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G = C2×C28.48D4  order 448 = 26·7

Direct product of C2 and C28.48D4

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

Aliases: C2×C28.48D4, C23⋊4Dic14, C24.67D14, (C22×C14)⋊7Q8, (C2×C28).477D4, C28.424(C2×D4), C14⋊4(C22⋊Q8), (C23×C4).10D7, (C23×C28).12C2, C4⋊Dic7⋊63C22, C22⋊3(C2×Dic14), C14.19(C22×Q8), (C2×C28).703C23, (C2×C14).282C24, Dic7⋊C4⋊43C22, C14.130(C22×D4), (C22×C4).446D14, (C22×Dic14)⋊12C2, (C2×Dic14)⋊58C22, C22.79(C4○D28), C2.20(C22×Dic14), C23.231(C22×D7), C22.301(C23×D7), (C22×C28).528C22, (C23×C14).104C22, (C22×C14).411C23, (C2×Dic7).148C23, C23.D7.129C22, (C22×Dic7).160C22, C7⋊5(C2×C22⋊Q8), (C2×C14)⋊6(C2×Q8), (C2×C4⋊Dic7)⋊28C2, C2.69(C2×C4○D28), C14.59(C2×C4○D4), C4.120(C2×C7⋊D4), C2.5(C22×C7⋊D4), (C2×Dic7⋊C4)⋊17C2, (C2×C14).571(C2×D4), (C2×C4).262(C7⋊D4), (C2×C4).656(C22×D7), C22.100(C2×C7⋊D4), (C2×C23.D7).23C2, (C2×C14).110(C4○D4), SmallGroup(448,1237)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C2×C28.48D4
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C22×Dic14 — C2×C28.48D4
Lower central
C7 — C2×C14 — C2×C28.48D4

Subgroups: 1092 in 322 conjugacy classes, 143 normal (23 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×4], C4 [×10], C22, C22 [×10], C22 [×12], C7, C2×C4 [×8], C2×C4 [×26], Q8 [×8], C23, C23 [×6], C23 [×4], C14 [×3], C14 [×4], C14 [×4], C22⋊C4 [×8], C4⋊C4 [×12], C22×C4 [×2], C22×C4 [×4], C22×C4 [×8], C2×Q8 [×8], C24, Dic7 [×8], C28 [×4], C28 [×2], C2×C14, C2×C14 [×10], C2×C14 [×12], C2×C22⋊C4 [×2], C2×C4⋊C4 [×3], C22⋊Q8 [×8], C23×C4, C22×Q8, Dic14 [×8], C2×Dic7 [×8], C2×Dic7 [×8], C2×C28 [×8], C2×C28 [×10], C22×C14, C22×C14 [×6], C22×C14 [×4], C2×C22⋊Q8, Dic7⋊C4 [×8], C4⋊Dic7 [×4], C23.D7 [×8], C2×Dic14 [×4], C2×Dic14 [×4], C22×Dic7 [×4], C22×C28 [×2], C22×C28 [×4], C22×C28 [×4], C23×C14, C2×Dic7⋊C4 [×2], C28.48D4 [×8], C2×C4⋊Dic7, C2×C23.D7 [×2], C22×Dic14, C23×C28, C2×C28.48D4

Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], Q8 [×4], C23 [×15], D7, C2×D4 [×6], C2×Q8 [×6], C4○D4 [×2], C24, D14 [×7], C22⋊Q8 [×4], C22×D4, C22×Q8, C2×C4○D4, Dic14 [×4], C7⋊D4 [×4], C22×D7 [×7], C2×C22⋊Q8, C2×Dic14 [×6], C4○D28 [×2], C2×C7⋊D4 [×6], C23×D7, C28.48D4 [×4], C22×Dic14, C2×C4○D28, C22×C7⋊D4, C2×C28.48D4

Generators and relations
 G = < a,b,c,d | a2=b28=c4=1, d2=b14, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b14c-1 >

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

(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)

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

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

Matrix representation ►G ⊆ GL6(𝔽29)

100000
010000
0028000
0002800
000010
000001
,
2100000
18180000
0010000
0015300
000090
00001513
,
14170000
9150000
00112000
00231800
00002123
000068
,
14170000
14150000
0018900
0091100
000086
0000421

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[21,18,0,0,0,0,0,18,0,0,0,0,0,0,10,15,0,0,0,0,0,3,0,0,0,0,0,0,9,15,0,0,0,0,0,13],[14,9,0,0,0,0,17,15,0,0,0,0,0,0,11,23,0,0,0,0,20,18,0,0,0,0,0,0,21,6,0,0,0,0,23,8],[14,14,0,0,0,0,17,15,0,0,0,0,0,0,18,9,0,0,0,0,9,11,0,0,0,0,0,0,8,4,0,0,0,0,6,21] >;
 

124 conjugacy classes

class 1 2A···2G2H2I2J2K4A···4H4I···4P7A7B7C14A···14AS28A···28AV
order12···222224···44···477714···1428···28
size11···122222···228···282222···22···2

124 irreducible representations

dim1111111222222222
type++++++++-+++-
imageC1C2C2C2C2C2C2D4Q8D7C4○D4D14D14C7⋊D4Dic14C4○D28
kernelC2×C28.48D4C2×Dic7⋊C4C28.48D4C2×C4⋊Dic7C2×C23.D7C22×Dic14C23×C28C2×C28C22×C14C23×C4C2×C14C22×C4C24C2×C4C23C22
# reps12812114434183242424

In GAP, Magma, Sage, TeX 

C_2\times C_{28}._{48}D_4
 
% in TeX
 
G:=Group("C2xC28.48D4");
 
// GroupNames label
 
G:=SmallGroup(448,1237);
 
// by ID
 
G=gap.SmallGroup(448,1237);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,184,675,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^2=b^28=c^4=1,d^2=b^14,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^14*c^-1>;
 
// generators/relations
 

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