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×C28).166C23, (C2×C14).108C24, 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, C23.105(C22×D7), C22.133(C23×D7), C23.D7.17C22, C23.18D14⋊19C2, (C22×C14).178C23, (C22×C28).366C22, C7⋊2(C22.33C24), (C2×Dic14).29C22, (C4×Dic7).207C22, 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
Generators and relations for C42.118D14
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 >
Subgroups: 916 in 218 conjugacy classes, 95 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, 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, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.33C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D4.10D14, C42.118D14
►On 224 points
Generators in S224
(1 131 12 138)(2 139 13 132)(3 133 14 140)(4 127 8 134)(5 135 9 128)(6 129 10 136)(7 137 11 130)(15 193 22 186)(16 187 23 194)(17 195 24 188)(18 189 25 196)(19 183 26 190)(20 191 27 184)(21 185 28 192)(29 156 50 163)(30 164 51 157)(31 158 52 165)(32 166 53 159)(33 160 54 167)(34 168 55 161)(35 162 56 155)(36 171 85 178)(37 179 86 172)(38 173 87 180)(39 181 88 174)(40 175 89 182)(41 169 90 176)(42 177 91 170)(43 145 79 152)(44 153 80 146)(45 147 81 154)(46 141 82 148)(47 149 83 142)(48 143 84 150)(49 151 78 144)(57 205 64 198)(58 199 65 206)(59 207 66 200)(60 201 67 208)(61 209 68 202)(62 203 69 210)(63 197 70 204)(71 218 110 211)(72 212 111 219)(73 220 112 213)(74 214 106 221)(75 222 107 215)(76 216 108 223)(77 224 109 217)(92 125 104 118)(93 119 105 126)(94 113 99 120)(95 121 100 114)(96 115 101 122)(97 123 102 116)(98 117 103 124)
(1 141 26 202)(2 149 27 210)(3 143 28 204)(4 151 22 198)(5 145 23 206)(6 153 24 200)(7 147 25 208)(8 144 15 205)(9 152 16 199)(10 146 17 207)(11 154 18 201)(12 148 19 209)(13 142 20 203)(14 150 21 197)(29 124 39 221)(30 118 40 215)(31 126 41 223)(32 120 42 217)(33 114 36 211)(34 122 37 219)(35 116 38 213)(43 187 65 128)(44 195 66 136)(45 189 67 130)(46 183 68 138)(47 191 69 132)(48 185 70 140)(49 193 64 134)(50 117 88 214)(51 125 89 222)(52 119 90 216)(53 113 91 224)(54 121 85 218)(55 115 86 212)(56 123 87 220)(57 127 78 186)(58 135 79 194)(59 129 80 188)(60 137 81 196)(61 131 82 190)(62 139 83 184)(63 133 84 192)(71 160 95 171)(72 168 96 179)(73 162 97 173)(74 156 98 181)(75 164 92 175)(76 158 93 169)(77 166 94 177)(99 170 109 159)(100 178 110 167)(101 172 111 161)(102 180 112 155)(103 174 106 163)(104 182 107 157)(105 176 108 165)
(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)
(1 125 12 118)(2 117 13 124)(3 123 14 116)(4 115 8 122)(5 121 9 114)(6 113 10 120)(7 119 11 126)(15 219 22 212)(16 211 23 218)(17 217 24 224)(18 223 25 216)(19 215 26 222)(20 221 27 214)(21 213 28 220)(29 149 50 142)(30 141 51 148)(31 147 52 154)(32 153 53 146)(33 145 54 152)(34 151 55 144)(35 143 56 150)(36 206 85 199)(37 198 86 205)(38 204 87 197)(39 210 88 203)(40 202 89 209)(41 208 90 201)(42 200 91 207)(43 178 79 171)(44 170 80 177)(45 176 81 169)(46 182 82 175)(47 174 83 181)(48 180 84 173)(49 172 78 179)(57 168 64 161)(58 160 65 167)(59 166 66 159)(60 158 67 165)(61 164 68 157)(62 156 69 163)(63 162 70 155)(71 128 110 135)(72 134 111 127)(73 140 112 133)(74 132 106 139)(75 138 107 131)(76 130 108 137)(77 136 109 129)(92 183 104 190)(93 189 105 196)(94 195 99 188)(95 187 100 194)(96 193 101 186)(97 185 102 192)(98 191 103 184)
G:=sub<Sym(224)| (1,131,12,138)(2,139,13,132)(3,133,14,140)(4,127,8,134)(5,135,9,128)(6,129,10,136)(7,137,11,130)(15,193,22,186)(16,187,23,194)(17,195,24,188)(18,189,25,196)(19,183,26,190)(20,191,27,184)(21,185,28,192)(29,156,50,163)(30,164,51,157)(31,158,52,165)(32,166,53,159)(33,160,54,167)(34,168,55,161)(35,162,56,155)(36,171,85,178)(37,179,86,172)(38,173,87,180)(39,181,88,174)(40,175,89,182)(41,169,90,176)(42,177,91,170)(43,145,79,152)(44,153,80,146)(45,147,81,154)(46,141,82,148)(47,149,83,142)(48,143,84,150)(49,151,78,144)(57,205,64,198)(58,199,65,206)(59,207,66,200)(60,201,67,208)(61,209,68,202)(62,203,69,210)(63,197,70,204)(71,218,110,211)(72,212,111,219)(73,220,112,213)(74,214,106,221)(75,222,107,215)(76,216,108,223)(77,224,109,217)(92,125,104,118)(93,119,105,126)(94,113,99,120)(95,121,100,114)(96,115,101,122)(97,123,102,116)(98,117,103,124), (1,141,26,202)(2,149,27,210)(3,143,28,204)(4,151,22,198)(5,145,23,206)(6,153,24,200)(7,147,25,208)(8,144,15,205)(9,152,16,199)(10,146,17,207)(11,154,18,201)(12,148,19,209)(13,142,20,203)(14,150,21,197)(29,124,39,221)(30,118,40,215)(31,126,41,223)(32,120,42,217)(33,114,36,211)(34,122,37,219)(35,116,38,213)(43,187,65,128)(44,195,66,136)(45,189,67,130)(46,183,68,138)(47,191,69,132)(48,185,70,140)(49,193,64,134)(50,117,88,214)(51,125,89,222)(52,119,90,216)(53,113,91,224)(54,121,85,218)(55,115,86,212)(56,123,87,220)(57,127,78,186)(58,135,79,194)(59,129,80,188)(60,137,81,196)(61,131,82,190)(62,139,83,184)(63,133,84,192)(71,160,95,171)(72,168,96,179)(73,162,97,173)(74,156,98,181)(75,164,92,175)(76,158,93,169)(77,166,94,177)(99,170,109,159)(100,178,110,167)(101,172,111,161)(102,180,112,155)(103,174,106,163)(104,182,107,157)(105,176,108,165), (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), (1,125,12,118)(2,117,13,124)(3,123,14,116)(4,115,8,122)(5,121,9,114)(6,113,10,120)(7,119,11,126)(15,219,22,212)(16,211,23,218)(17,217,24,224)(18,223,25,216)(19,215,26,222)(20,221,27,214)(21,213,28,220)(29,149,50,142)(30,141,51,148)(31,147,52,154)(32,153,53,146)(33,145,54,152)(34,151,55,144)(35,143,56,150)(36,206,85,199)(37,198,86,205)(38,204,87,197)(39,210,88,203)(40,202,89,209)(41,208,90,201)(42,200,91,207)(43,178,79,171)(44,170,80,177)(45,176,81,169)(46,182,82,175)(47,174,83,181)(48,180,84,173)(49,172,78,179)(57,168,64,161)(58,160,65,167)(59,166,66,159)(60,158,67,165)(61,164,68,157)(62,156,69,163)(63,162,70,155)(71,128,110,135)(72,134,111,127)(73,140,112,133)(74,132,106,139)(75,138,107,131)(76,130,108,137)(77,136,109,129)(92,183,104,190)(93,189,105,196)(94,195,99,188)(95,187,100,194)(96,193,101,186)(97,185,102,192)(98,191,103,184)>;
G:=Group( (1,131,12,138)(2,139,13,132)(3,133,14,140)(4,127,8,134)(5,135,9,128)(6,129,10,136)(7,137,11,130)(15,193,22,186)(16,187,23,194)(17,195,24,188)(18,189,25,196)(19,183,26,190)(20,191,27,184)(21,185,28,192)(29,156,50,163)(30,164,51,157)(31,158,52,165)(32,166,53,159)(33,160,54,167)(34,168,55,161)(35,162,56,155)(36,171,85,178)(37,179,86,172)(38,173,87,180)(39,181,88,174)(40,175,89,182)(41,169,90,176)(42,177,91,170)(43,145,79,152)(44,153,80,146)(45,147,81,154)(46,141,82,148)(47,149,83,142)(48,143,84,150)(49,151,78,144)(57,205,64,198)(58,199,65,206)(59,207,66,200)(60,201,67,208)(61,209,68,202)(62,203,69,210)(63,197,70,204)(71,218,110,211)(72,212,111,219)(73,220,112,213)(74,214,106,221)(75,222,107,215)(76,216,108,223)(77,224,109,217)(92,125,104,118)(93,119,105,126)(94,113,99,120)(95,121,100,114)(96,115,101,122)(97,123,102,116)(98,117,103,124), (1,141,26,202)(2,149,27,210)(3,143,28,204)(4,151,22,198)(5,145,23,206)(6,153,24,200)(7,147,25,208)(8,144,15,205)(9,152,16,199)(10,146,17,207)(11,154,18,201)(12,148,19,209)(13,142,20,203)(14,150,21,197)(29,124,39,221)(30,118,40,215)(31,126,41,223)(32,120,42,217)(33,114,36,211)(34,122,37,219)(35,116,38,213)(43,187,65,128)(44,195,66,136)(45,189,67,130)(46,183,68,138)(47,191,69,132)(48,185,70,140)(49,193,64,134)(50,117,88,214)(51,125,89,222)(52,119,90,216)(53,113,91,224)(54,121,85,218)(55,115,86,212)(56,123,87,220)(57,127,78,186)(58,135,79,194)(59,129,80,188)(60,137,81,196)(61,131,82,190)(62,139,83,184)(63,133,84,192)(71,160,95,171)(72,168,96,179)(73,162,97,173)(74,156,98,181)(75,164,92,175)(76,158,93,169)(77,166,94,177)(99,170,109,159)(100,178,110,167)(101,172,111,161)(102,180,112,155)(103,174,106,163)(104,182,107,157)(105,176,108,165), (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), (1,125,12,118)(2,117,13,124)(3,123,14,116)(4,115,8,122)(5,121,9,114)(6,113,10,120)(7,119,11,126)(15,219,22,212)(16,211,23,218)(17,217,24,224)(18,223,25,216)(19,215,26,222)(20,221,27,214)(21,213,28,220)(29,149,50,142)(30,141,51,148)(31,147,52,154)(32,153,53,146)(33,145,54,152)(34,151,55,144)(35,143,56,150)(36,206,85,199)(37,198,86,205)(38,204,87,197)(39,210,88,203)(40,202,89,209)(41,208,90,201)(42,200,91,207)(43,178,79,171)(44,170,80,177)(45,176,81,169)(46,182,82,175)(47,174,83,181)(48,180,84,173)(49,172,78,179)(57,168,64,161)(58,160,65,167)(59,166,66,159)(60,158,67,165)(61,164,68,157)(62,156,69,163)(63,162,70,155)(71,128,110,135)(72,134,111,127)(73,140,112,133)(74,132,106,139)(75,138,107,131)(76,130,108,137)(77,136,109,129)(92,183,104,190)(93,189,105,196)(94,195,99,188)(95,187,100,194)(96,193,101,186)(97,185,102,192)(98,191,103,184) );
G=PermutationGroup([[(1,131,12,138),(2,139,13,132),(3,133,14,140),(4,127,8,134),(5,135,9,128),(6,129,10,136),(7,137,11,130),(15,193,22,186),(16,187,23,194),(17,195,24,188),(18,189,25,196),(19,183,26,190),(20,191,27,184),(21,185,28,192),(29,156,50,163),(30,164,51,157),(31,158,52,165),(32,166,53,159),(33,160,54,167),(34,168,55,161),(35,162,56,155),(36,171,85,178),(37,179,86,172),(38,173,87,180),(39,181,88,174),(40,175,89,182),(41,169,90,176),(42,177,91,170),(43,145,79,152),(44,153,80,146),(45,147,81,154),(46,141,82,148),(47,149,83,142),(48,143,84,150),(49,151,78,144),(57,205,64,198),(58,199,65,206),(59,207,66,200),(60,201,67,208),(61,209,68,202),(62,203,69,210),(63,197,70,204),(71,218,110,211),(72,212,111,219),(73,220,112,213),(74,214,106,221),(75,222,107,215),(76,216,108,223),(77,224,109,217),(92,125,104,118),(93,119,105,126),(94,113,99,120),(95,121,100,114),(96,115,101,122),(97,123,102,116),(98,117,103,124)], [(1,141,26,202),(2,149,27,210),(3,143,28,204),(4,151,22,198),(5,145,23,206),(6,153,24,200),(7,147,25,208),(8,144,15,205),(9,152,16,199),(10,146,17,207),(11,154,18,201),(12,148,19,209),(13,142,20,203),(14,150,21,197),(29,124,39,221),(30,118,40,215),(31,126,41,223),(32,120,42,217),(33,114,36,211),(34,122,37,219),(35,116,38,213),(43,187,65,128),(44,195,66,136),(45,189,67,130),(46,183,68,138),(47,191,69,132),(48,185,70,140),(49,193,64,134),(50,117,88,214),(51,125,89,222),(52,119,90,216),(53,113,91,224),(54,121,85,218),(55,115,86,212),(56,123,87,220),(57,127,78,186),(58,135,79,194),(59,129,80,188),(60,137,81,196),(61,131,82,190),(62,139,83,184),(63,133,84,192),(71,160,95,171),(72,168,96,179),(73,162,97,173),(74,156,98,181),(75,164,92,175),(76,158,93,169),(77,166,94,177),(99,170,109,159),(100,178,110,167),(101,172,111,161),(102,180,112,155),(103,174,106,163),(104,182,107,157),(105,176,108,165)], [(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)], [(1,125,12,118),(2,117,13,124),(3,123,14,116),(4,115,8,122),(5,121,9,114),(6,113,10,120),(7,119,11,126),(15,219,22,212),(16,211,23,218),(17,217,24,224),(18,223,25,216),(19,215,26,222),(20,221,27,214),(21,213,28,220),(29,149,50,142),(30,141,51,148),(31,147,52,154),(32,153,53,146),(33,145,54,152),(34,151,55,144),(35,143,56,150),(36,206,85,199),(37,198,86,205),(38,204,87,197),(39,210,88,203),(40,202,89,209),(41,208,90,201),(42,200,91,207),(43,178,79,171),(44,170,80,177),(45,176,81,169),(46,182,82,175),(47,174,83,181),(48,180,84,173),(49,172,78,179),(57,168,64,161),(58,160,65,167),(59,166,66,159),(60,158,67,165),(61,164,68,157),(62,156,69,163),(63,162,70,155),(71,128,110,135),(72,134,111,127),(73,140,112,133),(74,132,106,139),(75,138,107,131),(76,130,108,137),(77,136,109,129),(92,183,104,190),(93,189,105,196),(94,195,99,188),(95,187,100,194),(96,193,101,186),(97,185,102,192),(98,191,103,184)]])
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 |
Matrix representation of C42.118D14 ►in 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] >;
C42.118D14 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