metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.118D14, C14.632- (1+4), C14.232+ (1+4), (C4×D4)⋊26D7, (D4×C28)⋊28C2, C4⋊C4.288D14, D14⋊Q8⋊9C2, Dic7.Q8⋊8C2, (C2×D4).225D14, C42⋊2D7⋊11C2, C28.6Q8⋊26C2, (C22×C4).49D14, D14.D4⋊10C2, C28.48D4⋊13C2, (C4×C28).220C22, (C2×C14).108C24, (C2×C28).166C23, D14⋊C4.67C22, C22⋊C4.120D14, Dic7⋊D4.4C2, C22.7(C4○D28), C22.D28⋊7C2, Dic7⋊C4.8C22, C4⋊Dic7.41C22, C2.25(D4⋊6D14), C22⋊Dic14⋊10C2, (D4×C14).309C22, C23.D14⋊10C2, C23.23D14⋊5C2, (C2×Dic7).48C23, (C22×D7).42C23, C22.133(C23×D7), C23.105(C22×D7), C23.D7.17C22, C23.18D14⋊19C2, (C22×C28).366C22, (C22×C14).178C23, C7⋊2(C22.33C24), (C4×Dic7).207C22, (C2×Dic14).29C22, C2.20(D4.10D14), (C22×Dic7).100C22, (C4×C7⋊D4)⋊47C2, C14.50(C2×C4○D4), C2.57(C2×C4○D28), (C2×Dic7⋊C4)⋊39C2, (C2×C4×D7).204C22, (C2×C14).18(C4○D4), (C7×C4⋊C4).336C22, (C2×C4).164(C22×D7), (C2×C7⋊D4).117C22, (C7×C22⋊C4).107C22, SmallGroup(448,1017)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 916 in 218 conjugacy classes, 95 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×2], C22 [×8], C7, C2×C4 [×5], C2×C4 [×13], D4 [×5], Q8, C23 [×2], C23, D7, C14 [×3], C14 [×3], C42, C42, C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×13], C22×C4 [×2], C22×C4 [×3], C2×D4, C2×D4 [×2], C2×Q8, Dic7 [×7], C28 [×5], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×5], C2×C4⋊C4, C4×D4, C4×D4, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×4], C42.C2 [×2], C42⋊2C2 [×2], Dic14, C4×D7, C2×Dic7 [×7], C2×Dic7 [×3], C7⋊D4 [×3], C2×C28 [×5], C2×C28 [×2], C7×D4 [×2], C22×D7, C22×C14 [×2], C22.33C24, C4×Dic7, Dic7⋊C4 [×10], C4⋊Dic7 [×3], D14⋊C4 [×4], C23.D7 [×4], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7 [×2], C2×C7⋊D4 [×2], C22×C28 [×2], D4×C14, C28.6Q8, C42⋊2D7, C22⋊Dic14, C23.D14, D14.D4, C22.D28, Dic7.Q8, D14⋊Q8, C2×Dic7⋊C4, C28.48D4, C4×C7⋊D4, C23.23D14, C23.18D14, Dic7⋊D4, D4×C28, C42.118D14
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], C22.33C24, C4○D28 [×2], C23×D7, C2×C4○D28, D4⋊6D14, D4.10D14, C42.118D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=a2b, dbd-1=b-1, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 197 12 204)(2 205 13 198)(3 199 14 206)(4 207 8 200)(5 201 9 208)(6 209 10 202)(7 203 11 210)(15 132 107 139)(16 140 108 133)(17 134 109 127)(18 128 110 135)(19 136 111 129)(20 130 112 137)(21 138 106 131)(22 165 86 158)(23 159 87 166)(24 167 88 160)(25 161 89 168)(26 155 90 162)(27 163 91 156)(28 157 85 164)(29 217 54 224)(30 211 55 218)(31 219 56 212)(32 213 50 220)(33 221 51 214)(34 215 52 222)(35 223 53 216)(36 170 95 177)(37 178 96 171)(38 172 97 179)(39 180 98 173)(40 174 92 181)(41 182 93 175)(42 176 94 169)(43 191 105 184)(44 185 99 192)(45 193 100 186)(46 187 101 194)(47 195 102 188)(48 189 103 196)(49 183 104 190)(57 149 64 142)(58 143 65 150)(59 151 66 144)(60 145 67 152)(61 153 68 146)(62 147 69 154)(63 141 70 148)(71 119 78 126)(72 113 79 120)(73 121 80 114)(74 115 81 122)(75 123 82 116)(76 117 83 124)(77 125 84 118)
(1 123 111 146)(2 117 112 154)(3 125 106 148)(4 119 107 142)(5 113 108 150)(6 121 109 144)(7 115 110 152)(8 126 15 149)(9 120 16 143)(10 114 17 151)(11 122 18 145)(12 116 19 153)(13 124 20 147)(14 118 21 141)(22 191 38 216)(23 185 39 224)(24 193 40 218)(25 187 41 212)(26 195 42 220)(27 189 36 214)(28 183 37 222)(29 159 99 180)(30 167 100 174)(31 161 101 182)(32 155 102 176)(33 163 103 170)(34 157 104 178)(35 165 105 172)(43 179 53 158)(44 173 54 166)(45 181 55 160)(46 175 56 168)(47 169 50 162)(48 177 51 156)(49 171 52 164)(57 207 78 139)(58 201 79 133)(59 209 80 127)(60 203 81 135)(61 197 82 129)(62 205 83 137)(63 199 84 131)(64 200 71 132)(65 208 72 140)(66 202 73 134)(67 210 74 128)(68 204 75 136)(69 198 76 130)(70 206 77 138)(85 190 96 215)(86 184 97 223)(87 192 98 217)(88 186 92 211)(89 194 93 219)(90 188 94 213)(91 196 95 221)
(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)
(1 170 12 177)(2 176 13 169)(3 182 14 175)(4 174 8 181)(5 180 9 173)(6 172 10 179)(7 178 11 171)(15 160 107 167)(16 166 108 159)(17 158 109 165)(18 164 110 157)(19 156 111 163)(20 162 112 155)(21 168 106 161)(22 202 86 209)(23 208 87 201)(24 200 88 207)(25 206 89 199)(26 198 90 205)(27 204 91 197)(28 210 85 203)(29 143 54 150)(30 149 55 142)(31 141 56 148)(32 147 50 154)(33 153 51 146)(34 145 52 152)(35 151 53 144)(36 136 95 129)(37 128 96 135)(38 134 97 127)(39 140 98 133)(40 132 92 139)(41 138 93 131)(42 130 94 137)(43 121 105 114)(44 113 99 120)(45 119 100 126)(46 125 101 118)(47 117 102 124)(48 123 103 116)(49 115 104 122)(57 193 64 186)(58 185 65 192)(59 191 66 184)(60 183 67 190)(61 189 68 196)(62 195 69 188)(63 187 70 194)(71 211 78 218)(72 217 79 224)(73 223 80 216)(74 215 81 222)(75 221 82 214)(76 213 83 220)(77 219 84 212)
G:=sub<Sym(224)| (1,197,12,204)(2,205,13,198)(3,199,14,206)(4,207,8,200)(5,201,9,208)(6,209,10,202)(7,203,11,210)(15,132,107,139)(16,140,108,133)(17,134,109,127)(18,128,110,135)(19,136,111,129)(20,130,112,137)(21,138,106,131)(22,165,86,158)(23,159,87,166)(24,167,88,160)(25,161,89,168)(26,155,90,162)(27,163,91,156)(28,157,85,164)(29,217,54,224)(30,211,55,218)(31,219,56,212)(32,213,50,220)(33,221,51,214)(34,215,52,222)(35,223,53,216)(36,170,95,177)(37,178,96,171)(38,172,97,179)(39,180,98,173)(40,174,92,181)(41,182,93,175)(42,176,94,169)(43,191,105,184)(44,185,99,192)(45,193,100,186)(46,187,101,194)(47,195,102,188)(48,189,103,196)(49,183,104,190)(57,149,64,142)(58,143,65,150)(59,151,66,144)(60,145,67,152)(61,153,68,146)(62,147,69,154)(63,141,70,148)(71,119,78,126)(72,113,79,120)(73,121,80,114)(74,115,81,122)(75,123,82,116)(76,117,83,124)(77,125,84,118), (1,123,111,146)(2,117,112,154)(3,125,106,148)(4,119,107,142)(5,113,108,150)(6,121,109,144)(7,115,110,152)(8,126,15,149)(9,120,16,143)(10,114,17,151)(11,122,18,145)(12,116,19,153)(13,124,20,147)(14,118,21,141)(22,191,38,216)(23,185,39,224)(24,193,40,218)(25,187,41,212)(26,195,42,220)(27,189,36,214)(28,183,37,222)(29,159,99,180)(30,167,100,174)(31,161,101,182)(32,155,102,176)(33,163,103,170)(34,157,104,178)(35,165,105,172)(43,179,53,158)(44,173,54,166)(45,181,55,160)(46,175,56,168)(47,169,50,162)(48,177,51,156)(49,171,52,164)(57,207,78,139)(58,201,79,133)(59,209,80,127)(60,203,81,135)(61,197,82,129)(62,205,83,137)(63,199,84,131)(64,200,71,132)(65,208,72,140)(66,202,73,134)(67,210,74,128)(68,204,75,136)(69,198,76,130)(70,206,77,138)(85,190,96,215)(86,184,97,223)(87,192,98,217)(88,186,92,211)(89,194,93,219)(90,188,94,213)(91,196,95,221), (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), (1,170,12,177)(2,176,13,169)(3,182,14,175)(4,174,8,181)(5,180,9,173)(6,172,10,179)(7,178,11,171)(15,160,107,167)(16,166,108,159)(17,158,109,165)(18,164,110,157)(19,156,111,163)(20,162,112,155)(21,168,106,161)(22,202,86,209)(23,208,87,201)(24,200,88,207)(25,206,89,199)(26,198,90,205)(27,204,91,197)(28,210,85,203)(29,143,54,150)(30,149,55,142)(31,141,56,148)(32,147,50,154)(33,153,51,146)(34,145,52,152)(35,151,53,144)(36,136,95,129)(37,128,96,135)(38,134,97,127)(39,140,98,133)(40,132,92,139)(41,138,93,131)(42,130,94,137)(43,121,105,114)(44,113,99,120)(45,119,100,126)(46,125,101,118)(47,117,102,124)(48,123,103,116)(49,115,104,122)(57,193,64,186)(58,185,65,192)(59,191,66,184)(60,183,67,190)(61,189,68,196)(62,195,69,188)(63,187,70,194)(71,211,78,218)(72,217,79,224)(73,223,80,216)(74,215,81,222)(75,221,82,214)(76,213,83,220)(77,219,84,212)>;
G:=Group( (1,197,12,204)(2,205,13,198)(3,199,14,206)(4,207,8,200)(5,201,9,208)(6,209,10,202)(7,203,11,210)(15,132,107,139)(16,140,108,133)(17,134,109,127)(18,128,110,135)(19,136,111,129)(20,130,112,137)(21,138,106,131)(22,165,86,158)(23,159,87,166)(24,167,88,160)(25,161,89,168)(26,155,90,162)(27,163,91,156)(28,157,85,164)(29,217,54,224)(30,211,55,218)(31,219,56,212)(32,213,50,220)(33,221,51,214)(34,215,52,222)(35,223,53,216)(36,170,95,177)(37,178,96,171)(38,172,97,179)(39,180,98,173)(40,174,92,181)(41,182,93,175)(42,176,94,169)(43,191,105,184)(44,185,99,192)(45,193,100,186)(46,187,101,194)(47,195,102,188)(48,189,103,196)(49,183,104,190)(57,149,64,142)(58,143,65,150)(59,151,66,144)(60,145,67,152)(61,153,68,146)(62,147,69,154)(63,141,70,148)(71,119,78,126)(72,113,79,120)(73,121,80,114)(74,115,81,122)(75,123,82,116)(76,117,83,124)(77,125,84,118), (1,123,111,146)(2,117,112,154)(3,125,106,148)(4,119,107,142)(5,113,108,150)(6,121,109,144)(7,115,110,152)(8,126,15,149)(9,120,16,143)(10,114,17,151)(11,122,18,145)(12,116,19,153)(13,124,20,147)(14,118,21,141)(22,191,38,216)(23,185,39,224)(24,193,40,218)(25,187,41,212)(26,195,42,220)(27,189,36,214)(28,183,37,222)(29,159,99,180)(30,167,100,174)(31,161,101,182)(32,155,102,176)(33,163,103,170)(34,157,104,178)(35,165,105,172)(43,179,53,158)(44,173,54,166)(45,181,55,160)(46,175,56,168)(47,169,50,162)(48,177,51,156)(49,171,52,164)(57,207,78,139)(58,201,79,133)(59,209,80,127)(60,203,81,135)(61,197,82,129)(62,205,83,137)(63,199,84,131)(64,200,71,132)(65,208,72,140)(66,202,73,134)(67,210,74,128)(68,204,75,136)(69,198,76,130)(70,206,77,138)(85,190,96,215)(86,184,97,223)(87,192,98,217)(88,186,92,211)(89,194,93,219)(90,188,94,213)(91,196,95,221), (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), (1,170,12,177)(2,176,13,169)(3,182,14,175)(4,174,8,181)(5,180,9,173)(6,172,10,179)(7,178,11,171)(15,160,107,167)(16,166,108,159)(17,158,109,165)(18,164,110,157)(19,156,111,163)(20,162,112,155)(21,168,106,161)(22,202,86,209)(23,208,87,201)(24,200,88,207)(25,206,89,199)(26,198,90,205)(27,204,91,197)(28,210,85,203)(29,143,54,150)(30,149,55,142)(31,141,56,148)(32,147,50,154)(33,153,51,146)(34,145,52,152)(35,151,53,144)(36,136,95,129)(37,128,96,135)(38,134,97,127)(39,140,98,133)(40,132,92,139)(41,138,93,131)(42,130,94,137)(43,121,105,114)(44,113,99,120)(45,119,100,126)(46,125,101,118)(47,117,102,124)(48,123,103,116)(49,115,104,122)(57,193,64,186)(58,185,65,192)(59,191,66,184)(60,183,67,190)(61,189,68,196)(62,195,69,188)(63,187,70,194)(71,211,78,218)(72,217,79,224)(73,223,80,216)(74,215,81,222)(75,221,82,214)(76,213,83,220)(77,219,84,212) );
G=PermutationGroup([(1,197,12,204),(2,205,13,198),(3,199,14,206),(4,207,8,200),(5,201,9,208),(6,209,10,202),(7,203,11,210),(15,132,107,139),(16,140,108,133),(17,134,109,127),(18,128,110,135),(19,136,111,129),(20,130,112,137),(21,138,106,131),(22,165,86,158),(23,159,87,166),(24,167,88,160),(25,161,89,168),(26,155,90,162),(27,163,91,156),(28,157,85,164),(29,217,54,224),(30,211,55,218),(31,219,56,212),(32,213,50,220),(33,221,51,214),(34,215,52,222),(35,223,53,216),(36,170,95,177),(37,178,96,171),(38,172,97,179),(39,180,98,173),(40,174,92,181),(41,182,93,175),(42,176,94,169),(43,191,105,184),(44,185,99,192),(45,193,100,186),(46,187,101,194),(47,195,102,188),(48,189,103,196),(49,183,104,190),(57,149,64,142),(58,143,65,150),(59,151,66,144),(60,145,67,152),(61,153,68,146),(62,147,69,154),(63,141,70,148),(71,119,78,126),(72,113,79,120),(73,121,80,114),(74,115,81,122),(75,123,82,116),(76,117,83,124),(77,125,84,118)], [(1,123,111,146),(2,117,112,154),(3,125,106,148),(4,119,107,142),(5,113,108,150),(6,121,109,144),(7,115,110,152),(8,126,15,149),(9,120,16,143),(10,114,17,151),(11,122,18,145),(12,116,19,153),(13,124,20,147),(14,118,21,141),(22,191,38,216),(23,185,39,224),(24,193,40,218),(25,187,41,212),(26,195,42,220),(27,189,36,214),(28,183,37,222),(29,159,99,180),(30,167,100,174),(31,161,101,182),(32,155,102,176),(33,163,103,170),(34,157,104,178),(35,165,105,172),(43,179,53,158),(44,173,54,166),(45,181,55,160),(46,175,56,168),(47,169,50,162),(48,177,51,156),(49,171,52,164),(57,207,78,139),(58,201,79,133),(59,209,80,127),(60,203,81,135),(61,197,82,129),(62,205,83,137),(63,199,84,131),(64,200,71,132),(65,208,72,140),(66,202,73,134),(67,210,74,128),(68,204,75,136),(69,198,76,130),(70,206,77,138),(85,190,96,215),(86,184,97,223),(87,192,98,217),(88,186,92,211),(89,194,93,219),(90,188,94,213),(91,196,95,221)], [(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)], [(1,170,12,177),(2,176,13,169),(3,182,14,175),(4,174,8,181),(5,180,9,173),(6,172,10,179),(7,178,11,171),(15,160,107,167),(16,166,108,159),(17,158,109,165),(18,164,110,157),(19,156,111,163),(20,162,112,155),(21,168,106,161),(22,202,86,209),(23,208,87,201),(24,200,88,207),(25,206,89,199),(26,198,90,205),(27,204,91,197),(28,210,85,203),(29,143,54,150),(30,149,55,142),(31,141,56,148),(32,147,50,154),(33,153,51,146),(34,145,52,152),(35,151,53,144),(36,136,95,129),(37,128,96,135),(38,134,97,127),(39,140,98,133),(40,132,92,139),(41,138,93,131),(42,130,94,137),(43,121,105,114),(44,113,99,120),(45,119,100,126),(46,125,101,118),(47,117,102,124),(48,123,103,116),(49,115,104,122),(57,193,64,186),(58,185,65,192),(59,191,66,184),(60,183,67,190),(61,189,68,196),(62,195,69,188),(63,187,70,194),(71,211,78,218),(72,217,79,224),(73,223,80,216),(74,215,81,222),(75,221,82,214),(76,213,83,220),(77,219,84,212)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 21 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 11 | 6 | 16 |
| 0 | 0 | 9 | 25 | 13 | 0 |
| 0 | 0 | 11 | 0 | 11 | 9 |
| 0 | 0 | 24 | 22 | 21 | 21 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 9 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 15 | 25 | 1 |
| 0 | 0 | 8 | 2 | 27 | 21 |
| 0 | 0 | 19 | 23 | 20 | 8 |
| 0 | 0 | 0 | 28 | 5 | 26 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 9 | 24 | 25 | 19 |
| 0 | 0 | 22 | 18 | 15 | 1 |
| 11 | 10 | 0 | 0 | 0 | 0 |
| 17 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 21 | 2 | 4 |
| 0 | 0 | 4 | 19 | 27 | 13 |
| 0 | 0 | 6 | 22 | 27 | 28 |
| 0 | 0 | 16 | 7 | 2 | 22 |
G:=sub<GL(6,GF(29))| [1,21,0,0,0,0,0,28,0,0,0,0,0,0,1,9,11,24,0,0,11,25,0,22,0,0,6,13,11,21,0,0,16,0,9,21],[17,9,0,0,0,0,0,12,0,0,0,0,0,0,10,8,19,0,0,0,15,2,23,28,0,0,25,27,20,5,0,0,1,21,8,26],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,10,19,9,22,0,0,10,22,24,18,0,0,0,0,25,15,0,0,0,0,19,1],[11,17,0,0,0,0,10,18,0,0,0,0,0,0,19,4,6,16,0,0,21,19,22,7,0,0,2,27,27,2,0,0,4,13,28,22] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | 2- (1+4) | D4⋊6D14 | D4.10D14 |
| kernel | C42.118D14 | C28.6Q8 | C42⋊2D7 | C22⋊Dic14 | C23.D14 | D14.D4 | C22.D28 | Dic7.Q8 | D14⋊Q8 | C2×Dic7⋊C4 | C28.48D4 | C4×C7⋊D4 | C23.23D14 | C23.18D14 | Dic7⋊D4 | D4×C28 | C4×D4 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{118}D_{14} % in TeX
G:=Group("C4^2.118D14"); // GroupNames label
G:=SmallGroup(448,1017);
// by ID
G=gap.SmallGroup(448,1017);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,675,570,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,c*b*c^-1=a^2*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀