metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.166D14, C14.752+ (1+4), C4⋊1D4.7D7, (D4×Dic7)⋊33C2, (C4×Dic14)⋊50C2, (C2×D4).114D14, C28.133(C4○D4), C4.17(D4⋊2D7), C28.17D4⋊25C2, (C2×C14).257C24, (C2×C28).634C23, (C4×C28).202C22, C2.79(D4⋊6D14), C23.63(C22×D7), (D4×C14).160C22, C4⋊Dic7.380C22, (C22×C14).71C23, C22.278(C23×D7), C23.D7.71C22, C23.18D14⋊26C2, Dic7⋊C4.163C22, C7⋊5(C22.53C24), (C4×Dic7).154C22, (C2×Dic7).133C23, (C2×Dic14).300C22, (C22×Dic7).156C22, C14.95(C2×C4○D4), (C7×C4⋊1D4).6C2, C2.59(C2×D4⋊2D7), (C2×C4).595(C22×D7), SmallGroup(448,1166)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 908 in 236 conjugacy classes, 99 normal (13 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×4], C4 [×9], C22, C22 [×12], C7, C2×C4, C2×C4 [×2], C2×C4 [×12], D4 [×10], Q8 [×4], C23 [×4], C14, C14 [×2], C14 [×4], C42, C42 [×4], C22⋊C4 [×12], C4⋊C4 [×6], C22×C4 [×4], C2×D4 [×6], C2×Q8 [×2], Dic7 [×8], C28 [×4], C28, C2×C14, C2×C14 [×12], C4×D4 [×4], C4×Q8 [×2], C22.D4 [×4], C4.4D4 [×4], C4⋊1D4, Dic14 [×4], C2×Dic7 [×8], C2×Dic7 [×4], C2×C28, C2×C28 [×2], C7×D4 [×10], C22×C14 [×4], C22.53C24, C4×Dic7 [×4], Dic7⋊C4 [×4], C4⋊Dic7 [×2], C23.D7 [×12], C4×C28, C2×Dic14 [×2], C22×Dic7 [×4], D4×C14 [×6], C4×Dic14 [×2], D4×Dic7 [×4], C23.18D14 [×4], C28.17D4 [×4], C7×C4⋊1D4, C42.166D14
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, D4⋊2D7 [×4], C23×D7, C2×D4⋊2D7 [×2], D4⋊6D14, C42.166D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=c-1 >
►On 224 points
Generators in S224
(1 105 159 94)(2 95 160 106)(3 107 161 96)(4 97 162 108)(5 109 163 98)(6 85 164 110)(7 111 165 86)(8 87 166 112)(9 99 167 88)(10 89 168 100)(11 101 155 90)(12 91 156 102)(13 103 157 92)(14 93 158 104)(15 75 35 46)(16 47 36 76)(17 77 37 48)(18 49 38 78)(19 79 39 50)(20 51 40 80)(21 81 41 52)(22 53 42 82)(23 83 29 54)(24 55 30 84)(25 71 31 56)(26 43 32 72)(27 73 33 44)(28 45 34 74)(57 122 217 170)(58 171 218 123)(59 124 219 172)(60 173 220 125)(61 126 221 174)(62 175 222 113)(63 114 223 176)(64 177 224 115)(65 116 211 178)(66 179 212 117)(67 118 213 180)(68 181 214 119)(69 120 215 182)(70 169 216 121)(127 202 187 142)(128 143 188 203)(129 204 189 144)(130 145 190 205)(131 206 191 146)(132 147 192 207)(133 208 193 148)(134 149 194 209)(135 210 195 150)(136 151 196 197)(137 198 183 152)(138 153 184 199)(139 200 185 154)(140 141 186 201)
(1 179 172 8)(2 9 173 180)(3 181 174 10)(4 11 175 182)(5 169 176 12)(6 13 177 170)(7 171 178 14)(15 22 209 202)(16 203 210 23)(17 24 197 204)(18 205 198 25)(19 26 199 206)(20 207 200 27)(21 28 201 208)(29 36 143 150)(30 151 144 37)(31 38 145 152)(32 153 146 39)(33 40 147 154)(34 141 148 41)(35 42 149 142)(43 138 191 79)(44 80 192 139)(45 140 193 81)(46 82 194 127)(47 128 195 83)(48 84 196 129)(49 130 183 71)(50 72 184 131)(51 132 185 73)(52 74 186 133)(53 134 187 75)(54 76 188 135)(55 136 189 77)(56 78 190 137)(57 85 103 224)(58 211 104 86)(59 87 105 212)(60 213 106 88)(61 89 107 214)(62 215 108 90)(63 91 109 216)(64 217 110 92)(65 93 111 218)(66 219 112 94)(67 95 99 220)(68 221 100 96)(69 97 101 222)(70 223 102 98)(113 120 162 155)(114 156 163 121)(115 122 164 157)(116 158 165 123)(117 124 166 159)(118 160 167 125)(119 126 168 161)
(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)
(1 191 172 43)(2 190 173 56)(3 189 174 55)(4 188 175 54)(5 187 176 53)(6 186 177 52)(7 185 178 51)(8 184 179 50)(9 183 180 49)(10 196 181 48)(11 195 182 47)(12 194 169 46)(13 193 170 45)(14 192 171 44)(15 102 209 70)(16 101 210 69)(17 100 197 68)(18 99 198 67)(19 112 199 66)(20 111 200 65)(21 110 201 64)(22 109 202 63)(23 108 203 62)(24 107 204 61)(25 106 205 60)(26 105 206 59)(27 104 207 58)(28 103 208 57)(29 97 143 222)(30 96 144 221)(31 95 145 220)(32 94 146 219)(33 93 147 218)(34 92 148 217)(35 91 149 216)(36 90 150 215)(37 89 151 214)(38 88 152 213)(39 87 153 212)(40 86 154 211)(41 85 141 224)(42 98 142 223)(71 160 130 125)(72 159 131 124)(73 158 132 123)(74 157 133 122)(75 156 134 121)(76 155 135 120)(77 168 136 119)(78 167 137 118)(79 166 138 117)(80 165 139 116)(81 164 140 115)(82 163 127 114)(83 162 128 113)(84 161 129 126)
G:=sub<Sym(224)| (1,105,159,94)(2,95,160,106)(3,107,161,96)(4,97,162,108)(5,109,163,98)(6,85,164,110)(7,111,165,86)(8,87,166,112)(9,99,167,88)(10,89,168,100)(11,101,155,90)(12,91,156,102)(13,103,157,92)(14,93,158,104)(15,75,35,46)(16,47,36,76)(17,77,37,48)(18,49,38,78)(19,79,39,50)(20,51,40,80)(21,81,41,52)(22,53,42,82)(23,83,29,54)(24,55,30,84)(25,71,31,56)(26,43,32,72)(27,73,33,44)(28,45,34,74)(57,122,217,170)(58,171,218,123)(59,124,219,172)(60,173,220,125)(61,126,221,174)(62,175,222,113)(63,114,223,176)(64,177,224,115)(65,116,211,178)(66,179,212,117)(67,118,213,180)(68,181,214,119)(69,120,215,182)(70,169,216,121)(127,202,187,142)(128,143,188,203)(129,204,189,144)(130,145,190,205)(131,206,191,146)(132,147,192,207)(133,208,193,148)(134,149,194,209)(135,210,195,150)(136,151,196,197)(137,198,183,152)(138,153,184,199)(139,200,185,154)(140,141,186,201), (1,179,172,8)(2,9,173,180)(3,181,174,10)(4,11,175,182)(5,169,176,12)(6,13,177,170)(7,171,178,14)(15,22,209,202)(16,203,210,23)(17,24,197,204)(18,205,198,25)(19,26,199,206)(20,207,200,27)(21,28,201,208)(29,36,143,150)(30,151,144,37)(31,38,145,152)(32,153,146,39)(33,40,147,154)(34,141,148,41)(35,42,149,142)(43,138,191,79)(44,80,192,139)(45,140,193,81)(46,82,194,127)(47,128,195,83)(48,84,196,129)(49,130,183,71)(50,72,184,131)(51,132,185,73)(52,74,186,133)(53,134,187,75)(54,76,188,135)(55,136,189,77)(56,78,190,137)(57,85,103,224)(58,211,104,86)(59,87,105,212)(60,213,106,88)(61,89,107,214)(62,215,108,90)(63,91,109,216)(64,217,110,92)(65,93,111,218)(66,219,112,94)(67,95,99,220)(68,221,100,96)(69,97,101,222)(70,223,102,98)(113,120,162,155)(114,156,163,121)(115,122,164,157)(116,158,165,123)(117,124,166,159)(118,160,167,125)(119,126,168,161), (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), (1,191,172,43)(2,190,173,56)(3,189,174,55)(4,188,175,54)(5,187,176,53)(6,186,177,52)(7,185,178,51)(8,184,179,50)(9,183,180,49)(10,196,181,48)(11,195,182,47)(12,194,169,46)(13,193,170,45)(14,192,171,44)(15,102,209,70)(16,101,210,69)(17,100,197,68)(18,99,198,67)(19,112,199,66)(20,111,200,65)(21,110,201,64)(22,109,202,63)(23,108,203,62)(24,107,204,61)(25,106,205,60)(26,105,206,59)(27,104,207,58)(28,103,208,57)(29,97,143,222)(30,96,144,221)(31,95,145,220)(32,94,146,219)(33,93,147,218)(34,92,148,217)(35,91,149,216)(36,90,150,215)(37,89,151,214)(38,88,152,213)(39,87,153,212)(40,86,154,211)(41,85,141,224)(42,98,142,223)(71,160,130,125)(72,159,131,124)(73,158,132,123)(74,157,133,122)(75,156,134,121)(76,155,135,120)(77,168,136,119)(78,167,137,118)(79,166,138,117)(80,165,139,116)(81,164,140,115)(82,163,127,114)(83,162,128,113)(84,161,129,126)>;
G:=Group( (1,105,159,94)(2,95,160,106)(3,107,161,96)(4,97,162,108)(5,109,163,98)(6,85,164,110)(7,111,165,86)(8,87,166,112)(9,99,167,88)(10,89,168,100)(11,101,155,90)(12,91,156,102)(13,103,157,92)(14,93,158,104)(15,75,35,46)(16,47,36,76)(17,77,37,48)(18,49,38,78)(19,79,39,50)(20,51,40,80)(21,81,41,52)(22,53,42,82)(23,83,29,54)(24,55,30,84)(25,71,31,56)(26,43,32,72)(27,73,33,44)(28,45,34,74)(57,122,217,170)(58,171,218,123)(59,124,219,172)(60,173,220,125)(61,126,221,174)(62,175,222,113)(63,114,223,176)(64,177,224,115)(65,116,211,178)(66,179,212,117)(67,118,213,180)(68,181,214,119)(69,120,215,182)(70,169,216,121)(127,202,187,142)(128,143,188,203)(129,204,189,144)(130,145,190,205)(131,206,191,146)(132,147,192,207)(133,208,193,148)(134,149,194,209)(135,210,195,150)(136,151,196,197)(137,198,183,152)(138,153,184,199)(139,200,185,154)(140,141,186,201), (1,179,172,8)(2,9,173,180)(3,181,174,10)(4,11,175,182)(5,169,176,12)(6,13,177,170)(7,171,178,14)(15,22,209,202)(16,203,210,23)(17,24,197,204)(18,205,198,25)(19,26,199,206)(20,207,200,27)(21,28,201,208)(29,36,143,150)(30,151,144,37)(31,38,145,152)(32,153,146,39)(33,40,147,154)(34,141,148,41)(35,42,149,142)(43,138,191,79)(44,80,192,139)(45,140,193,81)(46,82,194,127)(47,128,195,83)(48,84,196,129)(49,130,183,71)(50,72,184,131)(51,132,185,73)(52,74,186,133)(53,134,187,75)(54,76,188,135)(55,136,189,77)(56,78,190,137)(57,85,103,224)(58,211,104,86)(59,87,105,212)(60,213,106,88)(61,89,107,214)(62,215,108,90)(63,91,109,216)(64,217,110,92)(65,93,111,218)(66,219,112,94)(67,95,99,220)(68,221,100,96)(69,97,101,222)(70,223,102,98)(113,120,162,155)(114,156,163,121)(115,122,164,157)(116,158,165,123)(117,124,166,159)(118,160,167,125)(119,126,168,161), (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), (1,191,172,43)(2,190,173,56)(3,189,174,55)(4,188,175,54)(5,187,176,53)(6,186,177,52)(7,185,178,51)(8,184,179,50)(9,183,180,49)(10,196,181,48)(11,195,182,47)(12,194,169,46)(13,193,170,45)(14,192,171,44)(15,102,209,70)(16,101,210,69)(17,100,197,68)(18,99,198,67)(19,112,199,66)(20,111,200,65)(21,110,201,64)(22,109,202,63)(23,108,203,62)(24,107,204,61)(25,106,205,60)(26,105,206,59)(27,104,207,58)(28,103,208,57)(29,97,143,222)(30,96,144,221)(31,95,145,220)(32,94,146,219)(33,93,147,218)(34,92,148,217)(35,91,149,216)(36,90,150,215)(37,89,151,214)(38,88,152,213)(39,87,153,212)(40,86,154,211)(41,85,141,224)(42,98,142,223)(71,160,130,125)(72,159,131,124)(73,158,132,123)(74,157,133,122)(75,156,134,121)(76,155,135,120)(77,168,136,119)(78,167,137,118)(79,166,138,117)(80,165,139,116)(81,164,140,115)(82,163,127,114)(83,162,128,113)(84,161,129,126) );
G=PermutationGroup([(1,105,159,94),(2,95,160,106),(3,107,161,96),(4,97,162,108),(5,109,163,98),(6,85,164,110),(7,111,165,86),(8,87,166,112),(9,99,167,88),(10,89,168,100),(11,101,155,90),(12,91,156,102),(13,103,157,92),(14,93,158,104),(15,75,35,46),(16,47,36,76),(17,77,37,48),(18,49,38,78),(19,79,39,50),(20,51,40,80),(21,81,41,52),(22,53,42,82),(23,83,29,54),(24,55,30,84),(25,71,31,56),(26,43,32,72),(27,73,33,44),(28,45,34,74),(57,122,217,170),(58,171,218,123),(59,124,219,172),(60,173,220,125),(61,126,221,174),(62,175,222,113),(63,114,223,176),(64,177,224,115),(65,116,211,178),(66,179,212,117),(67,118,213,180),(68,181,214,119),(69,120,215,182),(70,169,216,121),(127,202,187,142),(128,143,188,203),(129,204,189,144),(130,145,190,205),(131,206,191,146),(132,147,192,207),(133,208,193,148),(134,149,194,209),(135,210,195,150),(136,151,196,197),(137,198,183,152),(138,153,184,199),(139,200,185,154),(140,141,186,201)], [(1,179,172,8),(2,9,173,180),(3,181,174,10),(4,11,175,182),(5,169,176,12),(6,13,177,170),(7,171,178,14),(15,22,209,202),(16,203,210,23),(17,24,197,204),(18,205,198,25),(19,26,199,206),(20,207,200,27),(21,28,201,208),(29,36,143,150),(30,151,144,37),(31,38,145,152),(32,153,146,39),(33,40,147,154),(34,141,148,41),(35,42,149,142),(43,138,191,79),(44,80,192,139),(45,140,193,81),(46,82,194,127),(47,128,195,83),(48,84,196,129),(49,130,183,71),(50,72,184,131),(51,132,185,73),(52,74,186,133),(53,134,187,75),(54,76,188,135),(55,136,189,77),(56,78,190,137),(57,85,103,224),(58,211,104,86),(59,87,105,212),(60,213,106,88),(61,89,107,214),(62,215,108,90),(63,91,109,216),(64,217,110,92),(65,93,111,218),(66,219,112,94),(67,95,99,220),(68,221,100,96),(69,97,101,222),(70,223,102,98),(113,120,162,155),(114,156,163,121),(115,122,164,157),(116,158,165,123),(117,124,166,159),(118,160,167,125),(119,126,168,161)], [(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)], [(1,191,172,43),(2,190,173,56),(3,189,174,55),(4,188,175,54),(5,187,176,53),(6,186,177,52),(7,185,178,51),(8,184,179,50),(9,183,180,49),(10,196,181,48),(11,195,182,47),(12,194,169,46),(13,193,170,45),(14,192,171,44),(15,102,209,70),(16,101,210,69),(17,100,197,68),(18,99,198,67),(19,112,199,66),(20,111,200,65),(21,110,201,64),(22,109,202,63),(23,108,203,62),(24,107,204,61),(25,106,205,60),(26,105,206,59),(27,104,207,58),(28,103,208,57),(29,97,143,222),(30,96,144,221),(31,95,145,220),(32,94,146,219),(33,93,147,218),(34,92,148,217),(35,91,149,216),(36,90,150,215),(37,89,151,214),(38,88,152,213),(39,87,153,212),(40,86,154,211),(41,85,141,224),(42,98,142,223),(71,160,130,125),(72,159,131,124),(73,158,132,123),(74,157,133,122),(75,156,134,121),(76,155,135,120),(77,168,136,119),(78,167,137,118),(79,166,138,117),(80,165,139,116),(81,164,140,115),(82,163,127,114),(83,162,128,113),(84,161,129,126)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 18 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 17 | 13 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [28,16,0,0,0,0,18,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,16,0,0,0,0,18,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[28,0,0,0,0,0,18,1,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[17,0,0,0,0,0,13,12,0,0,0,0,0,0,21,8,0,0,0,0,3,8,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2+ (1+4) | D4⋊2D7 | D4⋊6D14 |
| kernel | C42.166D14 | C4×Dic14 | D4×Dic7 | C23.18D14 | C28.17D4 | C7×C4⋊1D4 | C4⋊1D4 | C28 | C42 | C2×D4 | C14 | C4 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 8 | 3 | 18 | 1 | 12 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{166}D_{14} % in TeX
G:=Group("C4^2.166D14"); // GroupNames label
G:=SmallGroup(448,1166);
// by ID
G=gap.SmallGroup(448,1166);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,219,1571,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations
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