Copied to
clipboard

?

G = C2×C28⋊7D4  order 448 = 26·7

Direct product of C2 and C28⋊7D4

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

Aliases: C2×C28⋊7D4, C23⋊4D28, C24.71D14, (C2×C28)⋊37D4, C28⋊15(C2×D4), (C23×C4)⋊5D7, (C23×C28)⋊8C2, C22⋊2(C2×D28), C14⋊3(C4⋊D4), (C22×C4)⋊44D14, (C22×C14)⋊15D4, D14⋊C4⋊42C22, (C2×D28)⋊50C22, (C22×D28)⋊12C2, C4⋊Dic7⋊64C22, C2.33(C22×D28), (C2×C14).288C24, (C2×C28).705C23, (C22×C28)⋊60C22, C14.134(C22×D4), C22.83(C4○D28), (C23×D7).75C22, C23.234(C22×D7), C22.303(C23×D7), (C23×C14).110C22, (C22×C14).417C23, (C2×Dic7).150C23, (C22×D7).126C23, (C22×Dic7).162C22, C4⋊4(C2×C7⋊D4), C7⋊4(C2×C4⋊D4), (C2×C14)⋊11(C2×D4), (C2×D14⋊C4)⋊14C2, (C2×C4)⋊16(C7⋊D4), (C2×C4⋊Dic7)⋊29C2, C14.63(C2×C4○D4), C2.71(C2×C4○D28), C2.7(C22×C7⋊D4), (C2×C7⋊D4)⋊42C22, (C22×C7⋊D4)⋊11C2, (C2×C4).658(C22×D7), C22.104(C2×C7⋊D4), (C2×C14).114(C4○D4), SmallGroup(448,1243)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C2×C28⋊7D4
Chief series
C1 — C7 — C14 — C2×C14 — C22×D7 — C23×D7 — C22×D28 — C2×C28⋊7D4
Lower central
C7 — C2×C14 — C2×C28⋊7D4

Subgroups: 2116 in 426 conjugacy classes, 143 normal (23 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×4], C4 [×6], C22, C22 [×10], C22 [×32], C7, C2×C4 [×8], C2×C4 [×18], D4 [×24], C23, C23 [×6], C23 [×20], D7 [×4], C14 [×3], C14 [×4], C14 [×4], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×4], C22×C4 [×6], C2×D4 [×24], C24, C24 [×2], Dic7 [×4], C28 [×4], C28 [×2], D14 [×20], C2×C14, C2×C14 [×10], C2×C14 [×12], C2×C22⋊C4 [×2], C2×C4⋊C4, C4⋊D4 [×8], C23×C4, C22×D4 [×3], D28 [×8], C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×16], C2×C28 [×8], C2×C28 [×10], C22×D7 [×4], C22×D7 [×12], C22×C14, C22×C14 [×6], C22×C14 [×4], C2×C4⋊D4, C4⋊Dic7 [×4], D14⋊C4 [×8], C2×D28 [×4], C2×D28 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×8], C2×C7⋊D4 [×8], C22×C28 [×2], C22×C28 [×4], C22×C28 [×4], C23×D7 [×2], C23×C14, C2×C4⋊Dic7, C2×D14⋊C4 [×2], C28⋊7D4 [×8], C22×D28, C22×C7⋊D4 [×2], C23×C28, C2×C28⋊7D4

Quotients:
C1, C2 [×15], C22 [×35], D4 [×8], C23 [×15], D7, C2×D4 [×12], C4○D4 [×2], C24, D14 [×7], C4⋊D4 [×4], C22×D4 [×2], C2×C4○D4, D28 [×4], C7⋊D4 [×4], C22×D7 [×7], C2×C4⋊D4, C2×D28 [×6], C4○D28 [×2], C2×C7⋊D4 [×6], C23×D7, C28⋊7D4 [×4], C22×D28, C2×C4○D28, C22×C7⋊D4, C2×C28⋊7D4

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

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

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

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

Matrix representation ►G ⊆ GL5(𝔽29)

280000
01000
00100
00010
00001
,
10000
019000
0282600
0002125
000420
,
280000
028700
08100
000259
00084
,
10000
012200
002800
000420
0002125

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,19,28,0,0,0,0,26,0,0,0,0,0,21,4,0,0,0,25,20],[28,0,0,0,0,0,28,8,0,0,0,7,1,0,0,0,0,0,25,8,0,0,0,9,4],[1,0,0,0,0,0,1,0,0,0,0,22,28,0,0,0,0,0,4,21,0,0,0,20,25] >;
 

124 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O4A···4H4I4J4K4L7A7B7C14A···14AS28A···28AV
order12···2222222224···4444477714···1428···28
size11···12222282828282···2282828282222···22···2

124 irreducible representations

dim1111111222222222
type+++++++++++++
imageC1C2C2C2C2C2C2D4D4D7C4○D4D14D14C7⋊D4D28C4○D28
kernelC2×C28⋊7D4C2×C4⋊Dic7C2×D14⋊C4C28⋊7D4C22×D28C22×C7⋊D4C23×C28C2×C28C22×C14C23×C4C2×C14C22×C4C24C2×C4C23C22
# reps11281214434183242424

In GAP, Magma, Sage, TeX 

C_2\times C_{28}\rtimes_7D_4
 
% in TeX
 
G:=Group("C2xC28:7D4");
 
// GroupNames label
 
G:=SmallGroup(448,1243);
 
// by ID
 
G=gap.SmallGroup(448,1243);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,18822]);
 
// 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=d*b*d=b^-1,d*c*d=c^-1>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀