metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.136D14, C14.1132+ (1+4), (C4×Q8)⋊18D7, (C4×D28)⋊42C2, (Q8×C28)⋊20C2, C4⋊C4.303D14, D28⋊C4⋊18C2, (C4×Dic14)⋊42C2, C4.19(C4○D28), C4.D28⋊21C2, C4⋊D28.10C2, (C2×Q8).184D14, D14.5D4⋊10C2, C28.123(C4○D4), C28.23D4⋊10C2, (C2×C14).129C24, (C2×C28).592C23, (C4×C28).181C22, C4.51(Q8⋊2D7), (C2×D28).29C22, C2.25(D4⋊8D14), D14⋊C4.145C22, C4⋊Dic7.401C22, (Q8×C14).229C22, (C2×Dic7).59C23, (C4×Dic7).88C22, (C22×D7).51C23, C22.150(C23×D7), Dic7⋊C4.116C22, C7⋊2(C22.53C24), (C2×Dic14).244C22, C14.58(C2×C4○D4), C2.68(C2×C4○D28), C2.14(C2×Q8⋊2D7), (C2×C4×D7).207C22, (C7×C4⋊C4).357C22, (C2×C4).291(C22×D7), SmallGroup(448,1038)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1220 in 236 conjugacy classes, 99 normal (29 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×9], C22, C22 [×12], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×8], D4 [×10], Q8 [×4], C23 [×4], D7 [×4], C14 [×3], C42, C42 [×2], C42 [×2], C22⋊C4 [×12], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×3], C22×C4 [×4], C2×D4 [×6], C2×Q8, C2×Q8, Dic7 [×4], C28 [×4], C28 [×5], D14 [×12], C2×C14, C4×D4 [×4], C4×Q8, C4×Q8, C22.D4 [×4], C4.4D4 [×4], C4⋊1D4, Dic14 [×2], C4×D7 [×4], D28 [×10], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7 [×4], C22.53C24, C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7, D14⋊C4 [×12], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14, C2×C4×D7 [×4], C2×D28 [×6], Q8×C14, C4×Dic14, C4×D28 [×2], C4⋊D28, C4.D28 [×2], D28⋊C4 [×2], D14.5D4 [×4], C28.23D4 [×2], Q8×C28, C42.136D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.53C24, C4○D28 [×2], Q8⋊2D7 [×2], C23×D7, C2×C4○D28, C2×Q8⋊2D7, D4⋊8D14, C42.136D14
Generators and relations
G = < a,b,c,d | a4=b4=d2=1, c14=a2, ab=ba, cac-1=dad=a-1b2, bc=cb, dbd=b-1, dcd=a2c13 >
►On 224 points
Generators in S224
(1 208 15 222)(2 84 16 70)(3 210 17 224)(4 58 18 72)(5 212 19 198)(6 60 20 74)(7 214 21 200)(8 62 22 76)(9 216 23 202)(10 64 24 78)(11 218 25 204)(12 66 26 80)(13 220 27 206)(14 68 28 82)(29 213 43 199)(30 61 44 75)(31 215 45 201)(32 63 46 77)(33 217 47 203)(34 65 48 79)(35 219 49 205)(36 67 50 81)(37 221 51 207)(38 69 52 83)(39 223 53 209)(40 71 54 57)(41 197 55 211)(42 73 56 59)(85 194 99 180)(86 126 100 140)(87 196 101 182)(88 128 102 114)(89 170 103 184)(90 130 104 116)(91 172 105 186)(92 132 106 118)(93 174 107 188)(94 134 108 120)(95 176 109 190)(96 136 110 122)(97 178 111 192)(98 138 112 124)(113 143 127 157)(115 145 129 159)(117 147 131 161)(119 149 133 163)(121 151 135 165)(123 153 137 167)(125 155 139 141)(142 195 156 181)(144 169 158 183)(146 171 160 185)(148 173 162 187)(150 175 164 189)(152 177 166 191)(154 179 168 193)
(1 141 38 99)(2 142 39 100)(3 143 40 101)(4 144 41 102)(5 145 42 103)(6 146 43 104)(7 147 44 105)(8 148 45 106)(9 149 46 107)(10 150 47 108)(11 151 48 109)(12 152 49 110)(13 153 50 111)(14 154 51 112)(15 155 52 85)(16 156 53 86)(17 157 54 87)(18 158 55 88)(19 159 56 89)(20 160 29 90)(21 161 30 91)(22 162 31 92)(23 163 32 93)(24 164 33 94)(25 165 34 95)(26 166 35 96)(27 167 36 97)(28 168 37 98)(57 196 224 113)(58 169 197 114)(59 170 198 115)(60 171 199 116)(61 172 200 117)(62 173 201 118)(63 174 202 119)(64 175 203 120)(65 176 204 121)(66 177 205 122)(67 178 206 123)(68 179 207 124)(69 180 208 125)(70 181 209 126)(71 182 210 127)(72 183 211 128)(73 184 212 129)(74 185 213 130)(75 186 214 131)(76 187 215 132)(77 188 216 133)(78 189 217 134)(79 190 218 135)(80 191 219 136)(81 192 220 137)(82 193 221 138)(83 194 222 139)(84 195 223 140)
(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 91)(2 90)(3 89)(4 88)(5 87)(6 86)(7 85)(8 112)(9 111)(10 110)(11 109)(12 108)(13 107)(14 106)(15 105)(16 104)(17 103)(18 102)(19 101)(20 100)(21 99)(22 98)(23 97)(24 96)(25 95)(26 94)(27 93)(28 92)(29 142)(30 141)(31 168)(32 167)(33 166)(34 165)(35 164)(36 163)(37 162)(38 161)(39 160)(40 159)(41 158)(42 157)(43 156)(44 155)(45 154)(46 153)(47 152)(48 151)(49 150)(50 149)(51 148)(52 147)(53 146)(54 145)(55 144)(56 143)(57 170)(58 169)(59 196)(60 195)(61 194)(62 193)(63 192)(64 191)(65 190)(66 189)(67 188)(68 187)(69 186)(70 185)(71 184)(72 183)(73 182)(74 181)(75 180)(76 179)(77 178)(78 177)(79 176)(80 175)(81 174)(82 173)(83 172)(84 171)(113 198)(114 197)(115 224)(116 223)(117 222)(118 221)(119 220)(120 219)(121 218)(122 217)(123 216)(124 215)(125 214)(126 213)(127 212)(128 211)(129 210)(130 209)(131 208)(132 207)(133 206)(134 205)(135 204)(136 203)(137 202)(138 201)(139 200)(140 199)
G:=sub<Sym(224)| (1,208,15,222)(2,84,16,70)(3,210,17,224)(4,58,18,72)(5,212,19,198)(6,60,20,74)(7,214,21,200)(8,62,22,76)(9,216,23,202)(10,64,24,78)(11,218,25,204)(12,66,26,80)(13,220,27,206)(14,68,28,82)(29,213,43,199)(30,61,44,75)(31,215,45,201)(32,63,46,77)(33,217,47,203)(34,65,48,79)(35,219,49,205)(36,67,50,81)(37,221,51,207)(38,69,52,83)(39,223,53,209)(40,71,54,57)(41,197,55,211)(42,73,56,59)(85,194,99,180)(86,126,100,140)(87,196,101,182)(88,128,102,114)(89,170,103,184)(90,130,104,116)(91,172,105,186)(92,132,106,118)(93,174,107,188)(94,134,108,120)(95,176,109,190)(96,136,110,122)(97,178,111,192)(98,138,112,124)(113,143,127,157)(115,145,129,159)(117,147,131,161)(119,149,133,163)(121,151,135,165)(123,153,137,167)(125,155,139,141)(142,195,156,181)(144,169,158,183)(146,171,160,185)(148,173,162,187)(150,175,164,189)(152,177,166,191)(154,179,168,193), (1,141,38,99)(2,142,39,100)(3,143,40,101)(4,144,41,102)(5,145,42,103)(6,146,43,104)(7,147,44,105)(8,148,45,106)(9,149,46,107)(10,150,47,108)(11,151,48,109)(12,152,49,110)(13,153,50,111)(14,154,51,112)(15,155,52,85)(16,156,53,86)(17,157,54,87)(18,158,55,88)(19,159,56,89)(20,160,29,90)(21,161,30,91)(22,162,31,92)(23,163,32,93)(24,164,33,94)(25,165,34,95)(26,166,35,96)(27,167,36,97)(28,168,37,98)(57,196,224,113)(58,169,197,114)(59,170,198,115)(60,171,199,116)(61,172,200,117)(62,173,201,118)(63,174,202,119)(64,175,203,120)(65,176,204,121)(66,177,205,122)(67,178,206,123)(68,179,207,124)(69,180,208,125)(70,181,209,126)(71,182,210,127)(72,183,211,128)(73,184,212,129)(74,185,213,130)(75,186,214,131)(76,187,215,132)(77,188,216,133)(78,189,217,134)(79,190,218,135)(80,191,219,136)(81,192,220,137)(82,193,221,138)(83,194,222,139)(84,195,223,140), (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), (1,91)(2,90)(3,89)(4,88)(5,87)(6,86)(7,85)(8,112)(9,111)(10,110)(11,109)(12,108)(13,107)(14,106)(15,105)(16,104)(17,103)(18,102)(19,101)(20,100)(21,99)(22,98)(23,97)(24,96)(25,95)(26,94)(27,93)(28,92)(29,142)(30,141)(31,168)(32,167)(33,166)(34,165)(35,164)(36,163)(37,162)(38,161)(39,160)(40,159)(41,158)(42,157)(43,156)(44,155)(45,154)(46,153)(47,152)(48,151)(49,150)(50,149)(51,148)(52,147)(53,146)(54,145)(55,144)(56,143)(57,170)(58,169)(59,196)(60,195)(61,194)(62,193)(63,192)(64,191)(65,190)(66,189)(67,188)(68,187)(69,186)(70,185)(71,184)(72,183)(73,182)(74,181)(75,180)(76,179)(77,178)(78,177)(79,176)(80,175)(81,174)(82,173)(83,172)(84,171)(113,198)(114,197)(115,224)(116,223)(117,222)(118,221)(119,220)(120,219)(121,218)(122,217)(123,216)(124,215)(125,214)(126,213)(127,212)(128,211)(129,210)(130,209)(131,208)(132,207)(133,206)(134,205)(135,204)(136,203)(137,202)(138,201)(139,200)(140,199)>;
G:=Group( (1,208,15,222)(2,84,16,70)(3,210,17,224)(4,58,18,72)(5,212,19,198)(6,60,20,74)(7,214,21,200)(8,62,22,76)(9,216,23,202)(10,64,24,78)(11,218,25,204)(12,66,26,80)(13,220,27,206)(14,68,28,82)(29,213,43,199)(30,61,44,75)(31,215,45,201)(32,63,46,77)(33,217,47,203)(34,65,48,79)(35,219,49,205)(36,67,50,81)(37,221,51,207)(38,69,52,83)(39,223,53,209)(40,71,54,57)(41,197,55,211)(42,73,56,59)(85,194,99,180)(86,126,100,140)(87,196,101,182)(88,128,102,114)(89,170,103,184)(90,130,104,116)(91,172,105,186)(92,132,106,118)(93,174,107,188)(94,134,108,120)(95,176,109,190)(96,136,110,122)(97,178,111,192)(98,138,112,124)(113,143,127,157)(115,145,129,159)(117,147,131,161)(119,149,133,163)(121,151,135,165)(123,153,137,167)(125,155,139,141)(142,195,156,181)(144,169,158,183)(146,171,160,185)(148,173,162,187)(150,175,164,189)(152,177,166,191)(154,179,168,193), (1,141,38,99)(2,142,39,100)(3,143,40,101)(4,144,41,102)(5,145,42,103)(6,146,43,104)(7,147,44,105)(8,148,45,106)(9,149,46,107)(10,150,47,108)(11,151,48,109)(12,152,49,110)(13,153,50,111)(14,154,51,112)(15,155,52,85)(16,156,53,86)(17,157,54,87)(18,158,55,88)(19,159,56,89)(20,160,29,90)(21,161,30,91)(22,162,31,92)(23,163,32,93)(24,164,33,94)(25,165,34,95)(26,166,35,96)(27,167,36,97)(28,168,37,98)(57,196,224,113)(58,169,197,114)(59,170,198,115)(60,171,199,116)(61,172,200,117)(62,173,201,118)(63,174,202,119)(64,175,203,120)(65,176,204,121)(66,177,205,122)(67,178,206,123)(68,179,207,124)(69,180,208,125)(70,181,209,126)(71,182,210,127)(72,183,211,128)(73,184,212,129)(74,185,213,130)(75,186,214,131)(76,187,215,132)(77,188,216,133)(78,189,217,134)(79,190,218,135)(80,191,219,136)(81,192,220,137)(82,193,221,138)(83,194,222,139)(84,195,223,140), (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), (1,91)(2,90)(3,89)(4,88)(5,87)(6,86)(7,85)(8,112)(9,111)(10,110)(11,109)(12,108)(13,107)(14,106)(15,105)(16,104)(17,103)(18,102)(19,101)(20,100)(21,99)(22,98)(23,97)(24,96)(25,95)(26,94)(27,93)(28,92)(29,142)(30,141)(31,168)(32,167)(33,166)(34,165)(35,164)(36,163)(37,162)(38,161)(39,160)(40,159)(41,158)(42,157)(43,156)(44,155)(45,154)(46,153)(47,152)(48,151)(49,150)(50,149)(51,148)(52,147)(53,146)(54,145)(55,144)(56,143)(57,170)(58,169)(59,196)(60,195)(61,194)(62,193)(63,192)(64,191)(65,190)(66,189)(67,188)(68,187)(69,186)(70,185)(71,184)(72,183)(73,182)(74,181)(75,180)(76,179)(77,178)(78,177)(79,176)(80,175)(81,174)(82,173)(83,172)(84,171)(113,198)(114,197)(115,224)(116,223)(117,222)(118,221)(119,220)(120,219)(121,218)(122,217)(123,216)(124,215)(125,214)(126,213)(127,212)(128,211)(129,210)(130,209)(131,208)(132,207)(133,206)(134,205)(135,204)(136,203)(137,202)(138,201)(139,200)(140,199) );
G=PermutationGroup([(1,208,15,222),(2,84,16,70),(3,210,17,224),(4,58,18,72),(5,212,19,198),(6,60,20,74),(7,214,21,200),(8,62,22,76),(9,216,23,202),(10,64,24,78),(11,218,25,204),(12,66,26,80),(13,220,27,206),(14,68,28,82),(29,213,43,199),(30,61,44,75),(31,215,45,201),(32,63,46,77),(33,217,47,203),(34,65,48,79),(35,219,49,205),(36,67,50,81),(37,221,51,207),(38,69,52,83),(39,223,53,209),(40,71,54,57),(41,197,55,211),(42,73,56,59),(85,194,99,180),(86,126,100,140),(87,196,101,182),(88,128,102,114),(89,170,103,184),(90,130,104,116),(91,172,105,186),(92,132,106,118),(93,174,107,188),(94,134,108,120),(95,176,109,190),(96,136,110,122),(97,178,111,192),(98,138,112,124),(113,143,127,157),(115,145,129,159),(117,147,131,161),(119,149,133,163),(121,151,135,165),(123,153,137,167),(125,155,139,141),(142,195,156,181),(144,169,158,183),(146,171,160,185),(148,173,162,187),(150,175,164,189),(152,177,166,191),(154,179,168,193)], [(1,141,38,99),(2,142,39,100),(3,143,40,101),(4,144,41,102),(5,145,42,103),(6,146,43,104),(7,147,44,105),(8,148,45,106),(9,149,46,107),(10,150,47,108),(11,151,48,109),(12,152,49,110),(13,153,50,111),(14,154,51,112),(15,155,52,85),(16,156,53,86),(17,157,54,87),(18,158,55,88),(19,159,56,89),(20,160,29,90),(21,161,30,91),(22,162,31,92),(23,163,32,93),(24,164,33,94),(25,165,34,95),(26,166,35,96),(27,167,36,97),(28,168,37,98),(57,196,224,113),(58,169,197,114),(59,170,198,115),(60,171,199,116),(61,172,200,117),(62,173,201,118),(63,174,202,119),(64,175,203,120),(65,176,204,121),(66,177,205,122),(67,178,206,123),(68,179,207,124),(69,180,208,125),(70,181,209,126),(71,182,210,127),(72,183,211,128),(73,184,212,129),(74,185,213,130),(75,186,214,131),(76,187,215,132),(77,188,216,133),(78,189,217,134),(79,190,218,135),(80,191,219,136),(81,192,220,137),(82,193,221,138),(83,194,222,139),(84,195,223,140)], [(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)], [(1,91),(2,90),(3,89),(4,88),(5,87),(6,86),(7,85),(8,112),(9,111),(10,110),(11,109),(12,108),(13,107),(14,106),(15,105),(16,104),(17,103),(18,102),(19,101),(20,100),(21,99),(22,98),(23,97),(24,96),(25,95),(26,94),(27,93),(28,92),(29,142),(30,141),(31,168),(32,167),(33,166),(34,165),(35,164),(36,163),(37,162),(38,161),(39,160),(40,159),(41,158),(42,157),(43,156),(44,155),(45,154),(46,153),(47,152),(48,151),(49,150),(50,149),(51,148),(52,147),(53,146),(54,145),(55,144),(56,143),(57,170),(58,169),(59,196),(60,195),(61,194),(62,193),(63,192),(64,191),(65,190),(66,189),(67,188),(68,187),(69,186),(70,185),(71,184),(72,183),(73,182),(74,181),(75,180),(76,179),(77,178),(78,177),(79,176),(80,175),(81,174),(82,173),(83,172),(84,171),(113,198),(114,197),(115,224),(116,223),(117,222),(118,221),(119,220),(120,219),(121,218),(122,217),(123,216),(124,215),(125,214),(126,213),(127,212),(128,211),(129,210),(130,209),(131,208),(132,207),(133,206),(134,205),(135,204),(136,203),(137,202),(138,201),(139,200),(140,199)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 24 | 0 | 0 | 0 | 0 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 24 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 3 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,2,17],[1,12,0,0,0,0,24,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,17,0,0,0,0,5,1,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,28,12,0,0,0,0,24,1],[28,0,0,0,0,0,5,1,0,0,0,0,0,0,8,3,0,0,0,0,8,21,0,0,0,0,0,0,28,12,0,0,0,0,0,1] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | Q8⋊2D7 | D4⋊8D14 |
| kernel | C42.136D14 | C4×Dic14 | C4×D28 | C4⋊D28 | C4.D28 | D28⋊C4 | D14.5D4 | C28.23D4 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 8 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{136}D_{14} % in TeX
G:=Group("C4^2.136D14"); // GroupNames label
G:=SmallGroup(448,1038);
// by ID
G=gap.SmallGroup(448,1038);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,184,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=a^2,a*b=b*a,c*a*c^-1=d*a*d=a^-1*b^2,b*c=c*b,d*b*d=b^-1,d*c*d=a^2*c^13>;
// generators/relations
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