),(23,189),(24,190),(25,191),(26,192),(27,193),(28,194),(29,81),(30,82),(31,83),(32,84),(33,57),(34,58),(35,59),(36,60),(37,61),(38,62),(39,63),(40,64),(41,65),(42,66),(43,67),(44,68),(45,69),(46,70),(47,71),(48,72),(49,73),(50,74),(51,75),(52,76),(53,77),(54,78),(55,79),(56,80),(85,203),(86,204),(87,205),(88,206),(89,207),(90,208),(91,209),(92,210),(93,211),(94,212),(95,213),(96,214),(97,215),(98,216),(99,217),(100,218),(101,219),(102,220),(103,221),(104,222),(105,223),(106,224),(107,197),(108,198),(109,199),(110,200),(111,201),(112,202),(113,148),(114,149),(115,150),(116,151),(117,152),(118,153),(119,154),(120,155),(121,156),(122,157),(123,158),(124,159),(125,160),(126,161),(127,162),(128,163),(129,164),(130,165),(131,166),(132,167),(133,168),(134,141),(135,142),(136,143),(137,144),(138,145),(139,146),(140,147)])
Matrix representation ►G ⊆ 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] >;
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 |
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
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