metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.133D14, C14.132- (1+4), C14.1122+ (1+4), C28⋊Q8⋊17C2, (C4×Q8)⋊15D7, (C4×D28)⋊41C2, (Q8×C28)⋊17C2, C4⋊C4.300D14, D14⋊3Q8⋊10C2, D14⋊Q8⋊12C2, D14.5D4⋊9C2, C4.49(C4○D28), C28.23D4⋊9C2, C4.D28⋊29C2, C28⋊1D4.10C2, C42⋊D7⋊18C2, C42⋊2D7⋊12C2, D14⋊C4.7C22, (C2×Q8).181D14, C28.120(C4○D4), (C2×C28).171C23, (C2×C14).126C24, (C4×C28).178C22, C2.24(D4⋊8D14), (C2×D28).263C22, Dic7⋊C4.77C22, C4⋊Dic7.369C22, (Q8×C14).226C22, (C4×Dic7).86C22, (C2×Dic7).57C23, (C22×D7).48C23, C22.147(C23×D7), C7⋊3(C22.36C24), (C2×Dic14).32C22, C2.14(Q8.10D14), C14.56(C2×C4○D4), C2.65(C2×C4○D28), (C2×C4×D7).76C22, (C7×C4⋊C4).354C22, (C2×C4).171(C22×D7), SmallGroup(448,1035)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1060 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×11], C22, C22 [×9], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×9], D4 [×4], Q8 [×4], C23 [×3], D7 [×3], C14 [×3], C42, C42 [×2], C42, C22⋊C4 [×12], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×7], C22×C4 [×3], C2×D4 [×3], C2×Q8, C2×Q8 [×2], Dic7 [×5], C28 [×2], C28 [×6], D14 [×9], C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4 [×3], C42⋊2C2 [×2], C4⋊Q8, Dic14 [×2], C4×D7 [×4], D28 [×4], C2×Dic7 [×3], C2×Dic7 [×2], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7, C22×D7 [×2], C22.36C24, C4×Dic7, Dic7⋊C4 [×2], Dic7⋊C4 [×4], C4⋊Dic7, D14⋊C4 [×2], D14⋊C4 [×10], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14 [×2], C2×C4×D7, C2×C4×D7 [×2], C2×D28, C2×D28 [×2], Q8×C14, C42⋊D7, C4×D28, C4.D28 [×2], C42⋊2D7 [×2], C28⋊Q8, D14.5D4 [×2], C28⋊1D4, D14⋊Q8 [×2], D14⋊3Q8, C28.23D4, Q8×C28, C42.133D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4), 2- (1+4), C22×D7 [×7], C22.36C24, C4○D28 [×2], C23×D7, C2×C4○D28, Q8.10D14, D4⋊8D14, C42.133D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=b2c13 >
►On 224 points
Generators in S224
(1 77 15 63)(2 64 16 78)(3 79 17 65)(4 66 18 80)(5 81 19 67)(6 68 20 82)(7 83 21 69)(8 70 22 84)(9 57 23 71)(10 72 24 58)(11 59 25 73)(12 74 26 60)(13 61 27 75)(14 76 28 62)(29 99 43 85)(30 86 44 100)(31 101 45 87)(32 88 46 102)(33 103 47 89)(34 90 48 104)(35 105 49 91)(36 92 50 106)(37 107 51 93)(38 94 52 108)(39 109 53 95)(40 96 54 110)(41 111 55 97)(42 98 56 112)(113 144 127 158)(114 159 128 145)(115 146 129 160)(116 161 130 147)(117 148 131 162)(118 163 132 149)(119 150 133 164)(120 165 134 151)(121 152 135 166)(122 167 136 153)(123 154 137 168)(124 141 138 155)(125 156 139 142)(126 143 140 157)(169 215 183 201)(170 202 184 216)(171 217 185 203)(172 204 186 218)(173 219 187 205)(174 206 188 220)(175 221 189 207)(176 208 190 222)(177 223 191 209)(178 210 192 224)(179 197 193 211)(180 212 194 198)(181 199 195 213)(182 214 196 200)
(1 43 204 114)(2 44 205 115)(3 45 206 116)(4 46 207 117)(5 47 208 118)(6 48 209 119)(7 49 210 120)(8 50 211 121)(9 51 212 122)(10 52 213 123)(11 53 214 124)(12 54 215 125)(13 55 216 126)(14 56 217 127)(15 29 218 128)(16 30 219 129)(17 31 220 130)(18 32 221 131)(19 33 222 132)(20 34 223 133)(21 35 224 134)(22 36 197 135)(23 37 198 136)(24 38 199 137)(25 39 200 138)(26 40 201 139)(27 41 202 140)(28 42 203 113)(57 93 194 167)(58 94 195 168)(59 95 196 141)(60 96 169 142)(61 97 170 143)(62 98 171 144)(63 99 172 145)(64 100 173 146)(65 101 174 147)(66 102 175 148)(67 103 176 149)(68 104 177 150)(69 105 178 151)(70 106 179 152)(71 107 180 153)(72 108 181 154)(73 109 182 155)(74 110 183 156)(75 111 184 157)(76 112 185 158)(77 85 186 159)(78 86 187 160)(79 87 188 161)(80 88 189 162)(81 89 190 163)(82 90 191 164)(83 91 192 165)(84 92 193 166)
(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)
(1 134 218 49)(2 48 219 133)(3 132 220 47)(4 46 221 131)(5 130 222 45)(6 44 223 129)(7 128 224 43)(8 42 197 127)(9 126 198 41)(10 40 199 125)(11 124 200 39)(12 38 201 123)(13 122 202 37)(14 36 203 121)(15 120 204 35)(16 34 205 119)(17 118 206 33)(18 32 207 117)(19 116 208 31)(20 30 209 115)(21 114 210 29)(22 56 211 113)(23 140 212 55)(24 54 213 139)(25 138 214 53)(26 52 215 137)(27 136 216 51)(28 50 217 135)(57 157 180 97)(58 96 181 156)(59 155 182 95)(60 94 183 154)(61 153 184 93)(62 92 185 152)(63 151 186 91)(64 90 187 150)(65 149 188 89)(66 88 189 148)(67 147 190 87)(68 86 191 146)(69 145 192 85)(70 112 193 144)(71 143 194 111)(72 110 195 142)(73 141 196 109)(74 108 169 168)(75 167 170 107)(76 106 171 166)(77 165 172 105)(78 104 173 164)(79 163 174 103)(80 102 175 162)(81 161 176 101)(82 100 177 160)(83 159 178 99)(84 98 179 158)
G:=sub<Sym(224)| (1,77,15,63)(2,64,16,78)(3,79,17,65)(4,66,18,80)(5,81,19,67)(6,68,20,82)(7,83,21,69)(8,70,22,84)(9,57,23,71)(10,72,24,58)(11,59,25,73)(12,74,26,60)(13,61,27,75)(14,76,28,62)(29,99,43,85)(30,86,44,100)(31,101,45,87)(32,88,46,102)(33,103,47,89)(34,90,48,104)(35,105,49,91)(36,92,50,106)(37,107,51,93)(38,94,52,108)(39,109,53,95)(40,96,54,110)(41,111,55,97)(42,98,56,112)(113,144,127,158)(114,159,128,145)(115,146,129,160)(116,161,130,147)(117,148,131,162)(118,163,132,149)(119,150,133,164)(120,165,134,151)(121,152,135,166)(122,167,136,153)(123,154,137,168)(124,141,138,155)(125,156,139,142)(126,143,140,157)(169,215,183,201)(170,202,184,216)(171,217,185,203)(172,204,186,218)(173,219,187,205)(174,206,188,220)(175,221,189,207)(176,208,190,222)(177,223,191,209)(178,210,192,224)(179,197,193,211)(180,212,194,198)(181,199,195,213)(182,214,196,200), (1,43,204,114)(2,44,205,115)(3,45,206,116)(4,46,207,117)(5,47,208,118)(6,48,209,119)(7,49,210,120)(8,50,211,121)(9,51,212,122)(10,52,213,123)(11,53,214,124)(12,54,215,125)(13,55,216,126)(14,56,217,127)(15,29,218,128)(16,30,219,129)(17,31,220,130)(18,32,221,131)(19,33,222,132)(20,34,223,133)(21,35,224,134)(22,36,197,135)(23,37,198,136)(24,38,199,137)(25,39,200,138)(26,40,201,139)(27,41,202,140)(28,42,203,113)(57,93,194,167)(58,94,195,168)(59,95,196,141)(60,96,169,142)(61,97,170,143)(62,98,171,144)(63,99,172,145)(64,100,173,146)(65,101,174,147)(66,102,175,148)(67,103,176,149)(68,104,177,150)(69,105,178,151)(70,106,179,152)(71,107,180,153)(72,108,181,154)(73,109,182,155)(74,110,183,156)(75,111,184,157)(76,112,185,158)(77,85,186,159)(78,86,187,160)(79,87,188,161)(80,88,189,162)(81,89,190,163)(82,90,191,164)(83,91,192,165)(84,92,193,166), (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), (1,134,218,49)(2,48,219,133)(3,132,220,47)(4,46,221,131)(5,130,222,45)(6,44,223,129)(7,128,224,43)(8,42,197,127)(9,126,198,41)(10,40,199,125)(11,124,200,39)(12,38,201,123)(13,122,202,37)(14,36,203,121)(15,120,204,35)(16,34,205,119)(17,118,206,33)(18,32,207,117)(19,116,208,31)(20,30,209,115)(21,114,210,29)(22,56,211,113)(23,140,212,55)(24,54,213,139)(25,138,214,53)(26,52,215,137)(27,136,216,51)(28,50,217,135)(57,157,180,97)(58,96,181,156)(59,155,182,95)(60,94,183,154)(61,153,184,93)(62,92,185,152)(63,151,186,91)(64,90,187,150)(65,149,188,89)(66,88,189,148)(67,147,190,87)(68,86,191,146)(69,145,192,85)(70,112,193,144)(71,143,194,111)(72,110,195,142)(73,141,196,109)(74,108,169,168)(75,167,170,107)(76,106,171,166)(77,165,172,105)(78,104,173,164)(79,163,174,103)(80,102,175,162)(81,161,176,101)(82,100,177,160)(83,159,178,99)(84,98,179,158)>;
G:=Group( (1,77,15,63)(2,64,16,78)(3,79,17,65)(4,66,18,80)(5,81,19,67)(6,68,20,82)(7,83,21,69)(8,70,22,84)(9,57,23,71)(10,72,24,58)(11,59,25,73)(12,74,26,60)(13,61,27,75)(14,76,28,62)(29,99,43,85)(30,86,44,100)(31,101,45,87)(32,88,46,102)(33,103,47,89)(34,90,48,104)(35,105,49,91)(36,92,50,106)(37,107,51,93)(38,94,52,108)(39,109,53,95)(40,96,54,110)(41,111,55,97)(42,98,56,112)(113,144,127,158)(114,159,128,145)(115,146,129,160)(116,161,130,147)(117,148,131,162)(118,163,132,149)(119,150,133,164)(120,165,134,151)(121,152,135,166)(122,167,136,153)(123,154,137,168)(124,141,138,155)(125,156,139,142)(126,143,140,157)(169,215,183,201)(170,202,184,216)(171,217,185,203)(172,204,186,218)(173,219,187,205)(174,206,188,220)(175,221,189,207)(176,208,190,222)(177,223,191,209)(178,210,192,224)(179,197,193,211)(180,212,194,198)(181,199,195,213)(182,214,196,200), (1,43,204,114)(2,44,205,115)(3,45,206,116)(4,46,207,117)(5,47,208,118)(6,48,209,119)(7,49,210,120)(8,50,211,121)(9,51,212,122)(10,52,213,123)(11,53,214,124)(12,54,215,125)(13,55,216,126)(14,56,217,127)(15,29,218,128)(16,30,219,129)(17,31,220,130)(18,32,221,131)(19,33,222,132)(20,34,223,133)(21,35,224,134)(22,36,197,135)(23,37,198,136)(24,38,199,137)(25,39,200,138)(26,40,201,139)(27,41,202,140)(28,42,203,113)(57,93,194,167)(58,94,195,168)(59,95,196,141)(60,96,169,142)(61,97,170,143)(62,98,171,144)(63,99,172,145)(64,100,173,146)(65,101,174,147)(66,102,175,148)(67,103,176,149)(68,104,177,150)(69,105,178,151)(70,106,179,152)(71,107,180,153)(72,108,181,154)(73,109,182,155)(74,110,183,156)(75,111,184,157)(76,112,185,158)(77,85,186,159)(78,86,187,160)(79,87,188,161)(80,88,189,162)(81,89,190,163)(82,90,191,164)(83,91,192,165)(84,92,193,166), (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), (1,134,218,49)(2,48,219,133)(3,132,220,47)(4,46,221,131)(5,130,222,45)(6,44,223,129)(7,128,224,43)(8,42,197,127)(9,126,198,41)(10,40,199,125)(11,124,200,39)(12,38,201,123)(13,122,202,37)(14,36,203,121)(15,120,204,35)(16,34,205,119)(17,118,206,33)(18,32,207,117)(19,116,208,31)(20,30,209,115)(21,114,210,29)(22,56,211,113)(23,140,212,55)(24,54,213,139)(25,138,214,53)(26,52,215,137)(27,136,216,51)(28,50,217,135)(57,157,180,97)(58,96,181,156)(59,155,182,95)(60,94,183,154)(61,153,184,93)(62,92,185,152)(63,151,186,91)(64,90,187,150)(65,149,188,89)(66,88,189,148)(67,147,190,87)(68,86,191,146)(69,145,192,85)(70,112,193,144)(71,143,194,111)(72,110,195,142)(73,141,196,109)(74,108,169,168)(75,167,170,107)(76,106,171,166)(77,165,172,105)(78,104,173,164)(79,163,174,103)(80,102,175,162)(81,161,176,101)(82,100,177,160)(83,159,178,99)(84,98,179,158) );
G=PermutationGroup([(1,77,15,63),(2,64,16,78),(3,79,17,65),(4,66,18,80),(5,81,19,67),(6,68,20,82),(7,83,21,69),(8,70,22,84),(9,57,23,71),(10,72,24,58),(11,59,25,73),(12,74,26,60),(13,61,27,75),(14,76,28,62),(29,99,43,85),(30,86,44,100),(31,101,45,87),(32,88,46,102),(33,103,47,89),(34,90,48,104),(35,105,49,91),(36,92,50,106),(37,107,51,93),(38,94,52,108),(39,109,53,95),(40,96,54,110),(41,111,55,97),(42,98,56,112),(113,144,127,158),(114,159,128,145),(115,146,129,160),(116,161,130,147),(117,148,131,162),(118,163,132,149),(119,150,133,164),(120,165,134,151),(121,152,135,166),(122,167,136,153),(123,154,137,168),(124,141,138,155),(125,156,139,142),(126,143,140,157),(169,215,183,201),(170,202,184,216),(171,217,185,203),(172,204,186,218),(173,219,187,205),(174,206,188,220),(175,221,189,207),(176,208,190,222),(177,223,191,209),(178,210,192,224),(179,197,193,211),(180,212,194,198),(181,199,195,213),(182,214,196,200)], [(1,43,204,114),(2,44,205,115),(3,45,206,116),(4,46,207,117),(5,47,208,118),(6,48,209,119),(7,49,210,120),(8,50,211,121),(9,51,212,122),(10,52,213,123),(11,53,214,124),(12,54,215,125),(13,55,216,126),(14,56,217,127),(15,29,218,128),(16,30,219,129),(17,31,220,130),(18,32,221,131),(19,33,222,132),(20,34,223,133),(21,35,224,134),(22,36,197,135),(23,37,198,136),(24,38,199,137),(25,39,200,138),(26,40,201,139),(27,41,202,140),(28,42,203,113),(57,93,194,167),(58,94,195,168),(59,95,196,141),(60,96,169,142),(61,97,170,143),(62,98,171,144),(63,99,172,145),(64,100,173,146),(65,101,174,147),(66,102,175,148),(67,103,176,149),(68,104,177,150),(69,105,178,151),(70,106,179,152),(71,107,180,153),(72,108,181,154),(73,109,182,155),(74,110,183,156),(75,111,184,157),(76,112,185,158),(77,85,186,159),(78,86,187,160),(79,87,188,161),(80,88,189,162),(81,89,190,163),(82,90,191,164),(83,91,192,165),(84,92,193,166)], [(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)], [(1,134,218,49),(2,48,219,133),(3,132,220,47),(4,46,221,131),(5,130,222,45),(6,44,223,129),(7,128,224,43),(8,42,197,127),(9,126,198,41),(10,40,199,125),(11,124,200,39),(12,38,201,123),(13,122,202,37),(14,36,203,121),(15,120,204,35),(16,34,205,119),(17,118,206,33),(18,32,207,117),(19,116,208,31),(20,30,209,115),(21,114,210,29),(22,56,211,113),(23,140,212,55),(24,54,213,139),(25,138,214,53),(26,52,215,137),(27,136,216,51),(28,50,217,135),(57,157,180,97),(58,96,181,156),(59,155,182,95),(60,94,183,154),(61,153,184,93),(62,92,185,152),(63,151,186,91),(64,90,187,150),(65,149,188,89),(66,88,189,148),(67,147,190,87),(68,86,191,146),(69,145,192,85),(70,112,193,144),(71,143,194,111),(72,110,195,142),(73,141,196,109),(74,108,169,168),(75,167,170,107),(76,106,171,166),(77,165,172,105),(78,104,173,164),(79,163,174,103),(80,102,175,162),(81,161,176,101),(82,100,177,160),(83,159,178,99),(84,98,179,158)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 21 | 18 | 28 |
| 0 | 0 | 8 | 1 | 1 | 11 |
| 0 | 0 | 18 | 28 | 1 | 8 |
| 0 | 0 | 1 | 11 | 21 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 |
| 0 | 0 | 0 | 0 | 14 | 9 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 10 |
| 0 | 0 | 0 | 0 | 19 | 22 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 21 | 0 | 0 |
| 0 | 0 | 19 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 21 |
| 0 | 0 | 0 | 0 | 19 | 21 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,8,18,1,0,0,21,1,28,11,0,0,18,1,1,21,0,0,28,11,8,28],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,20,14,0,0,0,0,15,9,0,0,0,0,0,0,20,14,0,0,0,0,15,9],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,19,10,0,0,0,0,19,7,0,0,10,19,0,0,0,0,10,22,0,0],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,8,19,0,0,0,0,21,21,0,0,0,0,0,0,8,19,0,0,0,0,21,21] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | 2- (1+4) | Q8.10D14 | D4⋊8D14 |
| kernel | C42.133D14 | C42⋊D7 | C4×D28 | C4.D28 | C42⋊2D7 | C28⋊Q8 | D14.5D4 | C28⋊1D4 | D14⋊Q8 | D14⋊3Q8 | C28.23D4 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 9 | 9 | 3 | 24 | 1 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{133}D_{14} % in TeX
G:=Group("C4^2.133D14"); // GroupNames label
G:=SmallGroup(448,1035);
// by ID
G=gap.SmallGroup(448,1035);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^13>;
// generators/relations
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