metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.119D14, C14.1072+ 1+4, (C4×D4)⋊27D7, (C4×D28)⋊35C2, (D4×C28)⋊29C2, C28⋊7D4⋊13C2, C4⋊C4.289D14, (C2×D4).226D14, C28.6Q8⋊17C2, Dic7⋊D4⋊28C2, Dic7⋊4D4⋊48C2, D14.D4⋊11C2, C28.293(C4○D4), (C4×C28).162C22, (C2×C14).109C24, (C2×C28).588C23, C22⋊C4.121D14, C22.2(C4○D28), (C22×C4).216D14, C2.20(D4⋊8D14), C4.119(D4⋊2D7), D14⋊C4.144C22, (D4×C14).310C22, (C2×D28).215C22, Dic7⋊C4.67C22, C4⋊Dic7.398C22, (C22×C28).84C22, (C2×Dic7).49C23, (C22×D7).43C23, C23.106(C22×D7), C22.134(C23×D7), C23.21D14⋊10C2, (C22×C14).179C23, C7⋊5(C22.47C24), (C4×Dic7).208C22, C23.D7.109C22, (C22×Dic7).101C22, C4⋊C4⋊D7⋊9C2, (C2×C4⋊Dic7)⋊26C2, C2.58(C2×C4○D28), C14.51(C2×C4○D4), C2.25(C2×D4⋊2D7), (C2×C4×D7).205C22, (C2×C14).19(C4○D4), (C7×C4⋊C4).337C22, (C2×C4).165(C22×D7), (C2×C7⋊D4).21C22, (C7×C22⋊C4).131C22, SmallGroup(448,1018)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.119D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, bc=cb, dbd-1=b-1, dcd-1=a2c-1 >
Subgroups: 1076 in 238 conjugacy classes, 99 normal (51 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.47C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C28.6Q8, C4×D28, Dic7⋊4D4, D14.D4, C4⋊C4⋊D7, C2×C4⋊Dic7, C23.21D14, C28⋊7D4, Dic7⋊D4, D4×C28, C42.119D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D4⋊8D14, C42.119D14
►On 224 points
Generators in S224
(1 182 19 75)(2 38 20 214)(3 170 21 77)(4 40 22 216)(5 172 23 79)(6 42 24 218)(7 174 25 81)(8 30 26 220)(9 176 27 83)(10 32 28 222)(11 178 15 71)(12 34 16 224)(13 180 17 73)(14 36 18 212)(29 131 219 145)(31 133 221 147)(33 135 223 149)(35 137 211 151)(37 139 213 153)(39 127 215 141)(41 129 217 143)(43 90 116 202)(44 155 117 64)(45 92 118 204)(46 157 119 66)(47 94 120 206)(48 159 121 68)(49 96 122 208)(50 161 123 70)(51 98 124 210)(52 163 125 58)(53 86 126 198)(54 165 113 60)(55 88 114 200)(56 167 115 62)(57 188 162 101)(59 190 164 103)(61 192 166 105)(63 194 168 107)(65 196 156 109)(67 184 158 111)(69 186 160 99)(72 150 179 136)(74 152 181 138)(76 154 169 140)(78 142 171 128)(80 144 173 130)(82 146 175 132)(84 148 177 134)(85 102 197 189)(87 104 199 191)(89 106 201 193)(91 108 203 195)(93 110 205 183)(95 112 207 185)(97 100 209 187)
(1 30 139 82)(2 31 140 83)(3 32 127 84)(4 33 128 71)(5 34 129 72)(6 35 130 73)(7 36 131 74)(8 37 132 75)(9 38 133 76)(10 39 134 77)(11 40 135 78)(12 41 136 79)(13 42 137 80)(14 29 138 81)(15 216 149 171)(16 217 150 172)(17 218 151 173)(18 219 152 174)(19 220 153 175)(20 221 154 176)(21 222 141 177)(22 223 142 178)(23 224 143 179)(24 211 144 180)(25 212 145 181)(26 213 146 182)(27 214 147 169)(28 215 148 170)(43 161 107 209)(44 162 108 210)(45 163 109 197)(46 164 110 198)(47 165 111 199)(48 166 112 200)(49 167 99 201)(50 168 100 202)(51 155 101 203)(52 156 102 204)(53 157 103 205)(54 158 104 206)(55 159 105 207)(56 160 106 208)(57 195 98 117)(58 196 85 118)(59 183 86 119)(60 184 87 120)(61 185 88 121)(62 186 89 122)(63 187 90 123)(64 188 91 124)(65 189 92 125)(66 190 93 126)(67 191 94 113)(68 192 95 114)(69 193 96 115)(70 194 97 116)
(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)
(1 184 19 111)(2 110 20 183)(3 196 21 109)(4 108 22 195)(5 194 23 107)(6 106 24 193)(7 192 25 105)(8 104 26 191)(9 190 27 103)(10 102 28 189)(11 188 15 101)(12 100 16 187)(13 186 17 99)(14 112 18 185)(29 166 219 61)(30 60 220 165)(31 164 221 59)(32 58 222 163)(33 162 223 57)(34 70 224 161)(35 160 211 69)(36 68 212 159)(37 158 213 67)(38 66 214 157)(39 156 215 65)(40 64 216 155)(41 168 217 63)(42 62 218 167)(43 129 116 143)(44 142 117 128)(45 127 118 141)(46 154 119 140)(47 139 120 153)(48 152 121 138)(49 137 122 151)(50 150 123 136)(51 135 124 149)(52 148 125 134)(53 133 126 147)(54 146 113 132)(55 131 114 145)(56 144 115 130)(71 210 178 98)(72 97 179 209)(73 208 180 96)(74 95 181 207)(75 206 182 94)(76 93 169 205)(77 204 170 92)(78 91 171 203)(79 202 172 90)(80 89 173 201)(81 200 174 88)(82 87 175 199)(83 198 176 86)(84 85 177 197)
G:=sub<Sym(224)| (1,182,19,75)(2,38,20,214)(3,170,21,77)(4,40,22,216)(5,172,23,79)(6,42,24,218)(7,174,25,81)(8,30,26,220)(9,176,27,83)(10,32,28,222)(11,178,15,71)(12,34,16,224)(13,180,17,73)(14,36,18,212)(29,131,219,145)(31,133,221,147)(33,135,223,149)(35,137,211,151)(37,139,213,153)(39,127,215,141)(41,129,217,143)(43,90,116,202)(44,155,117,64)(45,92,118,204)(46,157,119,66)(47,94,120,206)(48,159,121,68)(49,96,122,208)(50,161,123,70)(51,98,124,210)(52,163,125,58)(53,86,126,198)(54,165,113,60)(55,88,114,200)(56,167,115,62)(57,188,162,101)(59,190,164,103)(61,192,166,105)(63,194,168,107)(65,196,156,109)(67,184,158,111)(69,186,160,99)(72,150,179,136)(74,152,181,138)(76,154,169,140)(78,142,171,128)(80,144,173,130)(82,146,175,132)(84,148,177,134)(85,102,197,189)(87,104,199,191)(89,106,201,193)(91,108,203,195)(93,110,205,183)(95,112,207,185)(97,100,209,187), (1,30,139,82)(2,31,140,83)(3,32,127,84)(4,33,128,71)(5,34,129,72)(6,35,130,73)(7,36,131,74)(8,37,132,75)(9,38,133,76)(10,39,134,77)(11,40,135,78)(12,41,136,79)(13,42,137,80)(14,29,138,81)(15,216,149,171)(16,217,150,172)(17,218,151,173)(18,219,152,174)(19,220,153,175)(20,221,154,176)(21,222,141,177)(22,223,142,178)(23,224,143,179)(24,211,144,180)(25,212,145,181)(26,213,146,182)(27,214,147,169)(28,215,148,170)(43,161,107,209)(44,162,108,210)(45,163,109,197)(46,164,110,198)(47,165,111,199)(48,166,112,200)(49,167,99,201)(50,168,100,202)(51,155,101,203)(52,156,102,204)(53,157,103,205)(54,158,104,206)(55,159,105,207)(56,160,106,208)(57,195,98,117)(58,196,85,118)(59,183,86,119)(60,184,87,120)(61,185,88,121)(62,186,89,122)(63,187,90,123)(64,188,91,124)(65,189,92,125)(66,190,93,126)(67,191,94,113)(68,192,95,114)(69,193,96,115)(70,194,97,116), (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), (1,184,19,111)(2,110,20,183)(3,196,21,109)(4,108,22,195)(5,194,23,107)(6,106,24,193)(7,192,25,105)(8,104,26,191)(9,190,27,103)(10,102,28,189)(11,188,15,101)(12,100,16,187)(13,186,17,99)(14,112,18,185)(29,166,219,61)(30,60,220,165)(31,164,221,59)(32,58,222,163)(33,162,223,57)(34,70,224,161)(35,160,211,69)(36,68,212,159)(37,158,213,67)(38,66,214,157)(39,156,215,65)(40,64,216,155)(41,168,217,63)(42,62,218,167)(43,129,116,143)(44,142,117,128)(45,127,118,141)(46,154,119,140)(47,139,120,153)(48,152,121,138)(49,137,122,151)(50,150,123,136)(51,135,124,149)(52,148,125,134)(53,133,126,147)(54,146,113,132)(55,131,114,145)(56,144,115,130)(71,210,178,98)(72,97,179,209)(73,208,180,96)(74,95,181,207)(75,206,182,94)(76,93,169,205)(77,204,170,92)(78,91,171,203)(79,202,172,90)(80,89,173,201)(81,200,174,88)(82,87,175,199)(83,198,176,86)(84,85,177,197)>;
G:=Group( (1,182,19,75)(2,38,20,214)(3,170,21,77)(4,40,22,216)(5,172,23,79)(6,42,24,218)(7,174,25,81)(8,30,26,220)(9,176,27,83)(10,32,28,222)(11,178,15,71)(12,34,16,224)(13,180,17,73)(14,36,18,212)(29,131,219,145)(31,133,221,147)(33,135,223,149)(35,137,211,151)(37,139,213,153)(39,127,215,141)(41,129,217,143)(43,90,116,202)(44,155,117,64)(45,92,118,204)(46,157,119,66)(47,94,120,206)(48,159,121,68)(49,96,122,208)(50,161,123,70)(51,98,124,210)(52,163,125,58)(53,86,126,198)(54,165,113,60)(55,88,114,200)(56,167,115,62)(57,188,162,101)(59,190,164,103)(61,192,166,105)(63,194,168,107)(65,196,156,109)(67,184,158,111)(69,186,160,99)(72,150,179,136)(74,152,181,138)(76,154,169,140)(78,142,171,128)(80,144,173,130)(82,146,175,132)(84,148,177,134)(85,102,197,189)(87,104,199,191)(89,106,201,193)(91,108,203,195)(93,110,205,183)(95,112,207,185)(97,100,209,187), (1,30,139,82)(2,31,140,83)(3,32,127,84)(4,33,128,71)(5,34,129,72)(6,35,130,73)(7,36,131,74)(8,37,132,75)(9,38,133,76)(10,39,134,77)(11,40,135,78)(12,41,136,79)(13,42,137,80)(14,29,138,81)(15,216,149,171)(16,217,150,172)(17,218,151,173)(18,219,152,174)(19,220,153,175)(20,221,154,176)(21,222,141,177)(22,223,142,178)(23,224,143,179)(24,211,144,180)(25,212,145,181)(26,213,146,182)(27,214,147,169)(28,215,148,170)(43,161,107,209)(44,162,108,210)(45,163,109,197)(46,164,110,198)(47,165,111,199)(48,166,112,200)(49,167,99,201)(50,168,100,202)(51,155,101,203)(52,156,102,204)(53,157,103,205)(54,158,104,206)(55,159,105,207)(56,160,106,208)(57,195,98,117)(58,196,85,118)(59,183,86,119)(60,184,87,120)(61,185,88,121)(62,186,89,122)(63,187,90,123)(64,188,91,124)(65,189,92,125)(66,190,93,126)(67,191,94,113)(68,192,95,114)(69,193,96,115)(70,194,97,116), (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), (1,184,19,111)(2,110,20,183)(3,196,21,109)(4,108,22,195)(5,194,23,107)(6,106,24,193)(7,192,25,105)(8,104,26,191)(9,190,27,103)(10,102,28,189)(11,188,15,101)(12,100,16,187)(13,186,17,99)(14,112,18,185)(29,166,219,61)(30,60,220,165)(31,164,221,59)(32,58,222,163)(33,162,223,57)(34,70,224,161)(35,160,211,69)(36,68,212,159)(37,158,213,67)(38,66,214,157)(39,156,215,65)(40,64,216,155)(41,168,217,63)(42,62,218,167)(43,129,116,143)(44,142,117,128)(45,127,118,141)(46,154,119,140)(47,139,120,153)(48,152,121,138)(49,137,122,151)(50,150,123,136)(51,135,124,149)(52,148,125,134)(53,133,126,147)(54,146,113,132)(55,131,114,145)(56,144,115,130)(71,210,178,98)(72,97,179,209)(73,208,180,96)(74,95,181,207)(75,206,182,94)(76,93,169,205)(77,204,170,92)(78,91,171,203)(79,202,172,90)(80,89,173,201)(81,200,174,88)(82,87,175,199)(83,198,176,86)(84,85,177,197) );
G=PermutationGroup([[(1,182,19,75),(2,38,20,214),(3,170,21,77),(4,40,22,216),(5,172,23,79),(6,42,24,218),(7,174,25,81),(8,30,26,220),(9,176,27,83),(10,32,28,222),(11,178,15,71),(12,34,16,224),(13,180,17,73),(14,36,18,212),(29,131,219,145),(31,133,221,147),(33,135,223,149),(35,137,211,151),(37,139,213,153),(39,127,215,141),(41,129,217,143),(43,90,116,202),(44,155,117,64),(45,92,118,204),(46,157,119,66),(47,94,120,206),(48,159,121,68),(49,96,122,208),(50,161,123,70),(51,98,124,210),(52,163,125,58),(53,86,126,198),(54,165,113,60),(55,88,114,200),(56,167,115,62),(57,188,162,101),(59,190,164,103),(61,192,166,105),(63,194,168,107),(65,196,156,109),(67,184,158,111),(69,186,160,99),(72,150,179,136),(74,152,181,138),(76,154,169,140),(78,142,171,128),(80,144,173,130),(82,146,175,132),(84,148,177,134),(85,102,197,189),(87,104,199,191),(89,106,201,193),(91,108,203,195),(93,110,205,183),(95,112,207,185),(97,100,209,187)], [(1,30,139,82),(2,31,140,83),(3,32,127,84),(4,33,128,71),(5,34,129,72),(6,35,130,73),(7,36,131,74),(8,37,132,75),(9,38,133,76),(10,39,134,77),(11,40,135,78),(12,41,136,79),(13,42,137,80),(14,29,138,81),(15,216,149,171),(16,217,150,172),(17,218,151,173),(18,219,152,174),(19,220,153,175),(20,221,154,176),(21,222,141,177),(22,223,142,178),(23,224,143,179),(24,211,144,180),(25,212,145,181),(26,213,146,182),(27,214,147,169),(28,215,148,170),(43,161,107,209),(44,162,108,210),(45,163,109,197),(46,164,110,198),(47,165,111,199),(48,166,112,200),(49,167,99,201),(50,168,100,202),(51,155,101,203),(52,156,102,204),(53,157,103,205),(54,158,104,206),(55,159,105,207),(56,160,106,208),(57,195,98,117),(58,196,85,118),(59,183,86,119),(60,184,87,120),(61,185,88,121),(62,186,89,122),(63,187,90,123),(64,188,91,124),(65,189,92,125),(66,190,93,126),(67,191,94,113),(68,192,95,114),(69,193,96,115),(70,194,97,116)], [(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)], [(1,184,19,111),(2,110,20,183),(3,196,21,109),(4,108,22,195),(5,194,23,107),(6,106,24,193),(7,192,25,105),(8,104,26,191),(9,190,27,103),(10,102,28,189),(11,188,15,101),(12,100,16,187),(13,186,17,99),(14,112,18,185),(29,166,219,61),(30,60,220,165),(31,164,221,59),(32,58,222,163),(33,162,223,57),(34,70,224,161),(35,160,211,69),(36,68,212,159),(37,158,213,67),(38,66,214,157),(39,156,215,65),(40,64,216,155),(41,168,217,63),(42,62,218,167),(43,129,116,143),(44,142,117,128),(45,127,118,141),(46,154,119,140),(47,139,120,153),(48,152,121,138),(49,137,122,151),(50,150,123,136),(51,135,124,149),(52,148,125,134),(53,133,126,147),(54,146,113,132),(55,131,114,145),(56,144,115,130),(71,210,178,98),(72,97,179,209),(73,208,180,96),(74,95,181,207),(75,206,182,94),(76,93,169,205),(77,204,170,92),(78,91,171,203),(79,202,172,90),(80,89,173,201),(81,200,174,88),(82,87,175,199),(83,198,176,86),(84,85,177,197)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 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 | 28 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 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 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊2D7 | D4⋊8D14 |
| kernel | C42.119D14 | C28.6Q8 | C4×D28 | Dic7⋊4D4 | D14.D4 | C4⋊C4⋊D7 | C2×C4⋊Dic7 | C23.21D14 | C28⋊7D4 | Dic7⋊D4 | D4×C28 | C4×D4 | C28 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.119D14 ►in GL4(𝔽29) generated by
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 13 | 18 | 0 | 0 |
| 26 | 16 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 2 | 28 | 0 | 0 |
| 5 | 26 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 17 | 12 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 17 |
G:=sub<GL(4,GF(29))| [12,0,0,0,0,12,0,0,0,0,0,1,0,0,28,0],[13,26,0,0,18,16,0,0,0,0,28,0,0,0,0,28],[2,5,0,0,28,26,0,0,0,0,0,1,0,0,1,0],[17,0,0,0,12,12,0,0,0,0,12,0,0,0,0,17] >;
C42.119D14 in GAP, Magma, Sage, TeX
C_4^2._{119}D_{14} % in TeX
G:=Group("C4^2.119D14"); // GroupNames label
G:=SmallGroup(448,1018);
// by ID
G=gap.SmallGroup(448,1018);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,192,18822]);
// 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=d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations