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G = C2×C28⋊D4  order 448 = 26·7

Direct product of C2 and C28⋊D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C28⋊D4, C24.40D14, C28⋊9(C2×D4), (C2×C28)⋊13D4, (C2×D4)⋊39D14, Dic7⋊2(C2×D4), (C22×D4)⋊9D7, C14⋊2(C4⋊1D4), (C2×Dic7)⋊14D4, (D4×C14)⋊44C22, (C22×D28)⋊19C2, (C2×D28)⋊56C22, C22.149(D4×D7), (C2×C14).298C24, (C2×C28).544C23, (C4×Dic7)⋊68C22, (C22×C4).380D14, C14.145(C22×D4), (C23×C14).78C22, (C23×D7).77C22, C23.135(C22×D7), C22.311(C23×D7), (C22×C14).232C23, (C22×C28).276C22, (C2×Dic7).285C23, (C22×D7).129C23, (C22×Dic7).232C22, (D4×C2×C14)⋊6C2, C7⋊3(C2×C4⋊1D4), C4⋊1(C2×C7⋊D4), C2.105(C2×D4×D7), (C2×C4×Dic7)⋊12C2, (C2×C4)⋊10(C7⋊D4), (C2×C14).581(C2×D4), (C22×C7⋊D4)⋊16C2, (C2×C7⋊D4)⋊47C22, C2.18(C22×C7⋊D4), (C2×C4).627(C22×D7), C22.111(C2×C7⋊D4), SmallGroup(448,1256)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C2×C28⋊D4
Chief series
C1 — C7 — C14 — C2×C14 — C22×D7 — C23×D7 — C22×D28 — C2×C28⋊D4
Lower central
C7 — C2×C14 — C2×C28⋊D4

Subgroups: 2580 in 498 conjugacy classes, 143 normal (15 characteristic)
C1, C2, C2 [×6], C2 [×8], C4 [×4], C4 [×8], C22, C22 [×6], C22 [×40], C7, C2×C4 [×6], C2×C4 [×12], D4 [×48], C23, C23 [×4], C23 [×28], D7 [×4], C14, C14 [×6], C14 [×4], C42 [×4], C22×C4, C22×C4 [×2], C2×D4 [×4], C2×D4 [×44], C24 [×2], C24 [×2], Dic7 [×8], C28 [×4], D14 [×20], C2×C14, C2×C14 [×6], C2×C14 [×20], C2×C42, C4⋊1D4 [×8], C22×D4, C22×D4 [×5], D28 [×8], C2×Dic7 [×12], C7⋊D4 [×32], C2×C28 [×6], C7×D4 [×8], C22×D7 [×4], C22×D7 [×12], C22×C14, C22×C14 [×4], C22×C14 [×12], C2×C4⋊1D4, C4×Dic7 [×4], C2×D28 [×4], C2×D28 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×16], C2×C7⋊D4 [×16], C22×C28, D4×C14 [×4], D4×C14 [×4], C23×D7 [×2], C23×C14 [×2], C2×C4×Dic7, C28⋊D4 [×8], C22×D28, C22×C7⋊D4 [×4], D4×C2×C14, C2×C28⋊D4

Quotients:
C1, C2 [×15], C22 [×35], D4 [×12], C23 [×15], D7, C2×D4 [×18], C24, D14 [×7], C4⋊1D4 [×4], C22×D4 [×3], C7⋊D4 [×4], C22×D7 [×7], C2×C4⋊1D4, D4×D7 [×4], C2×C7⋊D4 [×6], C23×D7, C28⋊D4 [×4], C2×D4×D7 [×2], C22×C7⋊D4, C2×C28⋊D4

Generators and relations
 G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b13, dbd=b-1, dcd=c-1 >

Smallest permutation representation
►On 224 points
Generators in S224
(1 68)(2 69)(3 70)(4 71)(5 72)(6 73)(7 74)(8 75)(9 76)(10 77)(11 78)(12 79)(13 80)(14 81)(15 82)(16 83)(17 84)(18 57)(19 58)(20 59)(21 60)(22 61)(23 62)(24 63)(25 64)(26 65)(27 66)(28 67)(29 192)(30 193)(31 194)(32 195)(33 196)(34 169)(35 170)(36 171)(37 172)(38 173)(39 174)(40 175)(41 176)(42 177)(43 178)(44 179)(45 180)(46 181)(47 182)(48 183)(49 184)(50 185)(51 186)(52 187)(53 188)(54 189)(55 190)(56 191)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 139)(108 140)(109 113)(110 114)(111 115)(112 116)(141 219)(142 220)(143 221)(144 222)(145 223)(146 224)(147 197)(148 198)(149 199)(150 200)(151 201)(152 202)(153 203)(154 204)(155 205)(156 206)(157 207)(158 208)(159 209)(160 210)(161 211)(162 212)(163 213)(164 214)(165 215)(166 216)(167 217)(168 218)

(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)

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

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

Matrix representation ►G ⊆ GL5(𝔽29)

280000
01000
00100
000280
000028
,
280000
0101700
0182200
000110
0002328
,
10000
082700
0182100
00010
00001
,
10000
0101700
011900
0002819
00001

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,10,18,0,0,0,17,22,0,0,0,0,0,1,23,0,0,0,10,28],[1,0,0,0,0,0,8,18,0,0,0,27,21,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,10,1,0,0,0,17,19,0,0,0,0,0,28,0,0,0,0,19,1] >;
 

88 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O4A4B4C4D4E···4L7A7B7C14A···14U14V···14AS28A···28L
order12···22222222244444···477714···1414···1428···28
size11···1444428282828222214···142222···24···44···4

88 irreducible representations

dim11111122222224
type+++++++++++++
imageC1C2C2C2C2C2D4D4D7D14D14D14C7⋊D4D4×D7
kernelC2×C28⋊D4C2×C4×Dic7C28⋊D4C22×D28C22×C7⋊D4D4×C2×C14C2×Dic7C2×C28C22×D4C22×C4C2×D4C24C2×C4C22
# reps11814184331262412

In GAP, Magma, Sage, TeX 

C_2\times C_{28}\rtimes D_4
 
% in TeX
 
G:=Group("C2xC28:D4");
 
// GroupNames label
 
G:=SmallGroup(448,1256);
 
// by ID
 
G=gap.SmallGroup(448,1256);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,297,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^13,d*b*d=b^-1,d*c*d=c^-1>;
 
// generators/relations
 

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