metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.159D14, C14.982- (1+4), C28⋊Q8⋊39C2, C42⋊2C2.D7, C4⋊C4.116D14, C28.6Q8⋊8C2, (C4×Dic14)⋊13C2, Dic7.Q8⋊36C2, (C4×C28).31C22, (C2×C28).93C23, C22⋊C4.39D14, C4.Dic14⋊38C2, Dic7⋊3Q8⋊39C2, (C2×C14).245C24, C4⋊Dic7.53C22, C23.51(C22×D7), Dic7.14(C4○D4), (C22×C14).59C23, C22⋊Dic14.4C2, C23.D14.3C2, C22.266(C23×D7), C23.D7.61C22, Dic7⋊C4.126C22, C7⋊6(C22.35C24), (C4×Dic7).217C22, (C2×Dic7).127C23, C23.11D14.3C2, C2.62(D4.10D14), (C2×Dic14).253C22, (C22×Dic7).148C22, C2.92(D7×C4○D4), C14.203(C2×C4○D4), (C7×C4⋊C4).200C22, (C7×C42⋊2C2).1C2, (C2×C4).302(C22×D7), (C7×C22⋊C4).70C22, SmallGroup(448,1154)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 716 in 192 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2, C4 [×15], C22, C22 [×3], C7, C2×C4 [×6], C2×C4 [×10], Q8 [×4], C23, C14 [×3], C14, C42, C42 [×5], C22⋊C4 [×3], C22⋊C4 [×3], C4⋊C4 [×3], C4⋊C4 [×17], C22×C4, C2×Q8 [×2], Dic7 [×2], Dic7 [×7], C28 [×6], C2×C14, C2×C14 [×3], C42⋊C2, C4×Q8 [×2], C22⋊Q8 [×2], C42.C2 [×5], C42⋊2C2, C42⋊2C2 [×3], C4⋊Q8, Dic14 [×4], C2×Dic7 [×8], C2×Dic7 [×2], C2×C28 [×6], C22×C14, C22.35C24, C4×Dic7 [×5], Dic7⋊C4 [×12], C4⋊Dic7 [×5], C23.D7 [×3], C4×C28, C7×C22⋊C4 [×3], C7×C4⋊C4 [×3], C2×Dic14 [×2], C22×Dic7, C4×Dic14, C28.6Q8, C23.11D14, C22⋊Dic14 [×2], C23.D14 [×3], Dic7⋊3Q8, C28⋊Q8, Dic7.Q8 [×3], C4.Dic14, C7×C42⋊2C2, C42.159D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2- (1+4) [×2], C22×D7 [×7], C22.35C24, C23×D7, D7×C4○D4, D4.10D14 [×2], C42.159D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 39 70 103)(2 54 71 90)(3 41 72 105)(4 56 73 92)(5 43 74 107)(6 30 75 94)(7 45 76 109)(8 32 77 96)(9 47 78 111)(10 34 79 98)(11 49 80 85)(12 36 81 100)(13 51 82 87)(14 38 83 102)(15 53 84 89)(16 40 57 104)(17 55 58 91)(18 42 59 106)(19 29 60 93)(20 44 61 108)(21 31 62 95)(22 46 63 110)(23 33 64 97)(24 48 65 112)(25 35 66 99)(26 50 67 86)(27 37 68 101)(28 52 69 88)(113 146 195 206)(114 161 196 221)(115 148 169 208)(116 163 170 223)(117 150 171 210)(118 165 172 197)(119 152 173 212)(120 167 174 199)(121 154 175 214)(122 141 176 201)(123 156 177 216)(124 143 178 203)(125 158 179 218)(126 145 180 205)(127 160 181 220)(128 147 182 207)(129 162 183 222)(130 149 184 209)(131 164 185 224)(132 151 186 211)(133 166 187 198)(134 153 188 213)(135 168 189 200)(136 155 190 215)(137 142 191 202)(138 157 192 217)(139 144 193 204)(140 159 194 219)
(1 32 15 46)(2 111 16 97)(3 34 17 48)(4 85 18 99)(5 36 19 50)(6 87 20 101)(7 38 21 52)(8 89 22 103)(9 40 23 54)(10 91 24 105)(11 42 25 56)(12 93 26 107)(13 44 27 30)(14 95 28 109)(29 67 43 81)(31 69 45 83)(33 71 47 57)(35 73 49 59)(37 75 51 61)(39 77 53 63)(41 79 55 65)(58 112 72 98)(60 86 74 100)(62 88 76 102)(64 90 78 104)(66 92 80 106)(68 94 82 108)(70 96 84 110)(113 153 127 167)(114 200 128 214)(115 155 129 141)(116 202 130 216)(117 157 131 143)(118 204 132 218)(119 159 133 145)(120 206 134 220)(121 161 135 147)(122 208 136 222)(123 163 137 149)(124 210 138 224)(125 165 139 151)(126 212 140 198)(142 184 156 170)(144 186 158 172)(146 188 160 174)(148 190 162 176)(150 192 164 178)(152 194 166 180)(154 196 168 182)(169 215 183 201)(171 217 185 203)(173 219 187 205)(175 221 189 207)(177 223 191 209)(179 197 193 211)(181 199 195 213)
(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)
(1 176 70 122)(2 189 71 135)(3 174 72 120)(4 187 73 133)(5 172 74 118)(6 185 75 131)(7 170 76 116)(8 183 77 129)(9 196 78 114)(10 181 79 127)(11 194 80 140)(12 179 81 125)(13 192 82 138)(14 177 83 123)(15 190 84 136)(16 175 57 121)(17 188 58 134)(18 173 59 119)(19 186 60 132)(20 171 61 117)(21 184 62 130)(22 169 63 115)(23 182 64 128)(24 195 65 113)(25 180 66 126)(26 193 67 139)(27 178 68 124)(28 191 69 137)(29 197 93 165)(30 210 94 150)(31 223 95 163)(32 208 96 148)(33 221 97 161)(34 206 98 146)(35 219 99 159)(36 204 100 144)(37 217 101 157)(38 202 102 142)(39 215 103 155)(40 200 104 168)(41 213 105 153)(42 198 106 166)(43 211 107 151)(44 224 108 164)(45 209 109 149)(46 222 110 162)(47 207 111 147)(48 220 112 160)(49 205 85 145)(50 218 86 158)(51 203 87 143)(52 216 88 156)(53 201 89 141)(54 214 90 154)(55 199 91 167)(56 212 92 152)
G:=sub<Sym(224)| (1,39,70,103)(2,54,71,90)(3,41,72,105)(4,56,73,92)(5,43,74,107)(6,30,75,94)(7,45,76,109)(8,32,77,96)(9,47,78,111)(10,34,79,98)(11,49,80,85)(12,36,81,100)(13,51,82,87)(14,38,83,102)(15,53,84,89)(16,40,57,104)(17,55,58,91)(18,42,59,106)(19,29,60,93)(20,44,61,108)(21,31,62,95)(22,46,63,110)(23,33,64,97)(24,48,65,112)(25,35,66,99)(26,50,67,86)(27,37,68,101)(28,52,69,88)(113,146,195,206)(114,161,196,221)(115,148,169,208)(116,163,170,223)(117,150,171,210)(118,165,172,197)(119,152,173,212)(120,167,174,199)(121,154,175,214)(122,141,176,201)(123,156,177,216)(124,143,178,203)(125,158,179,218)(126,145,180,205)(127,160,181,220)(128,147,182,207)(129,162,183,222)(130,149,184,209)(131,164,185,224)(132,151,186,211)(133,166,187,198)(134,153,188,213)(135,168,189,200)(136,155,190,215)(137,142,191,202)(138,157,192,217)(139,144,193,204)(140,159,194,219), (1,32,15,46)(2,111,16,97)(3,34,17,48)(4,85,18,99)(5,36,19,50)(6,87,20,101)(7,38,21,52)(8,89,22,103)(9,40,23,54)(10,91,24,105)(11,42,25,56)(12,93,26,107)(13,44,27,30)(14,95,28,109)(29,67,43,81)(31,69,45,83)(33,71,47,57)(35,73,49,59)(37,75,51,61)(39,77,53,63)(41,79,55,65)(58,112,72,98)(60,86,74,100)(62,88,76,102)(64,90,78,104)(66,92,80,106)(68,94,82,108)(70,96,84,110)(113,153,127,167)(114,200,128,214)(115,155,129,141)(116,202,130,216)(117,157,131,143)(118,204,132,218)(119,159,133,145)(120,206,134,220)(121,161,135,147)(122,208,136,222)(123,163,137,149)(124,210,138,224)(125,165,139,151)(126,212,140,198)(142,184,156,170)(144,186,158,172)(146,188,160,174)(148,190,162,176)(150,192,164,178)(152,194,166,180)(154,196,168,182)(169,215,183,201)(171,217,185,203)(173,219,187,205)(175,221,189,207)(177,223,191,209)(179,197,193,211)(181,199,195,213), (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), (1,176,70,122)(2,189,71,135)(3,174,72,120)(4,187,73,133)(5,172,74,118)(6,185,75,131)(7,170,76,116)(8,183,77,129)(9,196,78,114)(10,181,79,127)(11,194,80,140)(12,179,81,125)(13,192,82,138)(14,177,83,123)(15,190,84,136)(16,175,57,121)(17,188,58,134)(18,173,59,119)(19,186,60,132)(20,171,61,117)(21,184,62,130)(22,169,63,115)(23,182,64,128)(24,195,65,113)(25,180,66,126)(26,193,67,139)(27,178,68,124)(28,191,69,137)(29,197,93,165)(30,210,94,150)(31,223,95,163)(32,208,96,148)(33,221,97,161)(34,206,98,146)(35,219,99,159)(36,204,100,144)(37,217,101,157)(38,202,102,142)(39,215,103,155)(40,200,104,168)(41,213,105,153)(42,198,106,166)(43,211,107,151)(44,224,108,164)(45,209,109,149)(46,222,110,162)(47,207,111,147)(48,220,112,160)(49,205,85,145)(50,218,86,158)(51,203,87,143)(52,216,88,156)(53,201,89,141)(54,214,90,154)(55,199,91,167)(56,212,92,152)>;
G:=Group( (1,39,70,103)(2,54,71,90)(3,41,72,105)(4,56,73,92)(5,43,74,107)(6,30,75,94)(7,45,76,109)(8,32,77,96)(9,47,78,111)(10,34,79,98)(11,49,80,85)(12,36,81,100)(13,51,82,87)(14,38,83,102)(15,53,84,89)(16,40,57,104)(17,55,58,91)(18,42,59,106)(19,29,60,93)(20,44,61,108)(21,31,62,95)(22,46,63,110)(23,33,64,97)(24,48,65,112)(25,35,66,99)(26,50,67,86)(27,37,68,101)(28,52,69,88)(113,146,195,206)(114,161,196,221)(115,148,169,208)(116,163,170,223)(117,150,171,210)(118,165,172,197)(119,152,173,212)(120,167,174,199)(121,154,175,214)(122,141,176,201)(123,156,177,216)(124,143,178,203)(125,158,179,218)(126,145,180,205)(127,160,181,220)(128,147,182,207)(129,162,183,222)(130,149,184,209)(131,164,185,224)(132,151,186,211)(133,166,187,198)(134,153,188,213)(135,168,189,200)(136,155,190,215)(137,142,191,202)(138,157,192,217)(139,144,193,204)(140,159,194,219), (1,32,15,46)(2,111,16,97)(3,34,17,48)(4,85,18,99)(5,36,19,50)(6,87,20,101)(7,38,21,52)(8,89,22,103)(9,40,23,54)(10,91,24,105)(11,42,25,56)(12,93,26,107)(13,44,27,30)(14,95,28,109)(29,67,43,81)(31,69,45,83)(33,71,47,57)(35,73,49,59)(37,75,51,61)(39,77,53,63)(41,79,55,65)(58,112,72,98)(60,86,74,100)(62,88,76,102)(64,90,78,104)(66,92,80,106)(68,94,82,108)(70,96,84,110)(113,153,127,167)(114,200,128,214)(115,155,129,141)(116,202,130,216)(117,157,131,143)(118,204,132,218)(119,159,133,145)(120,206,134,220)(121,161,135,147)(122,208,136,222)(123,163,137,149)(124,210,138,224)(125,165,139,151)(126,212,140,198)(142,184,156,170)(144,186,158,172)(146,188,160,174)(148,190,162,176)(150,192,164,178)(152,194,166,180)(154,196,168,182)(169,215,183,201)(171,217,185,203)(173,219,187,205)(175,221,189,207)(177,223,191,209)(179,197,193,211)(181,199,195,213), (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), (1,176,70,122)(2,189,71,135)(3,174,72,120)(4,187,73,133)(5,172,74,118)(6,185,75,131)(7,170,76,116)(8,183,77,129)(9,196,78,114)(10,181,79,127)(11,194,80,140)(12,179,81,125)(13,192,82,138)(14,177,83,123)(15,190,84,136)(16,175,57,121)(17,188,58,134)(18,173,59,119)(19,186,60,132)(20,171,61,117)(21,184,62,130)(22,169,63,115)(23,182,64,128)(24,195,65,113)(25,180,66,126)(26,193,67,139)(27,178,68,124)(28,191,69,137)(29,197,93,165)(30,210,94,150)(31,223,95,163)(32,208,96,148)(33,221,97,161)(34,206,98,146)(35,219,99,159)(36,204,100,144)(37,217,101,157)(38,202,102,142)(39,215,103,155)(40,200,104,168)(41,213,105,153)(42,198,106,166)(43,211,107,151)(44,224,108,164)(45,209,109,149)(46,222,110,162)(47,207,111,147)(48,220,112,160)(49,205,85,145)(50,218,86,158)(51,203,87,143)(52,216,88,156)(53,201,89,141)(54,214,90,154)(55,199,91,167)(56,212,92,152) );
G=PermutationGroup([(1,39,70,103),(2,54,71,90),(3,41,72,105),(4,56,73,92),(5,43,74,107),(6,30,75,94),(7,45,76,109),(8,32,77,96),(9,47,78,111),(10,34,79,98),(11,49,80,85),(12,36,81,100),(13,51,82,87),(14,38,83,102),(15,53,84,89),(16,40,57,104),(17,55,58,91),(18,42,59,106),(19,29,60,93),(20,44,61,108),(21,31,62,95),(22,46,63,110),(23,33,64,97),(24,48,65,112),(25,35,66,99),(26,50,67,86),(27,37,68,101),(28,52,69,88),(113,146,195,206),(114,161,196,221),(115,148,169,208),(116,163,170,223),(117,150,171,210),(118,165,172,197),(119,152,173,212),(120,167,174,199),(121,154,175,214),(122,141,176,201),(123,156,177,216),(124,143,178,203),(125,158,179,218),(126,145,180,205),(127,160,181,220),(128,147,182,207),(129,162,183,222),(130,149,184,209),(131,164,185,224),(132,151,186,211),(133,166,187,198),(134,153,188,213),(135,168,189,200),(136,155,190,215),(137,142,191,202),(138,157,192,217),(139,144,193,204),(140,159,194,219)], [(1,32,15,46),(2,111,16,97),(3,34,17,48),(4,85,18,99),(5,36,19,50),(6,87,20,101),(7,38,21,52),(8,89,22,103),(9,40,23,54),(10,91,24,105),(11,42,25,56),(12,93,26,107),(13,44,27,30),(14,95,28,109),(29,67,43,81),(31,69,45,83),(33,71,47,57),(35,73,49,59),(37,75,51,61),(39,77,53,63),(41,79,55,65),(58,112,72,98),(60,86,74,100),(62,88,76,102),(64,90,78,104),(66,92,80,106),(68,94,82,108),(70,96,84,110),(113,153,127,167),(114,200,128,214),(115,155,129,141),(116,202,130,216),(117,157,131,143),(118,204,132,218),(119,159,133,145),(120,206,134,220),(121,161,135,147),(122,208,136,222),(123,163,137,149),(124,210,138,224),(125,165,139,151),(126,212,140,198),(142,184,156,170),(144,186,158,172),(146,188,160,174),(148,190,162,176),(150,192,164,178),(152,194,166,180),(154,196,168,182),(169,215,183,201),(171,217,185,203),(173,219,187,205),(175,221,189,207),(177,223,191,209),(179,197,193,211),(181,199,195,213)], [(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)], [(1,176,70,122),(2,189,71,135),(3,174,72,120),(4,187,73,133),(5,172,74,118),(6,185,75,131),(7,170,76,116),(8,183,77,129),(9,196,78,114),(10,181,79,127),(11,194,80,140),(12,179,81,125),(13,192,82,138),(14,177,83,123),(15,190,84,136),(16,175,57,121),(17,188,58,134),(18,173,59,119),(19,186,60,132),(20,171,61,117),(21,184,62,130),(22,169,63,115),(23,182,64,128),(24,195,65,113),(25,180,66,126),(26,193,67,139),(27,178,68,124),(28,191,69,137),(29,197,93,165),(30,210,94,150),(31,223,95,163),(32,208,96,148),(33,221,97,161),(34,206,98,146),(35,219,99,159),(36,204,100,144),(37,217,101,157),(38,202,102,142),(39,215,103,155),(40,200,104,168),(41,213,105,153),(42,198,106,166),(43,211,107,151),(44,224,108,164),(45,209,109,149),(46,222,110,162),(47,207,111,147),(48,220,112,160),(49,205,85,145),(50,218,86,158),(51,203,87,143),(52,216,88,156),(53,201,89,141),(54,214,90,154),(55,199,91,167),(56,212,92,152)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 25 | 16 | 0 | 0 | 0 | 0 |
| 19 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 11 |
| 0 | 0 | 0 | 0 | 18 | 2 |
| 10 | 18 | 0 | 0 | 0 | 0 |
| 9 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 12 | 17 | 0 | 0 |
| 0 | 0 | 12 | 5 | 0 | 0 |
| 25 | 16 | 0 | 0 | 0 | 0 |
| 8 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 17 | 0 | 0 |
| 0 | 0 | 9 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 12 |
| 0 | 0 | 0 | 0 | 20 | 7 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,1,0,0,0,0,0,0,1,0,0],[25,19,0,0,0,0,16,4,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,27,18,0,0,0,0,11,2],[10,9,0,0,0,0,18,19,0,0,0,0,0,0,0,0,12,12,0,0,0,0,17,5,0,0,12,12,0,0,0,0,17,5,0,0],[25,8,0,0,0,0,16,4,0,0,0,0,0,0,7,9,0,0,0,0,17,22,0,0,0,0,0,0,22,20,0,0,0,0,12,7] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2- (1+4) | D7×C4○D4 | D4.10D14 |
| kernel | C42.159D14 | C4×Dic14 | C28.6Q8 | C23.11D14 | C22⋊Dic14 | C23.D14 | Dic7⋊3Q8 | C28⋊Q8 | Dic7.Q8 | C4.Dic14 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | C42 | C22⋊C4 | C4⋊C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 4 | 3 | 9 | 9 | 2 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{159}D_{14} % in TeX
G:=Group("C4^2.159D14"); // GroupNames label
G:=SmallGroup(448,1154);
// by ID
G=gap.SmallGroup(448,1154);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,219,268,675,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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