metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.151D14, C14.292- (1+4), C42.C2⋊7D7, C4⋊C4.112D14, D14⋊Q8⋊36C2, C42⋊D7⋊37C2, Dic7.Q8⋊34C2, (C2×C28).89C23, D14.24(C4○D4), Dic7⋊3Q8⋊36C2, D28⋊C4.12C2, (C2×C14).237C24, (C4×C28).240C22, D14.5D4.2C2, D14⋊C4.137C22, Dic7.30(C4○D4), (C2×D28).165C22, Dic7⋊C4.53C22, C4⋊Dic7.242C22, C22.258(C23×D7), C7⋊9(C22.46C24), (C4×Dic7).215C22, (C2×Dic7).259C23, (C22×D7).222C23, C2.30(Q8.10D14), (C2×Dic14).181C22, (D7×C4⋊C4)⋊37C2, C2.88(D7×C4○D4), C4⋊C4⋊D7⋊35C2, C4⋊C4⋊7D7⋊36C2, C14.199(C2×C4○D4), (C7×C42.C2)⋊10C2, (C2×C4×D7).127C22, (C7×C4⋊C4).192C22, (C2×C4).204(C22×D7), SmallGroup(448,1146)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 924 in 214 conjugacy classes, 95 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×14], C22, C22 [×7], C7, C2×C4 [×7], C2×C4 [×14], D4 [×2], Q8 [×2], C23 [×2], D7 [×3], C14 [×3], C42, C42 [×4], C22⋊C4 [×8], C4⋊C4 [×6], C4⋊C4 [×10], C22×C4 [×4], C2×D4, C2×Q8, Dic7 [×2], Dic7 [×5], C28 [×7], D14 [×2], D14 [×5], C2×C14, C2×C4⋊C4, C42⋊C2 [×3], C4×D4, C4×Q8, C22⋊Q8 [×2], C22.D4 [×2], C42.C2, C42.C2 [×2], C42⋊2C2 [×2], Dic14 [×2], C4×D7 [×8], D28 [×2], C2×Dic7 [×6], C2×C28 [×7], C22×D7 [×2], C22.46C24, C4×Dic7 [×4], Dic7⋊C4 [×8], C4⋊Dic7 [×2], D14⋊C4 [×8], C4×C28, C7×C4⋊C4 [×6], C2×Dic14, C2×C4×D7 [×4], C2×D28, C42⋊D7 [×2], Dic7⋊3Q8, Dic7.Q8 [×2], D7×C4⋊C4, C4⋊C4⋊7D7, D28⋊C4, D14.5D4 [×2], D14⋊Q8 [×2], C4⋊C4⋊D7 [×2], C7×C42.C2, C42.151D14
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], C22.46C24, C23×D7, Q8.10D14, D7×C4○D4 [×2], C42.151D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b, bd=db, dcd-1=c13 >
►On 224 points
Generators in S224
(1 166 15 152)(2 114 16 128)(3 168 17 154)(4 116 18 130)(5 142 19 156)(6 118 20 132)(7 144 21 158)(8 120 22 134)(9 146 23 160)(10 122 24 136)(11 148 25 162)(12 124 26 138)(13 150 27 164)(14 126 28 140)(29 60 43 74)(30 92 44 106)(31 62 45 76)(32 94 46 108)(33 64 47 78)(34 96 48 110)(35 66 49 80)(36 98 50 112)(37 68 51 82)(38 100 52 86)(39 70 53 84)(40 102 54 88)(41 72 55 58)(42 104 56 90)(57 198 71 212)(59 200 73 214)(61 202 75 216)(63 204 77 218)(65 206 79 220)(67 208 81 222)(69 210 83 224)(85 223 99 209)(87 197 101 211)(89 199 103 213)(91 201 105 215)(93 203 107 217)(95 205 109 219)(97 207 111 221)(113 195 127 181)(115 169 129 183)(117 171 131 185)(119 173 133 187)(121 175 135 189)(123 177 137 191)(125 179 139 193)(141 170 155 184)(143 172 157 186)(145 174 159 188)(147 176 161 190)(149 178 163 192)(151 180 165 194)(153 182 167 196)
(1 41 181 199)(2 56 182 214)(3 43 183 201)(4 30 184 216)(5 45 185 203)(6 32 186 218)(7 47 187 205)(8 34 188 220)(9 49 189 207)(10 36 190 222)(11 51 191 209)(12 38 192 224)(13 53 193 211)(14 40 194 198)(15 55 195 213)(16 42 196 200)(17 29 169 215)(18 44 170 202)(19 31 171 217)(20 46 172 204)(21 33 173 219)(22 48 174 206)(23 35 175 221)(24 50 176 208)(25 37 177 223)(26 52 178 210)(27 39 179 197)(28 54 180 212)(57 140 88 165)(58 127 89 152)(59 114 90 167)(60 129 91 154)(61 116 92 141)(62 131 93 156)(63 118 94 143)(64 133 95 158)(65 120 96 145)(66 135 97 160)(67 122 98 147)(68 137 99 162)(69 124 100 149)(70 139 101 164)(71 126 102 151)(72 113 103 166)(73 128 104 153)(74 115 105 168)(75 130 106 155)(76 117 107 142)(77 132 108 157)(78 119 109 144)(79 134 110 159)(80 121 111 146)(81 136 112 161)(82 123 85 148)(83 138 86 163)(84 125 87 150)
(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 52 43 38)(30 37 44 51)(31 50 45 36)(32 35 46 49)(33 48 47 34)(39 42 53 56)(40 55 54 41)(57 72 71 58)(59 70 73 84)(60 83 74 69)(61 68 75 82)(62 81 76 67)(63 66 77 80)(64 79 78 65)(85 92 99 106)(86 105 100 91)(87 90 101 104)(88 103 102 89)(93 112 107 98)(94 97 108 111)(95 110 109 96)(113 126 127 140)(114 139 128 125)(115 124 129 138)(116 137 130 123)(117 122 131 136)(118 135 132 121)(119 120 133 134)(141 162 155 148)(142 147 156 161)(143 160 157 146)(144 145 158 159)(149 154 163 168)(150 167 164 153)(151 152 165 166)(169 178 183 192)(170 191 184 177)(171 176 185 190)(172 189 186 175)(173 174 187 188)(179 196 193 182)(180 181 194 195)(197 200 211 214)(198 213 212 199)(201 224 215 210)(202 209 216 223)(203 222 217 208)(204 207 218 221)(205 220 219 206)
G:=sub<Sym(224)| (1,166,15,152)(2,114,16,128)(3,168,17,154)(4,116,18,130)(5,142,19,156)(6,118,20,132)(7,144,21,158)(8,120,22,134)(9,146,23,160)(10,122,24,136)(11,148,25,162)(12,124,26,138)(13,150,27,164)(14,126,28,140)(29,60,43,74)(30,92,44,106)(31,62,45,76)(32,94,46,108)(33,64,47,78)(34,96,48,110)(35,66,49,80)(36,98,50,112)(37,68,51,82)(38,100,52,86)(39,70,53,84)(40,102,54,88)(41,72,55,58)(42,104,56,90)(57,198,71,212)(59,200,73,214)(61,202,75,216)(63,204,77,218)(65,206,79,220)(67,208,81,222)(69,210,83,224)(85,223,99,209)(87,197,101,211)(89,199,103,213)(91,201,105,215)(93,203,107,217)(95,205,109,219)(97,207,111,221)(113,195,127,181)(115,169,129,183)(117,171,131,185)(119,173,133,187)(121,175,135,189)(123,177,137,191)(125,179,139,193)(141,170,155,184)(143,172,157,186)(145,174,159,188)(147,176,161,190)(149,178,163,192)(151,180,165,194)(153,182,167,196), (1,41,181,199)(2,56,182,214)(3,43,183,201)(4,30,184,216)(5,45,185,203)(6,32,186,218)(7,47,187,205)(8,34,188,220)(9,49,189,207)(10,36,190,222)(11,51,191,209)(12,38,192,224)(13,53,193,211)(14,40,194,198)(15,55,195,213)(16,42,196,200)(17,29,169,215)(18,44,170,202)(19,31,171,217)(20,46,172,204)(21,33,173,219)(22,48,174,206)(23,35,175,221)(24,50,176,208)(25,37,177,223)(26,52,178,210)(27,39,179,197)(28,54,180,212)(57,140,88,165)(58,127,89,152)(59,114,90,167)(60,129,91,154)(61,116,92,141)(62,131,93,156)(63,118,94,143)(64,133,95,158)(65,120,96,145)(66,135,97,160)(67,122,98,147)(68,137,99,162)(69,124,100,149)(70,139,101,164)(71,126,102,151)(72,113,103,166)(73,128,104,153)(74,115,105,168)(75,130,106,155)(76,117,107,142)(77,132,108,157)(78,119,109,144)(79,134,110,159)(80,121,111,146)(81,136,112,161)(82,123,85,148)(83,138,86,163)(84,125,87,150), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,92,99,106)(86,105,100,91)(87,90,101,104)(88,103,102,89)(93,112,107,98)(94,97,108,111)(95,110,109,96)(113,126,127,140)(114,139,128,125)(115,124,129,138)(116,137,130,123)(117,122,131,136)(118,135,132,121)(119,120,133,134)(141,162,155,148)(142,147,156,161)(143,160,157,146)(144,145,158,159)(149,154,163,168)(150,167,164,153)(151,152,165,166)(169,178,183,192)(170,191,184,177)(171,176,185,190)(172,189,186,175)(173,174,187,188)(179,196,193,182)(180,181,194,195)(197,200,211,214)(198,213,212,199)(201,224,215,210)(202,209,216,223)(203,222,217,208)(204,207,218,221)(205,220,219,206)>;
G:=Group( (1,166,15,152)(2,114,16,128)(3,168,17,154)(4,116,18,130)(5,142,19,156)(6,118,20,132)(7,144,21,158)(8,120,22,134)(9,146,23,160)(10,122,24,136)(11,148,25,162)(12,124,26,138)(13,150,27,164)(14,126,28,140)(29,60,43,74)(30,92,44,106)(31,62,45,76)(32,94,46,108)(33,64,47,78)(34,96,48,110)(35,66,49,80)(36,98,50,112)(37,68,51,82)(38,100,52,86)(39,70,53,84)(40,102,54,88)(41,72,55,58)(42,104,56,90)(57,198,71,212)(59,200,73,214)(61,202,75,216)(63,204,77,218)(65,206,79,220)(67,208,81,222)(69,210,83,224)(85,223,99,209)(87,197,101,211)(89,199,103,213)(91,201,105,215)(93,203,107,217)(95,205,109,219)(97,207,111,221)(113,195,127,181)(115,169,129,183)(117,171,131,185)(119,173,133,187)(121,175,135,189)(123,177,137,191)(125,179,139,193)(141,170,155,184)(143,172,157,186)(145,174,159,188)(147,176,161,190)(149,178,163,192)(151,180,165,194)(153,182,167,196), (1,41,181,199)(2,56,182,214)(3,43,183,201)(4,30,184,216)(5,45,185,203)(6,32,186,218)(7,47,187,205)(8,34,188,220)(9,49,189,207)(10,36,190,222)(11,51,191,209)(12,38,192,224)(13,53,193,211)(14,40,194,198)(15,55,195,213)(16,42,196,200)(17,29,169,215)(18,44,170,202)(19,31,171,217)(20,46,172,204)(21,33,173,219)(22,48,174,206)(23,35,175,221)(24,50,176,208)(25,37,177,223)(26,52,178,210)(27,39,179,197)(28,54,180,212)(57,140,88,165)(58,127,89,152)(59,114,90,167)(60,129,91,154)(61,116,92,141)(62,131,93,156)(63,118,94,143)(64,133,95,158)(65,120,96,145)(66,135,97,160)(67,122,98,147)(68,137,99,162)(69,124,100,149)(70,139,101,164)(71,126,102,151)(72,113,103,166)(73,128,104,153)(74,115,105,168)(75,130,106,155)(76,117,107,142)(77,132,108,157)(78,119,109,144)(79,134,110,159)(80,121,111,146)(81,136,112,161)(82,123,85,148)(83,138,86,163)(84,125,87,150), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,92,99,106)(86,105,100,91)(87,90,101,104)(88,103,102,89)(93,112,107,98)(94,97,108,111)(95,110,109,96)(113,126,127,140)(114,139,128,125)(115,124,129,138)(116,137,130,123)(117,122,131,136)(118,135,132,121)(119,120,133,134)(141,162,155,148)(142,147,156,161)(143,160,157,146)(144,145,158,159)(149,154,163,168)(150,167,164,153)(151,152,165,166)(169,178,183,192)(170,191,184,177)(171,176,185,190)(172,189,186,175)(173,174,187,188)(179,196,193,182)(180,181,194,195)(197,200,211,214)(198,213,212,199)(201,224,215,210)(202,209,216,223)(203,222,217,208)(204,207,218,221)(205,220,219,206) );
G=PermutationGroup([(1,166,15,152),(2,114,16,128),(3,168,17,154),(4,116,18,130),(5,142,19,156),(6,118,20,132),(7,144,21,158),(8,120,22,134),(9,146,23,160),(10,122,24,136),(11,148,25,162),(12,124,26,138),(13,150,27,164),(14,126,28,140),(29,60,43,74),(30,92,44,106),(31,62,45,76),(32,94,46,108),(33,64,47,78),(34,96,48,110),(35,66,49,80),(36,98,50,112),(37,68,51,82),(38,100,52,86),(39,70,53,84),(40,102,54,88),(41,72,55,58),(42,104,56,90),(57,198,71,212),(59,200,73,214),(61,202,75,216),(63,204,77,218),(65,206,79,220),(67,208,81,222),(69,210,83,224),(85,223,99,209),(87,197,101,211),(89,199,103,213),(91,201,105,215),(93,203,107,217),(95,205,109,219),(97,207,111,221),(113,195,127,181),(115,169,129,183),(117,171,131,185),(119,173,133,187),(121,175,135,189),(123,177,137,191),(125,179,139,193),(141,170,155,184),(143,172,157,186),(145,174,159,188),(147,176,161,190),(149,178,163,192),(151,180,165,194),(153,182,167,196)], [(1,41,181,199),(2,56,182,214),(3,43,183,201),(4,30,184,216),(5,45,185,203),(6,32,186,218),(7,47,187,205),(8,34,188,220),(9,49,189,207),(10,36,190,222),(11,51,191,209),(12,38,192,224),(13,53,193,211),(14,40,194,198),(15,55,195,213),(16,42,196,200),(17,29,169,215),(18,44,170,202),(19,31,171,217),(20,46,172,204),(21,33,173,219),(22,48,174,206),(23,35,175,221),(24,50,176,208),(25,37,177,223),(26,52,178,210),(27,39,179,197),(28,54,180,212),(57,140,88,165),(58,127,89,152),(59,114,90,167),(60,129,91,154),(61,116,92,141),(62,131,93,156),(63,118,94,143),(64,133,95,158),(65,120,96,145),(66,135,97,160),(67,122,98,147),(68,137,99,162),(69,124,100,149),(70,139,101,164),(71,126,102,151),(72,113,103,166),(73,128,104,153),(74,115,105,168),(75,130,106,155),(76,117,107,142),(77,132,108,157),(78,119,109,144),(79,134,110,159),(80,121,111,146),(81,136,112,161),(82,123,85,148),(83,138,86,163),(84,125,87,150)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,52,43,38),(30,37,44,51),(31,50,45,36),(32,35,46,49),(33,48,47,34),(39,42,53,56),(40,55,54,41),(57,72,71,58),(59,70,73,84),(60,83,74,69),(61,68,75,82),(62,81,76,67),(63,66,77,80),(64,79,78,65),(85,92,99,106),(86,105,100,91),(87,90,101,104),(88,103,102,89),(93,112,107,98),(94,97,108,111),(95,110,109,96),(113,126,127,140),(114,139,128,125),(115,124,129,138),(116,137,130,123),(117,122,131,136),(118,135,132,121),(119,120,133,134),(141,162,155,148),(142,147,156,161),(143,160,157,146),(144,145,158,159),(149,154,163,168),(150,167,164,153),(151,152,165,166),(169,178,183,192),(170,191,184,177),(171,176,185,190),(172,189,186,175),(173,174,187,188),(179,196,193,182),(180,181,194,195),(197,200,211,214),(198,213,212,199),(201,224,215,210),(202,209,216,223),(203,222,217,208),(204,207,218,221),(205,220,219,206)])
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 | 26 | 1 |
| 0 | 0 | 0 | 0 | 21 | 3 |
| 13 | 7 | 0 | 0 | 0 | 0 |
| 5 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 1 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 8 | 0 | 0 |
| 0 | 0 | 13 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 1 | 17 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 26 | 0 | 0 |
| 0 | 0 | 22 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 1 | 17 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,26,21,0,0,0,0,1,3],[13,5,0,0,0,0,7,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,1,0,0,0,0,0,17,0,0,0,0,0,0,9,13,0,0,0,0,8,2,0,0,0,0,0,0,12,1,0,0,0,0,2,17],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,26,22,0,0,0,0,26,3,0,0,0,0,0,0,12,1,0,0,0,0,2,17] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 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 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 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 | C4○D4 | D14 | D14 | 2- (1+4) | Q8.10D14 | D7×C4○D4 |
| kernel | C42.151D14 | C42⋊D7 | Dic7⋊3Q8 | Dic7.Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | D14⋊Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | Dic7 | D14 | C42 | C4⋊C4 | C14 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 18 | 1 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{151}D_{14} % in TeX
G:=Group("C4^2.151D14"); // GroupNames label
G:=SmallGroup(448,1146);
// by ID
G=gap.SmallGroup(448,1146);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,346,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=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,b*d=d*b,d*c*d^-1=c^13>;
// generators/relations
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