G = C4⋊(D14⋊C4) order 448 = 26·7
The semidirect product of C4 and D14⋊C4 acting via D14⋊C4/C22×D7=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊3(C4⋊C4), C4⋊3(D14⋊C4), C28⋊1(C22⋊C4), (C2×C4).143D28, (C2×C28).141D4, (C22×D7).9Q8, C22.26(Q8×D7), C2.4(C28⋊2D4), C2.4(C4⋊D28), (C22×D7).57D4, C22.47(C2×D28), C22.110(D4×D7), C14.53(C4⋊D4), C7⋊3(C23.7Q8), C2.3(D14⋊3Q8), C2.5(D14⋊2Q8), (C22×C4).334D14, C14.72(C22⋊Q8), C14.C42⋊19C2, (C23×D7).89C22, C23.295(C22×D7), C14.37(C42⋊C2), C22.59(D4⋊2D7), (C22×C14).351C23, (C22×C28).143C22, C22.27(Q8⋊2D7), (C22×Dic7).58C22, (C2×C4×D7)⋊4C4, (C2×C4⋊C4)⋊5D7, (C14×C4⋊C4)⋊5C2, C2.21(D7×C4⋊C4), C14.20(C2×C4⋊C4), (D7×C22×C4).1C2, (C2×C28).85(C2×C4), (C2×C4⋊Dic7)⋊30C2, C2.15(C2×D14⋊C4), (C2×C4).154(C4×D7), (C2×C14).83(C2×Q8), C22.136(C2×C4×D7), (C2×D14⋊C4).11C2, (C2×C14).451(C2×D4), C14.42(C2×C22⋊C4), C22.66(C2×C7⋊D4), C2.13(C4⋊C4⋊7D7), (C2×C4).184(C7⋊D4), (C2×Dic7).96(C2×C4), (C22×D7).61(C2×C4), (C2×C14).156(C4○D4), (C2×C14).119(C22×C4), SmallGroup(448,521)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊(D14⋊C4)
G = < a,b,c,d | a4=b14=c2=d4=1, ab=ba, ac=ca, dad-1=a-1, cbc=b-1, bd=db, dcd-1=b7c >
Subgroups: 1156 in 234 conjugacy classes, 87 normal (41 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic7, C28, C28, D14, D14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C23×C4, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.7Q8, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C2×C4⋊Dic7, C2×D14⋊C4, C14×C4⋊C4, D7×C22×C4, C4⋊(D14⋊C4)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C2×C22⋊C4, C2×C4⋊C4, C42⋊C2, C4⋊D4, C22⋊Q8, C4×D7, D28, C7⋊D4, C22×D7, C23.7Q8, D14⋊C4, C2×C4×D7, C2×D28, D4×D7, D4⋊2D7, Q8×D7, Q8⋊2D7, C2×C7⋊D4, D7×C4⋊C4, C4⋊C4⋊7D7, C4⋊D28, D14⋊2Q8, C2×D14⋊C4, C28⋊2D4, D14⋊3Q8, C4⋊(D14⋊C4)
►On 224 points
Generators in S224
(1 143 75 211)(2 144 76 212)(3 145 77 213)(4 146 78 214)(5 147 79 215)(6 148 80 216)(7 149 81 217)(8 150 82 218)(9 151 83 219)(10 152 84 220)(11 153 71 221)(12 154 72 222)(13 141 73 223)(14 142 74 224)(15 115 188 202)(16 116 189 203)(17 117 190 204)(18 118 191 205)(19 119 192 206)(20 120 193 207)(21 121 194 208)(22 122 195 209)(23 123 196 210)(24 124 183 197)(25 125 184 198)(26 126 185 199)(27 113 186 200)(28 114 187 201)(29 163 66 105)(30 164 67 106)(31 165 68 107)(32 166 69 108)(33 167 70 109)(34 168 57 110)(35 155 58 111)(36 156 59 112)(37 157 60 99)(38 158 61 100)(39 159 62 101)(40 160 63 102)(41 161 64 103)(42 162 65 104)(43 93 132 182)(44 94 133 169)(45 95 134 170)(46 96 135 171)(47 97 136 172)(48 98 137 173)(49 85 138 174)(50 86 139 175)(51 87 140 176)(52 88 127 177)(53 89 128 178)(54 90 129 179)(55 91 130 180)(56 92 131 181)
(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 74)(2 73)(3 72)(4 71)(5 84)(6 83)(7 82)(8 81)(9 80)(10 79)(11 78)(12 77)(13 76)(14 75)(15 192)(16 191)(17 190)(18 189)(19 188)(20 187)(21 186)(22 185)(23 184)(24 183)(25 196)(26 195)(27 194)(28 193)(29 57)(30 70)(31 69)(32 68)(33 67)(34 66)(35 65)(36 64)(37 63)(38 62)(39 61)(40 60)(41 59)(42 58)(43 138)(44 137)(45 136)(46 135)(47 134)(48 133)(49 132)(50 131)(51 130)(52 129)(53 128)(54 127)(55 140)(56 139)(85 182)(86 181)(87 180)(88 179)(89 178)(90 177)(91 176)(92 175)(93 174)(94 173)(95 172)(96 171)(97 170)(98 169)(99 160)(100 159)(101 158)(102 157)(103 156)(104 155)(105 168)(106 167)(107 166)(108 165)(109 164)(110 163)(111 162)(112 161)(113 208)(114 207)(115 206)(116 205)(117 204)(118 203)(119 202)(120 201)(121 200)(122 199)(123 198)(124 197)(125 210)(126 209)(141 212)(142 211)(143 224)(144 223)(145 222)(146 221)(147 220)(148 219)(149 218)(150 217)(151 216)(152 215)(153 214)(154 213)
(1 201 32 93)(2 202 33 94)(3 203 34 95)(4 204 35 96)(5 205 36 97)(6 206 37 98)(7 207 38 85)(8 208 39 86)(9 209 40 87)(10 210 41 88)(11 197 42 89)(12 198 29 90)(13 199 30 91)(14 200 31 92)(15 109 133 212)(16 110 134 213)(17 111 135 214)(18 112 136 215)(19 99 137 216)(20 100 138 217)(21 101 139 218)(22 102 140 219)(23 103 127 220)(24 104 128 221)(25 105 129 222)(26 106 130 223)(27 107 131 224)(28 108 132 211)(43 143 187 166)(44 144 188 167)(45 145 189 168)(46 146 190 155)(47 147 191 156)(48 148 192 157)(49 149 193 158)(50 150 194 159)(51 151 195 160)(52 152 196 161)(53 153 183 162)(54 154 184 163)(55 141 185 164)(56 142 186 165)(57 170 77 116)(58 171 78 117)(59 172 79 118)(60 173 80 119)(61 174 81 120)(62 175 82 121)(63 176 83 122)(64 177 84 123)(65 178 71 124)(66 179 72 125)(67 180 73 126)(68 181 74 113)(69 182 75 114)(70 169 76 115)
G:=sub<Sym(224)| (1,143,75,211)(2,144,76,212)(3,145,77,213)(4,146,78,214)(5,147,79,215)(6,148,80,216)(7,149,81,217)(8,150,82,218)(9,151,83,219)(10,152,84,220)(11,153,71,221)(12,154,72,222)(13,141,73,223)(14,142,74,224)(15,115,188,202)(16,116,189,203)(17,117,190,204)(18,118,191,205)(19,119,192,206)(20,120,193,207)(21,121,194,208)(22,122,195,209)(23,123,196,210)(24,124,183,197)(25,125,184,198)(26,126,185,199)(27,113,186,200)(28,114,187,201)(29,163,66,105)(30,164,67,106)(31,165,68,107)(32,166,69,108)(33,167,70,109)(34,168,57,110)(35,155,58,111)(36,156,59,112)(37,157,60,99)(38,158,61,100)(39,159,62,101)(40,160,63,102)(41,161,64,103)(42,162,65,104)(43,93,132,182)(44,94,133,169)(45,95,134,170)(46,96,135,171)(47,97,136,172)(48,98,137,173)(49,85,138,174)(50,86,139,175)(51,87,140,176)(52,88,127,177)(53,89,128,178)(54,90,129,179)(55,91,130,180)(56,92,131,181), (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), (1,74)(2,73)(3,72)(4,71)(5,84)(6,83)(7,82)(8,81)(9,80)(10,79)(11,78)(12,77)(13,76)(14,75)(15,192)(16,191)(17,190)(18,189)(19,188)(20,187)(21,186)(22,185)(23,184)(24,183)(25,196)(26,195)(27,194)(28,193)(29,57)(30,70)(31,69)(32,68)(33,67)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,60)(41,59)(42,58)(43,138)(44,137)(45,136)(46,135)(47,134)(48,133)(49,132)(50,131)(51,130)(52,129)(53,128)(54,127)(55,140)(56,139)(85,182)(86,181)(87,180)(88,179)(89,178)(90,177)(91,176)(92,175)(93,174)(94,173)(95,172)(96,171)(97,170)(98,169)(99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,168)(106,167)(107,166)(108,165)(109,164)(110,163)(111,162)(112,161)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)(121,200)(122,199)(123,198)(124,197)(125,210)(126,209)(141,212)(142,211)(143,224)(144,223)(145,222)(146,221)(147,220)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213), (1,201,32,93)(2,202,33,94)(3,203,34,95)(4,204,35,96)(5,205,36,97)(6,206,37,98)(7,207,38,85)(8,208,39,86)(9,209,40,87)(10,210,41,88)(11,197,42,89)(12,198,29,90)(13,199,30,91)(14,200,31,92)(15,109,133,212)(16,110,134,213)(17,111,135,214)(18,112,136,215)(19,99,137,216)(20,100,138,217)(21,101,139,218)(22,102,140,219)(23,103,127,220)(24,104,128,221)(25,105,129,222)(26,106,130,223)(27,107,131,224)(28,108,132,211)(43,143,187,166)(44,144,188,167)(45,145,189,168)(46,146,190,155)(47,147,191,156)(48,148,192,157)(49,149,193,158)(50,150,194,159)(51,151,195,160)(52,152,196,161)(53,153,183,162)(54,154,184,163)(55,141,185,164)(56,142,186,165)(57,170,77,116)(58,171,78,117)(59,172,79,118)(60,173,80,119)(61,174,81,120)(62,175,82,121)(63,176,83,122)(64,177,84,123)(65,178,71,124)(66,179,72,125)(67,180,73,126)(68,181,74,113)(69,182,75,114)(70,169,76,115)>;
G:=Group( (1,143,75,211)(2,144,76,212)(3,145,77,213)(4,146,78,214)(5,147,79,215)(6,148,80,216)(7,149,81,217)(8,150,82,218)(9,151,83,219)(10,152,84,220)(11,153,71,221)(12,154,72,222)(13,141,73,223)(14,142,74,224)(15,115,188,202)(16,116,189,203)(17,117,190,204)(18,118,191,205)(19,119,192,206)(20,120,193,207)(21,121,194,208)(22,122,195,209)(23,123,196,210)(24,124,183,197)(25,125,184,198)(26,126,185,199)(27,113,186,200)(28,114,187,201)(29,163,66,105)(30,164,67,106)(31,165,68,107)(32,166,69,108)(33,167,70,109)(34,168,57,110)(35,155,58,111)(36,156,59,112)(37,157,60,99)(38,158,61,100)(39,159,62,101)(40,160,63,102)(41,161,64,103)(42,162,65,104)(43,93,132,182)(44,94,133,169)(45,95,134,170)(46,96,135,171)(47,97,136,172)(48,98,137,173)(49,85,138,174)(50,86,139,175)(51,87,140,176)(52,88,127,177)(53,89,128,178)(54,90,129,179)(55,91,130,180)(56,92,131,181), (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), (1,74)(2,73)(3,72)(4,71)(5,84)(6,83)(7,82)(8,81)(9,80)(10,79)(11,78)(12,77)(13,76)(14,75)(15,192)(16,191)(17,190)(18,189)(19,188)(20,187)(21,186)(22,185)(23,184)(24,183)(25,196)(26,195)(27,194)(28,193)(29,57)(30,70)(31,69)(32,68)(33,67)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,60)(41,59)(42,58)(43,138)(44,137)(45,136)(46,135)(47,134)(48,133)(49,132)(50,131)(51,130)(52,129)(53,128)(54,127)(55,140)(56,139)(85,182)(86,181)(87,180)(88,179)(89,178)(90,177)(91,176)(92,175)(93,174)(94,173)(95,172)(96,171)(97,170)(98,169)(99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,168)(106,167)(107,166)(108,165)(109,164)(110,163)(111,162)(112,161)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)(121,200)(122,199)(123,198)(124,197)(125,210)(126,209)(141,212)(142,211)(143,224)(144,223)(145,222)(146,221)(147,220)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213), (1,201,32,93)(2,202,33,94)(3,203,34,95)(4,204,35,96)(5,205,36,97)(6,206,37,98)(7,207,38,85)(8,208,39,86)(9,209,40,87)(10,210,41,88)(11,197,42,89)(12,198,29,90)(13,199,30,91)(14,200,31,92)(15,109,133,212)(16,110,134,213)(17,111,135,214)(18,112,136,215)(19,99,137,216)(20,100,138,217)(21,101,139,218)(22,102,140,219)(23,103,127,220)(24,104,128,221)(25,105,129,222)(26,106,130,223)(27,107,131,224)(28,108,132,211)(43,143,187,166)(44,144,188,167)(45,145,189,168)(46,146,190,155)(47,147,191,156)(48,148,192,157)(49,149,193,158)(50,150,194,159)(51,151,195,160)(52,152,196,161)(53,153,183,162)(54,154,184,163)(55,141,185,164)(56,142,186,165)(57,170,77,116)(58,171,78,117)(59,172,79,118)(60,173,80,119)(61,174,81,120)(62,175,82,121)(63,176,83,122)(64,177,84,123)(65,178,71,124)(66,179,72,125)(67,180,73,126)(68,181,74,113)(69,182,75,114)(70,169,76,115) );
G=PermutationGroup([[(1,143,75,211),(2,144,76,212),(3,145,77,213),(4,146,78,214),(5,147,79,215),(6,148,80,216),(7,149,81,217),(8,150,82,218),(9,151,83,219),(10,152,84,220),(11,153,71,221),(12,154,72,222),(13,141,73,223),(14,142,74,224),(15,115,188,202),(16,116,189,203),(17,117,190,204),(18,118,191,205),(19,119,192,206),(20,120,193,207),(21,121,194,208),(22,122,195,209),(23,123,196,210),(24,124,183,197),(25,125,184,198),(26,126,185,199),(27,113,186,200),(28,114,187,201),(29,163,66,105),(30,164,67,106),(31,165,68,107),(32,166,69,108),(33,167,70,109),(34,168,57,110),(35,155,58,111),(36,156,59,112),(37,157,60,99),(38,158,61,100),(39,159,62,101),(40,160,63,102),(41,161,64,103),(42,162,65,104),(43,93,132,182),(44,94,133,169),(45,95,134,170),(46,96,135,171),(47,97,136,172),(48,98,137,173),(49,85,138,174),(50,86,139,175),(51,87,140,176),(52,88,127,177),(53,89,128,178),(54,90,129,179),(55,91,130,180),(56,92,131,181)], [(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)], [(1,74),(2,73),(3,72),(4,71),(5,84),(6,83),(7,82),(8,81),(9,80),(10,79),(11,78),(12,77),(13,76),(14,75),(15,192),(16,191),(17,190),(18,189),(19,188),(20,187),(21,186),(22,185),(23,184),(24,183),(25,196),(26,195),(27,194),(28,193),(29,57),(30,70),(31,69),(32,68),(33,67),(34,66),(35,65),(36,64),(37,63),(38,62),(39,61),(40,60),(41,59),(42,58),(43,138),(44,137),(45,136),(46,135),(47,134),(48,133),(49,132),(50,131),(51,130),(52,129),(53,128),(54,127),(55,140),(56,139),(85,182),(86,181),(87,180),(88,179),(89,178),(90,177),(91,176),(92,175),(93,174),(94,173),(95,172),(96,171),(97,170),(98,169),(99,160),(100,159),(101,158),(102,157),(103,156),(104,155),(105,168),(106,167),(107,166),(108,165),(109,164),(110,163),(111,162),(112,161),(113,208),(114,207),(115,206),(116,205),(117,204),(118,203),(119,202),(120,201),(121,200),(122,199),(123,198),(124,197),(125,210),(126,209),(141,212),(142,211),(143,224),(144,223),(145,222),(146,221),(147,220),(148,219),(149,218),(150,217),(151,216),(152,215),(153,214),(154,213)], [(1,201,32,93),(2,202,33,94),(3,203,34,95),(4,204,35,96),(5,205,36,97),(6,206,37,98),(7,207,38,85),(8,208,39,86),(9,209,40,87),(10,210,41,88),(11,197,42,89),(12,198,29,90),(13,199,30,91),(14,200,31,92),(15,109,133,212),(16,110,134,213),(17,111,135,214),(18,112,136,215),(19,99,137,216),(20,100,138,217),(21,101,139,218),(22,102,140,219),(23,103,127,220),(24,104,128,221),(25,105,129,222),(26,106,130,223),(27,107,131,224),(28,108,132,211),(43,143,187,166),(44,144,188,167),(45,145,189,168),(46,146,190,155),(47,147,191,156),(48,148,192,157),(49,149,193,158),(50,150,194,159),(51,151,195,160),(52,152,196,161),(53,153,183,162),(54,154,184,163),(55,141,185,164),(56,142,186,165),(57,170,77,116),(58,171,78,117),(59,172,79,118),(60,173,80,119),(61,174,81,120),(62,175,82,121),(63,176,83,122),(64,177,84,123),(65,178,71,124),(66,179,72,125),(67,180,73,126),(68,181,74,113),(69,182,75,114),(70,169,76,115)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | C4×D7 | D28 | C7⋊D4 | D4×D7 | D4⋊2D7 | Q8×D7 | Q8⋊2D7 |
| kernel | C4⋊(D14⋊C4) | C14.C42 | C2×C4⋊Dic7 | C2×D14⋊C4 | C14×C4⋊C4 | D7×C22×C4 | C2×C4×D7 | C2×C28 | C22×D7 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 8 | 4 | 2 | 2 | 3 | 4 | 9 | 12 | 12 | 12 | 3 | 3 | 3 | 3 |
Matrix representation of C4⋊(D14⋊C4) ►in GL6(𝔽29)
| 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 | 17 | 15 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 18 | 25 | 0 | 0 | 0 | 0 |
| 4 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 25 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 18 | 25 | 0 | 0 | 0 | 0 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 28 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 6 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 13 | 5 | 0 | 0 | 0 | 0 |
| 24 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 10 |
| 0 | 0 | 0 | 0 | 24 | 14 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,15,12],[18,4,0,0,0,0,25,4,0,0,0,0,0,0,11,25,0,0,0,0,4,25,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[18,1,0,0,0,0,25,11,0,0,0,0,0,0,11,28,0,0,0,0,4,18,0,0,0,0,0,0,1,0,0,0,0,0,6,28],[13,24,0,0,0,0,5,16,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,15,24,0,0,0,0,10,14] >;
C4⋊(D14⋊C4) in GAP, Magma, Sage, TeX
C_4\rtimes (D_{14}\rtimes C_4) % in TeX
G:=Group("C4:(D14:C4)"); // GroupNames label
G:=SmallGroup(448,521);
// by ID
G=gap.SmallGroup(448,521);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,422,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^14=c^2=d^4=1,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c=b^-1,b*d=d*b,d*c*d^-1=b^7*c>;
// generators/relations