direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C4⋊D4, C4⋊3(D4×C14), C28⋊17(C2×D4), (C2×C28)⋊40D4, C23⋊5(C7×D4), (C23×C4)⋊7C14, C22⋊1(D4×C14), (C23×C28)⋊14C2, (C22×D4)⋊4C14, (C22×C14)⋊14D4, (D4×C14)⋊61C22, C24.15(C2×C14), (C2×C28).655C23, (C2×C14).342C24, (C22×C28)⋊65C22, C14.181(C22×D4), C22.16(C23×C14), C23.69(C22×C14), (C23×C14).12C22, (C22×C14).257C23, C4⋊C4⋊9(C2×C14), C2.5(D4×C2×C14), (D4×C2×C14)⋊19C2, (C2×C4)⋊10(C7×D4), (C14×C4⋊C4)⋊41C2, (C2×C4⋊C4)⋊14C14, (C2×D4)⋊9(C2×C14), (C2×C14)⋊10(C2×D4), C2.5(C14×C4○D4), (C7×C4⋊C4)⋊65C22, (C2×C22⋊C4)⋊9C14, C22⋊C4⋊11(C2×C14), (C14×C22⋊C4)⋊29C2, (C22×C4)⋊18(C2×C14), C14.224(C2×C4○D4), C22.29(C7×C4○D4), (C7×C22⋊C4)⋊65C22, (C2×C4).11(C22×C14), (C2×C14).229(C4○D4), SmallGroup(448,1305)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 706 in 426 conjugacy classes, 194 normal (26 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×4], C4 [×6], C22, C22 [×10], C22 [×32], C7, C2×C4 [×12], C2×C4 [×14], D4 [×24], C23, C23 [×10], C23 [×16], C14 [×3], C14 [×4], C14 [×8], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×6], C22×C4 [×4], C2×D4 [×12], C2×D4 [×12], C24, C24 [×2], C28 [×4], C28 [×6], C2×C14, C2×C14 [×10], C2×C14 [×32], C2×C22⋊C4 [×2], C2×C4⋊C4, C4⋊D4 [×8], C23×C4, C22×D4, C22×D4 [×2], C2×C28 [×12], C2×C28 [×14], C7×D4 [×24], C22×C14, C22×C14 [×10], C22×C14 [×16], C2×C4⋊D4, C7×C22⋊C4 [×8], C7×C4⋊C4 [×4], C22×C28 [×2], C22×C28 [×6], C22×C28 [×4], D4×C14 [×12], D4×C14 [×12], C23×C14, C23×C14 [×2], C14×C22⋊C4 [×2], C14×C4⋊C4, C7×C4⋊D4 [×8], C23×C28, D4×C2×C14, D4×C2×C14 [×2], C14×C4⋊D4
Quotients:
C1, C2 [×15], C22 [×35], C7, D4 [×8], C23 [×15], C14 [×15], C2×D4 [×12], C4○D4 [×2], C24, C2×C14 [×35], C4⋊D4 [×4], C22×D4 [×2], C2×C4○D4, C7×D4 [×8], C22×C14 [×15], C2×C4⋊D4, D4×C14 [×12], C7×C4○D4 [×2], C23×C14, C7×C4⋊D4 [×4], D4×C2×C14 [×2], C14×C4○D4, C14×C4⋊D4
Generators and relations
G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
►On 224 points
Generators in S224
(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)
(1 153 75 215)(2 154 76 216)(3 141 77 217)(4 142 78 218)(5 143 79 219)(6 144 80 220)(7 145 81 221)(8 146 82 222)(9 147 83 223)(10 148 84 224)(11 149 71 211)(12 150 72 212)(13 151 73 213)(14 152 74 214)(15 184 180 52)(16 185 181 53)(17 186 182 54)(18 187 169 55)(19 188 170 56)(20 189 171 43)(21 190 172 44)(22 191 173 45)(23 192 174 46)(24 193 175 47)(25 194 176 48)(26 195 177 49)(27 196 178 50)(28 183 179 51)(29 107 124 135)(30 108 125 136)(31 109 126 137)(32 110 113 138)(33 111 114 139)(34 112 115 140)(35 99 116 127)(36 100 117 128)(37 101 118 129)(38 102 119 130)(39 103 120 131)(40 104 121 132)(41 105 122 133)(42 106 123 134)(57 86 200 164)(58 87 201 165)(59 88 202 166)(60 89 203 167)(61 90 204 168)(62 91 205 155)(63 92 206 156)(64 93 207 157)(65 94 208 158)(66 95 209 159)(67 96 210 160)(68 97 197 161)(69 98 198 162)(70 85 199 163)
(1 34 18 65)(2 35 19 66)(3 36 20 67)(4 37 21 68)(5 38 22 69)(6 39 23 70)(7 40 24 57)(8 41 25 58)(9 42 26 59)(10 29 27 60)(11 30 28 61)(12 31 15 62)(13 32 16 63)(14 33 17 64)(43 96 217 100)(44 97 218 101)(45 98 219 102)(46 85 220 103)(47 86 221 104)(48 87 222 105)(49 88 223 106)(50 89 224 107)(51 90 211 108)(52 91 212 109)(53 92 213 110)(54 93 214 111)(55 94 215 112)(56 95 216 99)(71 125 179 204)(72 126 180 205)(73 113 181 206)(74 114 182 207)(75 115 169 208)(76 116 170 209)(77 117 171 210)(78 118 172 197)(79 119 173 198)(80 120 174 199)(81 121 175 200)(82 122 176 201)(83 123 177 202)(84 124 178 203)(127 188 159 154)(128 189 160 141)(129 190 161 142)(130 191 162 143)(131 192 163 144)(132 193 164 145)(133 194 165 146)(134 195 166 147)(135 196 167 148)(136 183 168 149)(137 184 155 150)(138 185 156 151)(139 186 157 152)(140 187 158 153)
(1 122)(2 123)(3 124)(4 125)(5 126)(6 113)(7 114)(8 115)(9 116)(10 117)(11 118)(12 119)(13 120)(14 121)(15 198)(16 199)(17 200)(18 201)(19 202)(20 203)(21 204)(22 205)(23 206)(24 207)(25 208)(26 209)(27 210)(28 197)(29 77)(30 78)(31 79)(32 80)(33 81)(34 82)(35 83)(36 84)(37 71)(38 72)(39 73)(40 74)(41 75)(42 76)(43 167)(44 168)(45 155)(46 156)(47 157)(48 158)(49 159)(50 160)(51 161)(52 162)(53 163)(54 164)(55 165)(56 166)(57 182)(58 169)(59 170)(60 171)(61 172)(62 173)(63 174)(64 175)(65 176)(66 177)(67 178)(68 179)(69 180)(70 181)(85 185)(86 186)(87 187)(88 188)(89 189)(90 190)(91 191)(92 192)(93 193)(94 194)(95 195)(96 196)(97 183)(98 184)(99 147)(100 148)(101 149)(102 150)(103 151)(104 152)(105 153)(106 154)(107 141)(108 142)(109 143)(110 144)(111 145)(112 146)(127 223)(128 224)(129 211)(130 212)(131 213)(132 214)(133 215)(134 216)(135 217)(136 218)(137 219)(138 220)(139 221)(140 222)
G:=sub<Sym(224)| (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), (1,153,75,215)(2,154,76,216)(3,141,77,217)(4,142,78,218)(5,143,79,219)(6,144,80,220)(7,145,81,221)(8,146,82,222)(9,147,83,223)(10,148,84,224)(11,149,71,211)(12,150,72,212)(13,151,73,213)(14,152,74,214)(15,184,180,52)(16,185,181,53)(17,186,182,54)(18,187,169,55)(19,188,170,56)(20,189,171,43)(21,190,172,44)(22,191,173,45)(23,192,174,46)(24,193,175,47)(25,194,176,48)(26,195,177,49)(27,196,178,50)(28,183,179,51)(29,107,124,135)(30,108,125,136)(31,109,126,137)(32,110,113,138)(33,111,114,139)(34,112,115,140)(35,99,116,127)(36,100,117,128)(37,101,118,129)(38,102,119,130)(39,103,120,131)(40,104,121,132)(41,105,122,133)(42,106,123,134)(57,86,200,164)(58,87,201,165)(59,88,202,166)(60,89,203,167)(61,90,204,168)(62,91,205,155)(63,92,206,156)(64,93,207,157)(65,94,208,158)(66,95,209,159)(67,96,210,160)(68,97,197,161)(69,98,198,162)(70,85,199,163), (1,34,18,65)(2,35,19,66)(3,36,20,67)(4,37,21,68)(5,38,22,69)(6,39,23,70)(7,40,24,57)(8,41,25,58)(9,42,26,59)(10,29,27,60)(11,30,28,61)(12,31,15,62)(13,32,16,63)(14,33,17,64)(43,96,217,100)(44,97,218,101)(45,98,219,102)(46,85,220,103)(47,86,221,104)(48,87,222,105)(49,88,223,106)(50,89,224,107)(51,90,211,108)(52,91,212,109)(53,92,213,110)(54,93,214,111)(55,94,215,112)(56,95,216,99)(71,125,179,204)(72,126,180,205)(73,113,181,206)(74,114,182,207)(75,115,169,208)(76,116,170,209)(77,117,171,210)(78,118,172,197)(79,119,173,198)(80,120,174,199)(81,121,175,200)(82,122,176,201)(83,123,177,202)(84,124,178,203)(127,188,159,154)(128,189,160,141)(129,190,161,142)(130,191,162,143)(131,192,163,144)(132,193,164,145)(133,194,165,146)(134,195,166,147)(135,196,167,148)(136,183,168,149)(137,184,155,150)(138,185,156,151)(139,186,157,152)(140,187,158,153), (1,122)(2,123)(3,124)(4,125)(5,126)(6,113)(7,114)(8,115)(9,116)(10,117)(11,118)(12,119)(13,120)(14,121)(15,198)(16,199)(17,200)(18,201)(19,202)(20,203)(21,204)(22,205)(23,206)(24,207)(25,208)(26,209)(27,210)(28,197)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,71)(38,72)(39,73)(40,74)(41,75)(42,76)(43,167)(44,168)(45,155)(46,156)(47,157)(48,158)(49,159)(50,160)(51,161)(52,162)(53,163)(54,164)(55,165)(56,166)(57,182)(58,169)(59,170)(60,171)(61,172)(62,173)(63,174)(64,175)(65,176)(66,177)(67,178)(68,179)(69,180)(70,181)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,183)(98,184)(99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(127,223)(128,224)(129,211)(130,212)(131,213)(132,214)(133,215)(134,216)(135,217)(136,218)(137,219)(138,220)(139,221)(140,222)>;
G:=Group( (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), (1,153,75,215)(2,154,76,216)(3,141,77,217)(4,142,78,218)(5,143,79,219)(6,144,80,220)(7,145,81,221)(8,146,82,222)(9,147,83,223)(10,148,84,224)(11,149,71,211)(12,150,72,212)(13,151,73,213)(14,152,74,214)(15,184,180,52)(16,185,181,53)(17,186,182,54)(18,187,169,55)(19,188,170,56)(20,189,171,43)(21,190,172,44)(22,191,173,45)(23,192,174,46)(24,193,175,47)(25,194,176,48)(26,195,177,49)(27,196,178,50)(28,183,179,51)(29,107,124,135)(30,108,125,136)(31,109,126,137)(32,110,113,138)(33,111,114,139)(34,112,115,140)(35,99,116,127)(36,100,117,128)(37,101,118,129)(38,102,119,130)(39,103,120,131)(40,104,121,132)(41,105,122,133)(42,106,123,134)(57,86,200,164)(58,87,201,165)(59,88,202,166)(60,89,203,167)(61,90,204,168)(62,91,205,155)(63,92,206,156)(64,93,207,157)(65,94,208,158)(66,95,209,159)(67,96,210,160)(68,97,197,161)(69,98,198,162)(70,85,199,163), (1,34,18,65)(2,35,19,66)(3,36,20,67)(4,37,21,68)(5,38,22,69)(6,39,23,70)(7,40,24,57)(8,41,25,58)(9,42,26,59)(10,29,27,60)(11,30,28,61)(12,31,15,62)(13,32,16,63)(14,33,17,64)(43,96,217,100)(44,97,218,101)(45,98,219,102)(46,85,220,103)(47,86,221,104)(48,87,222,105)(49,88,223,106)(50,89,224,107)(51,90,211,108)(52,91,212,109)(53,92,213,110)(54,93,214,111)(55,94,215,112)(56,95,216,99)(71,125,179,204)(72,126,180,205)(73,113,181,206)(74,114,182,207)(75,115,169,208)(76,116,170,209)(77,117,171,210)(78,118,172,197)(79,119,173,198)(80,120,174,199)(81,121,175,200)(82,122,176,201)(83,123,177,202)(84,124,178,203)(127,188,159,154)(128,189,160,141)(129,190,161,142)(130,191,162,143)(131,192,163,144)(132,193,164,145)(133,194,165,146)(134,195,166,147)(135,196,167,148)(136,183,168,149)(137,184,155,150)(138,185,156,151)(139,186,157,152)(140,187,158,153), (1,122)(2,123)(3,124)(4,125)(5,126)(6,113)(7,114)(8,115)(9,116)(10,117)(11,118)(12,119)(13,120)(14,121)(15,198)(16,199)(17,200)(18,201)(19,202)(20,203)(21,204)(22,205)(23,206)(24,207)(25,208)(26,209)(27,210)(28,197)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,71)(38,72)(39,73)(40,74)(41,75)(42,76)(43,167)(44,168)(45,155)(46,156)(47,157)(48,158)(49,159)(50,160)(51,161)(52,162)(53,163)(54,164)(55,165)(56,166)(57,182)(58,169)(59,170)(60,171)(61,172)(62,173)(63,174)(64,175)(65,176)(66,177)(67,178)(68,179)(69,180)(70,181)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,183)(98,184)(99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(127,223)(128,224)(129,211)(130,212)(131,213)(132,214)(133,215)(134,216)(135,217)(136,218)(137,219)(138,220)(139,221)(140,222) );
G=PermutationGroup([(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)], [(1,153,75,215),(2,154,76,216),(3,141,77,217),(4,142,78,218),(5,143,79,219),(6,144,80,220),(7,145,81,221),(8,146,82,222),(9,147,83,223),(10,148,84,224),(11,149,71,211),(12,150,72,212),(13,151,73,213),(14,152,74,214),(15,184,180,52),(16,185,181,53),(17,186,182,54),(18,187,169,55),(19,188,170,56),(20,189,171,43),(21,190,172,44),(22,191,173,45),(23,192,174,46),(24,193,175,47),(25,194,176,48),(26,195,177,49),(27,196,178,50),(28,183,179,51),(29,107,124,135),(30,108,125,136),(31,109,126,137),(32,110,113,138),(33,111,114,139),(34,112,115,140),(35,99,116,127),(36,100,117,128),(37,101,118,129),(38,102,119,130),(39,103,120,131),(40,104,121,132),(41,105,122,133),(42,106,123,134),(57,86,200,164),(58,87,201,165),(59,88,202,166),(60,89,203,167),(61,90,204,168),(62,91,205,155),(63,92,206,156),(64,93,207,157),(65,94,208,158),(66,95,209,159),(67,96,210,160),(68,97,197,161),(69,98,198,162),(70,85,199,163)], [(1,34,18,65),(2,35,19,66),(3,36,20,67),(4,37,21,68),(5,38,22,69),(6,39,23,70),(7,40,24,57),(8,41,25,58),(9,42,26,59),(10,29,27,60),(11,30,28,61),(12,31,15,62),(13,32,16,63),(14,33,17,64),(43,96,217,100),(44,97,218,101),(45,98,219,102),(46,85,220,103),(47,86,221,104),(48,87,222,105),(49,88,223,106),(50,89,224,107),(51,90,211,108),(52,91,212,109),(53,92,213,110),(54,93,214,111),(55,94,215,112),(56,95,216,99),(71,125,179,204),(72,126,180,205),(73,113,181,206),(74,114,182,207),(75,115,169,208),(76,116,170,209),(77,117,171,210),(78,118,172,197),(79,119,173,198),(80,120,174,199),(81,121,175,200),(82,122,176,201),(83,123,177,202),(84,124,178,203),(127,188,159,154),(128,189,160,141),(129,190,161,142),(130,191,162,143),(131,192,163,144),(132,193,164,145),(133,194,165,146),(134,195,166,147),(135,196,167,148),(136,183,168,149),(137,184,155,150),(138,185,156,151),(139,186,157,152),(140,187,158,153)], [(1,122),(2,123),(3,124),(4,125),(5,126),(6,113),(7,114),(8,115),(9,116),(10,117),(11,118),(12,119),(13,120),(14,121),(15,198),(16,199),(17,200),(18,201),(19,202),(20,203),(21,204),(22,205),(23,206),(24,207),(25,208),(26,209),(27,210),(28,197),(29,77),(30,78),(31,79),(32,80),(33,81),(34,82),(35,83),(36,84),(37,71),(38,72),(39,73),(40,74),(41,75),(42,76),(43,167),(44,168),(45,155),(46,156),(47,157),(48,158),(49,159),(50,160),(51,161),(52,162),(53,163),(54,164),(55,165),(56,166),(57,182),(58,169),(59,170),(60,171),(61,172),(62,173),(63,174),(64,175),(65,176),(66,177),(67,178),(68,179),(69,180),(70,181),(85,185),(86,186),(87,187),(88,188),(89,189),(90,190),(91,191),(92,192),(93,193),(94,194),(95,195),(96,196),(97,183),(98,184),(99,147),(100,148),(101,149),(102,150),(103,151),(104,152),(105,153),(106,154),(107,141),(108,142),(109,143),(110,144),(111,145),(112,146),(127,223),(128,224),(129,211),(130,212),(131,213),(132,214),(133,215),(134,216),(135,217),(136,218),(137,219),(138,220),(139,221),(140,222)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 0 |
| 0 | 0 | 0 | 0 | 0 | 25 |
| 12 | 25 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 23 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 10 | 22 | 0 | 0 | 0 | 0 |
| 2 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 27 | 0 | 0 |
| 0 | 0 | 26 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 27 |
| 0 | 0 | 0 | 0 | 17 | 2 |
| 10 | 23 | 0 | 0 | 0 | 0 |
| 2 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 27 | 0 | 0 |
| 0 | 0 | 25 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 2 |
| 0 | 0 | 0 | 0 | 13 | 27 |
G:=sub<GL(6,GF(29))| [5,0,0,0,0,0,0,5,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,25,0,0,0,0,0,0,25],[12,0,0,0,0,0,25,17,0,0,0,0,0,0,17,23,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[10,2,0,0,0,0,22,19,0,0,0,0,0,0,15,26,0,0,0,0,27,14,0,0,0,0,0,0,27,17,0,0,0,0,27,2],[10,2,0,0,0,0,23,19,0,0,0,0,0,0,15,25,0,0,0,0,27,14,0,0,0,0,0,0,2,13,0,0,0,0,2,27] >;
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 14BO | ··· | 14CL | 28A | ··· | 28AV | 28AW | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C4○D4 | C7×D4 | C7×D4 | C7×C4○D4 |
| kernel | C14×C4⋊D4 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C4⋊D4 | C23×C28 | D4×C2×C14 | C2×C4⋊D4 | C2×C22⋊C4 | C2×C4⋊C4 | C4⋊D4 | C23×C4 | C22×D4 | C2×C28 | C22×C14 | C2×C14 | C2×C4 | C23 | C22 |
| # reps | 1 | 2 | 1 | 8 | 1 | 3 | 6 | 12 | 6 | 48 | 6 | 18 | 4 | 4 | 4 | 24 | 24 | 24 |
In GAP, Magma, Sage, TeX
C_{14}\times C_4\rtimes D_4 % in TeX
G:=Group("C14xC4:D4"); // GroupNames label
G:=SmallGroup(448,1305);
// by ID
G=gap.SmallGroup(448,1305);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,792,4790]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=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
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