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G = C4○D28⋊C4order 448 = 26·7

3rd semidirect product of C4○D28 and C4 acting via C4/C2=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C4○D283C4, D2820(C2×C4), (C2×C4).43D28, C4.60(C2×D28), C4⋊C4.226D14, (C2×C28).134D4, C28.140(C2×D4), C14.D824C2, C4.37(D14⋊C4), Dic1418(C2×C4), C14.Q1624C2, C28.60(C22×C4), (C22×C4).93D14, C14.83(C8⋊C22), C28.20(C22⋊C4), (C2×C28).319C23, C22.4(D14⋊C4), (C22×C14).184D4, C23.76(C7⋊D4), C73(C23.36D4), C2.2(D4.D14), C2.2(C28.C23), (C2×D28).233C22, C14.83(C8.C22), (C22×C28).134C22, (C2×Dic14).260C22, (C2×C4⋊C4)⋊2D7, (C14×C4⋊C4)⋊2C2, C4.49(C2×C4×D7), (C2×C4).39(C4×D7), (C2×C28).78(C2×C4), C2.12(C2×D14⋊C4), (C2×C4○D28).6C2, (C2×C7⋊C8).80C22, (C2×C4.Dic7)⋊8C2, (C2×C14).439(C2×D4), C14.39(C2×C22⋊C4), C22.58(C2×C7⋊D4), (C2×C4).182(C7⋊D4), (C7×C4⋊C4).257C22, (C2×C4).419(C22×D7), (C2×C14).58(C22⋊C4), SmallGroup(448,500)

Series: Derived Chief Lower central Upper central

C1C28 — C4○D28⋊C4
C1C7C14C2×C14C2×C28C2×D28C2×C4○D28 — C4○D28⋊C4
C7C14C28 — C4○D28⋊C4
C1C22C22×C4C2×C4⋊C4

Generators and relations for C4○D28⋊C4
 G = < a,b,c,d | a4=c2=d4=1, b14=a2, ab=ba, ac=ca, dad-1=a-1, cbc=a2b13, dbd-1=a2b, dcd-1=b7c >

Subgroups: 772 in 162 conjugacy classes, 63 normal (29 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×6], C7, C8 [×2], C2×C4 [×2], C2×C4 [×4], C2×C4 [×9], D4 [×7], Q8 [×3], C23, C23, D7 [×2], C14 [×3], C14 [×2], C4⋊C4 [×2], C4⋊C4, C2×C8 [×2], M4(2) [×2], C22×C4, C22×C4 [×2], C2×D4 [×2], C2×Q8, C4○D4 [×6], Dic7 [×2], C28 [×2], C28 [×2], C28 [×2], D14 [×4], C2×C14, C2×C14 [×2], C2×C14 [×2], D4⋊C4 [×2], Q8⋊C4 [×2], C2×C4⋊C4, C2×M4(2), C2×C4○D4, C7⋊C8 [×2], Dic14 [×2], Dic14, C4×D7 [×4], D28 [×2], D28, C2×Dic7, C7⋊D4 [×4], C2×C28 [×2], C2×C28 [×4], C2×C28 [×4], C22×D7, C22×C14, C23.36D4, C2×C7⋊C8 [×2], C4.Dic7 [×2], C7×C4⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28 [×4], C4○D28 [×2], C2×C7⋊D4, C22×C28, C22×C28, C14.D8 [×2], C14.Q16 [×2], C2×C4.Dic7, C14×C4⋊C4, C2×C4○D28, C4○D28⋊C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], C23, D7, C22⋊C4 [×4], C22×C4, C2×D4 [×2], D14 [×3], C2×C22⋊C4, C8⋊C22, C8.C22, C4×D7 [×2], D28 [×2], C7⋊D4 [×2], C22×D7, C23.36D4, D14⋊C4 [×4], C2×C4×D7, C2×D28, C2×C7⋊D4, C2×D14⋊C4, D4.D14, C28.C23, C4○D28⋊C4

Smallest permutation representation of C4○D28⋊C4
On 224 points
Generators in S224
(1 8 15 22)(2 9 16 23)(3 10 17 24)(4 11 18 25)(5 12 19 26)(6 13 20 27)(7 14 21 28)(29 36 43 50)(30 37 44 51)(31 38 45 52)(32 39 46 53)(33 40 47 54)(34 41 48 55)(35 42 49 56)(57 64 71 78)(58 65 72 79)(59 66 73 80)(60 67 74 81)(61 68 75 82)(62 69 76 83)(63 70 77 84)(85 92 99 106)(86 93 100 107)(87 94 101 108)(88 95 102 109)(89 96 103 110)(90 97 104 111)(91 98 105 112)(113 134 127 120)(114 135 128 121)(115 136 129 122)(116 137 130 123)(117 138 131 124)(118 139 132 125)(119 140 133 126)(141 162 155 148)(142 163 156 149)(143 164 157 150)(144 165 158 151)(145 166 159 152)(146 167 160 153)(147 168 161 154)(169 190 183 176)(170 191 184 177)(171 192 185 178)(172 193 186 179)(173 194 187 180)(174 195 188 181)(175 196 189 182)(197 218 211 204)(198 219 212 205)(199 220 213 206)(200 221 214 207)(201 222 215 208)(202 223 216 209)(203 224 217 210)
(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)
(1 136)(2 135)(3 134)(4 133)(5 132)(6 131)(7 130)(8 129)(9 128)(10 127)(11 126)(12 125)(13 124)(14 123)(15 122)(16 121)(17 120)(18 119)(19 118)(20 117)(21 116)(22 115)(23 114)(24 113)(25 140)(26 139)(27 138)(28 137)(29 156)(30 155)(31 154)(32 153)(33 152)(34 151)(35 150)(36 149)(37 148)(38 147)(39 146)(40 145)(41 144)(42 143)(43 142)(44 141)(45 168)(46 167)(47 166)(48 165)(49 164)(50 163)(51 162)(52 161)(53 160)(54 159)(55 158)(56 157)(57 192)(58 191)(59 190)(60 189)(61 188)(62 187)(63 186)(64 185)(65 184)(66 183)(67 182)(68 181)(69 180)(70 179)(71 178)(72 177)(73 176)(74 175)(75 174)(76 173)(77 172)(78 171)(79 170)(80 169)(81 196)(82 195)(83 194)(84 193)(85 201)(86 200)(87 199)(88 198)(89 197)(90 224)(91 223)(92 222)(93 221)(94 220)(95 219)(96 218)(97 217)(98 216)(99 215)(100 214)(101 213)(102 212)(103 211)(104 210)(105 209)(106 208)(107 207)(108 206)(109 205)(110 204)(111 203)(112 202)
(1 102 56 62)(2 89 29 77)(3 104 30 64)(4 91 31 79)(5 106 32 66)(6 93 33 81)(7 108 34 68)(8 95 35 83)(9 110 36 70)(10 97 37 57)(11 112 38 72)(12 99 39 59)(13 86 40 74)(14 101 41 61)(15 88 42 76)(16 103 43 63)(17 90 44 78)(18 105 45 65)(19 92 46 80)(20 107 47 67)(21 94 48 82)(22 109 49 69)(23 96 50 84)(24 111 51 71)(25 98 52 58)(26 85 53 73)(27 100 54 60)(28 87 55 75)(113 224 162 171)(114 211 163 186)(115 198 164 173)(116 213 165 188)(117 200 166 175)(118 215 167 190)(119 202 168 177)(120 217 141 192)(121 204 142 179)(122 219 143 194)(123 206 144 181)(124 221 145 196)(125 208 146 183)(126 223 147 170)(127 210 148 185)(128 197 149 172)(129 212 150 187)(130 199 151 174)(131 214 152 189)(132 201 153 176)(133 216 154 191)(134 203 155 178)(135 218 156 193)(136 205 157 180)(137 220 158 195)(138 207 159 182)(139 222 160 169)(140 209 161 184)

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

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

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

82 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I4J7A7B7C8A8B8C8D14A···14U28A···28AJ
order122222224444444444777888814···1428···28
size1111222828222244442828222282828282···24···4

82 irreducible representations

dim11111112222222224444
type+++++++++++++-
imageC1C2C2C2C2C2C4D4D4D7D14D14C4×D7D28C7⋊D4C7⋊D4C8⋊C22C8.C22D4.D14C28.C23
kernelC4○D28⋊C4C14.D8C14.Q16C2×C4.Dic7C14×C4⋊C4C2×C4○D28C4○D28C2×C28C22×C14C2×C4⋊C4C4⋊C4C22×C4C2×C4C2×C4C2×C4C23C14C14C2C2
# reps1221118313631212661166

Matrix representation of C4○D28⋊C4 in GL6(𝔽113)

100000
010000
00011200
001000
00000112
000010
,
11200000
01120000
00010600
007000
0000097
0000160
,
52160000
50610000
0000097
0000160
00010600
007000
,
70340000
32430000
00667400
00744700
00007447
00004739

G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,112,0,0,0,0,0,0,0,0,1,0,0,0,0,112,0],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,7,0,0,0,0,106,0,0,0,0,0,0,0,0,16,0,0,0,0,97,0],[52,50,0,0,0,0,16,61,0,0,0,0,0,0,0,0,0,7,0,0,0,0,106,0,0,0,0,16,0,0,0,0,97,0,0,0],[70,32,0,0,0,0,34,43,0,0,0,0,0,0,66,74,0,0,0,0,74,47,0,0,0,0,0,0,74,47,0,0,0,0,47,39] >;

C4○D28⋊C4 in GAP, Magma, Sage, TeX

C_4\circ D_{28}\rtimes C_4
% in TeX

G:=Group("C4oD28:C4");
// GroupNames label

G:=SmallGroup(448,500);
// by ID

G=gap.SmallGroup(448,500);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,422,387,58,1684,438,102,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=c^2=d^4=1,b^14=a^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c=a^2*b^13,d*b*d^-1=a^2*b,d*c*d^-1=b^7*c>;
// generators/relations

׿
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𝔽