metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.95D14, C14.972+ 1+4, (C4×D28)⋊10C2, D14⋊D4⋊3C2, C4⋊D28⋊12C2, C28⋊7D4⋊29C2, C4⋊C4.272D14, C42⋊2D7⋊4C2, D28⋊C4⋊12C2, D14.D4⋊4C2, C4.96(C4○D28), C42⋊C2⋊14D7, (C2×C14).74C24, (C4×C28).25C22, D14⋊C4.3C22, C22⋊C4.98D14, C28.3Q8⋊13C2, D14.28(C4○D4), C28.198(C4○D4), C2.9(D4⋊8D14), (C2×C28).149C23, (C22×C4).195D14, C23.86(C22×D7), (C2×D28).137C22, Dic7⋊C4.98C22, C4⋊Dic7.195C22, (C2×Dic7).27C23, (C4×Dic7).70C22, (C22×D7).22C23, C22.103(C23×D7), C23.D7.97C22, (C22×C14).144C23, (C22×C28).232C22, C7⋊2(C22.47C24), (D7×C4⋊C4)⋊13C2, (C4×C7⋊D4)⋊12C2, C2.13(D7×C4○D4), C2.33(C2×C4○D28), (C2×C4×D7).61C22, C14.134(C2×C4○D4), (C7×C42⋊C2)⋊16C2, (C7×C4⋊C4).310C22, (C2×C4).276(C22×D7), (C2×C7⋊D4).104C22, (C7×C22⋊C4).114C22, SmallGroup(448,983)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.95D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=ab2, bc=cb, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1172 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, 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, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C22.47C24, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C2×C7⋊D4, C2×C7⋊D4, C22×C28, C4×D28, C42⋊2D7, D14.D4, D14⋊D4, C28.3Q8, D7×C4⋊C4, D28⋊C4, C4⋊D28, C4×C7⋊D4, C28⋊7D4, C7×C42⋊C2, C42.95D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, D4⋊8D14, C42.95D14
►On 224 points
Generators in S224
(1 200 106 80)(2 215 107 67)(3 202 108 82)(4 217 109 69)(5 204 110 84)(6 219 111 71)(7 206 112 58)(8 221 85 73)(9 208 86 60)(10 223 87 75)(11 210 88 62)(12 197 89 77)(13 212 90 64)(14 199 91 79)(15 214 92 66)(16 201 93 81)(17 216 94 68)(18 203 95 83)(19 218 96 70)(20 205 97 57)(21 220 98 72)(22 207 99 59)(23 222 100 74)(24 209 101 61)(25 224 102 76)(26 211 103 63)(27 198 104 78)(28 213 105 65)(29 173 149 128)(30 188 150 115)(31 175 151 130)(32 190 152 117)(33 177 153 132)(34 192 154 119)(35 179 155 134)(36 194 156 121)(37 181 157 136)(38 196 158 123)(39 183 159 138)(40 170 160 125)(41 185 161 140)(42 172 162 127)(43 187 163 114)(44 174 164 129)(45 189 165 116)(46 176 166 131)(47 191 167 118)(48 178 168 133)(49 193 141 120)(50 180 142 135)(51 195 143 122)(52 182 144 137)(53 169 145 124)(54 184 146 139)(55 171 147 126)(56 186 148 113)
(1 127 15 113)(2 128 16 114)(3 129 17 115)(4 130 18 116)(5 131 19 117)(6 132 20 118)(7 133 21 119)(8 134 22 120)(9 135 23 121)(10 136 24 122)(11 137 25 123)(12 138 26 124)(13 139 27 125)(14 140 28 126)(29 201 43 215)(30 202 44 216)(31 203 45 217)(32 204 46 218)(33 205 47 219)(34 206 48 220)(35 207 49 221)(36 208 50 222)(37 209 51 223)(38 210 52 224)(39 211 53 197)(40 212 54 198)(41 213 55 199)(42 214 56 200)(57 167 71 153)(58 168 72 154)(59 141 73 155)(60 142 74 156)(61 143 75 157)(62 144 76 158)(63 145 77 159)(64 146 78 160)(65 147 79 161)(66 148 80 162)(67 149 81 163)(68 150 82 164)(69 151 83 165)(70 152 84 166)(85 179 99 193)(86 180 100 194)(87 181 101 195)(88 182 102 196)(89 183 103 169)(90 184 104 170)(91 185 105 171)(92 186 106 172)(93 187 107 173)(94 188 108 174)(95 189 109 175)(96 190 110 176)(97 191 111 177)(98 192 112 178)
(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 28 15 14)(2 13 16 27)(3 26 17 12)(4 11 18 25)(5 24 19 10)(6 9 20 23)(7 22 21 8)(29 146 43 160)(30 159 44 145)(31 144 45 158)(32 157 46 143)(33 142 47 156)(34 155 48 141)(35 168 49 154)(36 153 50 167)(37 166 51 152)(38 151 52 165)(39 164 53 150)(40 149 54 163)(41 162 55 148)(42 147 56 161)(57 60 71 74)(58 73 72 59)(61 84 75 70)(62 69 76 83)(63 82 77 68)(64 67 78 81)(65 80 79 66)(85 112 99 98)(86 97 100 111)(87 110 101 96)(88 95 102 109)(89 108 103 94)(90 93 104 107)(91 106 105 92)(113 171 127 185)(114 184 128 170)(115 169 129 183)(116 182 130 196)(117 195 131 181)(118 180 132 194)(119 193 133 179)(120 178 134 192)(121 191 135 177)(122 176 136 190)(123 189 137 175)(124 174 138 188)(125 187 139 173)(126 172 140 186)(197 216 211 202)(198 201 212 215)(199 214 213 200)(203 210 217 224)(204 223 218 209)(205 208 219 222)(206 221 220 207)
G:=sub<Sym(224)| (1,200,106,80)(2,215,107,67)(3,202,108,82)(4,217,109,69)(5,204,110,84)(6,219,111,71)(7,206,112,58)(8,221,85,73)(9,208,86,60)(10,223,87,75)(11,210,88,62)(12,197,89,77)(13,212,90,64)(14,199,91,79)(15,214,92,66)(16,201,93,81)(17,216,94,68)(18,203,95,83)(19,218,96,70)(20,205,97,57)(21,220,98,72)(22,207,99,59)(23,222,100,74)(24,209,101,61)(25,224,102,76)(26,211,103,63)(27,198,104,78)(28,213,105,65)(29,173,149,128)(30,188,150,115)(31,175,151,130)(32,190,152,117)(33,177,153,132)(34,192,154,119)(35,179,155,134)(36,194,156,121)(37,181,157,136)(38,196,158,123)(39,183,159,138)(40,170,160,125)(41,185,161,140)(42,172,162,127)(43,187,163,114)(44,174,164,129)(45,189,165,116)(46,176,166,131)(47,191,167,118)(48,178,168,133)(49,193,141,120)(50,180,142,135)(51,195,143,122)(52,182,144,137)(53,169,145,124)(54,184,146,139)(55,171,147,126)(56,186,148,113), (1,127,15,113)(2,128,16,114)(3,129,17,115)(4,130,18,116)(5,131,19,117)(6,132,20,118)(7,133,21,119)(8,134,22,120)(9,135,23,121)(10,136,24,122)(11,137,25,123)(12,138,26,124)(13,139,27,125)(14,140,28,126)(29,201,43,215)(30,202,44,216)(31,203,45,217)(32,204,46,218)(33,205,47,219)(34,206,48,220)(35,207,49,221)(36,208,50,222)(37,209,51,223)(38,210,52,224)(39,211,53,197)(40,212,54,198)(41,213,55,199)(42,214,56,200)(57,167,71,153)(58,168,72,154)(59,141,73,155)(60,142,74,156)(61,143,75,157)(62,144,76,158)(63,145,77,159)(64,146,78,160)(65,147,79,161)(66,148,80,162)(67,149,81,163)(68,150,82,164)(69,151,83,165)(70,152,84,166)(85,179,99,193)(86,180,100,194)(87,181,101,195)(88,182,102,196)(89,183,103,169)(90,184,104,170)(91,185,105,171)(92,186,106,172)(93,187,107,173)(94,188,108,174)(95,189,109,175)(96,190,110,176)(97,191,111,177)(98,192,112,178), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,146,43,160)(30,159,44,145)(31,144,45,158)(32,157,46,143)(33,142,47,156)(34,155,48,141)(35,168,49,154)(36,153,50,167)(37,166,51,152)(38,151,52,165)(39,164,53,150)(40,149,54,163)(41,162,55,148)(42,147,56,161)(57,60,71,74)(58,73,72,59)(61,84,75,70)(62,69,76,83)(63,82,77,68)(64,67,78,81)(65,80,79,66)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,171,127,185)(114,184,128,170)(115,169,129,183)(116,182,130,196)(117,195,131,181)(118,180,132,194)(119,193,133,179)(120,178,134,192)(121,191,135,177)(122,176,136,190)(123,189,137,175)(124,174,138,188)(125,187,139,173)(126,172,140,186)(197,216,211,202)(198,201,212,215)(199,214,213,200)(203,210,217,224)(204,223,218,209)(205,208,219,222)(206,221,220,207)>;
G:=Group( (1,200,106,80)(2,215,107,67)(3,202,108,82)(4,217,109,69)(5,204,110,84)(6,219,111,71)(7,206,112,58)(8,221,85,73)(9,208,86,60)(10,223,87,75)(11,210,88,62)(12,197,89,77)(13,212,90,64)(14,199,91,79)(15,214,92,66)(16,201,93,81)(17,216,94,68)(18,203,95,83)(19,218,96,70)(20,205,97,57)(21,220,98,72)(22,207,99,59)(23,222,100,74)(24,209,101,61)(25,224,102,76)(26,211,103,63)(27,198,104,78)(28,213,105,65)(29,173,149,128)(30,188,150,115)(31,175,151,130)(32,190,152,117)(33,177,153,132)(34,192,154,119)(35,179,155,134)(36,194,156,121)(37,181,157,136)(38,196,158,123)(39,183,159,138)(40,170,160,125)(41,185,161,140)(42,172,162,127)(43,187,163,114)(44,174,164,129)(45,189,165,116)(46,176,166,131)(47,191,167,118)(48,178,168,133)(49,193,141,120)(50,180,142,135)(51,195,143,122)(52,182,144,137)(53,169,145,124)(54,184,146,139)(55,171,147,126)(56,186,148,113), (1,127,15,113)(2,128,16,114)(3,129,17,115)(4,130,18,116)(5,131,19,117)(6,132,20,118)(7,133,21,119)(8,134,22,120)(9,135,23,121)(10,136,24,122)(11,137,25,123)(12,138,26,124)(13,139,27,125)(14,140,28,126)(29,201,43,215)(30,202,44,216)(31,203,45,217)(32,204,46,218)(33,205,47,219)(34,206,48,220)(35,207,49,221)(36,208,50,222)(37,209,51,223)(38,210,52,224)(39,211,53,197)(40,212,54,198)(41,213,55,199)(42,214,56,200)(57,167,71,153)(58,168,72,154)(59,141,73,155)(60,142,74,156)(61,143,75,157)(62,144,76,158)(63,145,77,159)(64,146,78,160)(65,147,79,161)(66,148,80,162)(67,149,81,163)(68,150,82,164)(69,151,83,165)(70,152,84,166)(85,179,99,193)(86,180,100,194)(87,181,101,195)(88,182,102,196)(89,183,103,169)(90,184,104,170)(91,185,105,171)(92,186,106,172)(93,187,107,173)(94,188,108,174)(95,189,109,175)(96,190,110,176)(97,191,111,177)(98,192,112,178), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,146,43,160)(30,159,44,145)(31,144,45,158)(32,157,46,143)(33,142,47,156)(34,155,48,141)(35,168,49,154)(36,153,50,167)(37,166,51,152)(38,151,52,165)(39,164,53,150)(40,149,54,163)(41,162,55,148)(42,147,56,161)(57,60,71,74)(58,73,72,59)(61,84,75,70)(62,69,76,83)(63,82,77,68)(64,67,78,81)(65,80,79,66)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,171,127,185)(114,184,128,170)(115,169,129,183)(116,182,130,196)(117,195,131,181)(118,180,132,194)(119,193,133,179)(120,178,134,192)(121,191,135,177)(122,176,136,190)(123,189,137,175)(124,174,138,188)(125,187,139,173)(126,172,140,186)(197,216,211,202)(198,201,212,215)(199,214,213,200)(203,210,217,224)(204,223,218,209)(205,208,219,222)(206,221,220,207) );
G=PermutationGroup([[(1,200,106,80),(2,215,107,67),(3,202,108,82),(4,217,109,69),(5,204,110,84),(6,219,111,71),(7,206,112,58),(8,221,85,73),(9,208,86,60),(10,223,87,75),(11,210,88,62),(12,197,89,77),(13,212,90,64),(14,199,91,79),(15,214,92,66),(16,201,93,81),(17,216,94,68),(18,203,95,83),(19,218,96,70),(20,205,97,57),(21,220,98,72),(22,207,99,59),(23,222,100,74),(24,209,101,61),(25,224,102,76),(26,211,103,63),(27,198,104,78),(28,213,105,65),(29,173,149,128),(30,188,150,115),(31,175,151,130),(32,190,152,117),(33,177,153,132),(34,192,154,119),(35,179,155,134),(36,194,156,121),(37,181,157,136),(38,196,158,123),(39,183,159,138),(40,170,160,125),(41,185,161,140),(42,172,162,127),(43,187,163,114),(44,174,164,129),(45,189,165,116),(46,176,166,131),(47,191,167,118),(48,178,168,133),(49,193,141,120),(50,180,142,135),(51,195,143,122),(52,182,144,137),(53,169,145,124),(54,184,146,139),(55,171,147,126),(56,186,148,113)], [(1,127,15,113),(2,128,16,114),(3,129,17,115),(4,130,18,116),(5,131,19,117),(6,132,20,118),(7,133,21,119),(8,134,22,120),(9,135,23,121),(10,136,24,122),(11,137,25,123),(12,138,26,124),(13,139,27,125),(14,140,28,126),(29,201,43,215),(30,202,44,216),(31,203,45,217),(32,204,46,218),(33,205,47,219),(34,206,48,220),(35,207,49,221),(36,208,50,222),(37,209,51,223),(38,210,52,224),(39,211,53,197),(40,212,54,198),(41,213,55,199),(42,214,56,200),(57,167,71,153),(58,168,72,154),(59,141,73,155),(60,142,74,156),(61,143,75,157),(62,144,76,158),(63,145,77,159),(64,146,78,160),(65,147,79,161),(66,148,80,162),(67,149,81,163),(68,150,82,164),(69,151,83,165),(70,152,84,166),(85,179,99,193),(86,180,100,194),(87,181,101,195),(88,182,102,196),(89,183,103,169),(90,184,104,170),(91,185,105,171),(92,186,106,172),(93,187,107,173),(94,188,108,174),(95,189,109,175),(96,190,110,176),(97,191,111,177),(98,192,112,178)], [(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)], [(1,28,15,14),(2,13,16,27),(3,26,17,12),(4,11,18,25),(5,24,19,10),(6,9,20,23),(7,22,21,8),(29,146,43,160),(30,159,44,145),(31,144,45,158),(32,157,46,143),(33,142,47,156),(34,155,48,141),(35,168,49,154),(36,153,50,167),(37,166,51,152),(38,151,52,165),(39,164,53,150),(40,149,54,163),(41,162,55,148),(42,147,56,161),(57,60,71,74),(58,73,72,59),(61,84,75,70),(62,69,76,83),(63,82,77,68),(64,67,78,81),(65,80,79,66),(85,112,99,98),(86,97,100,111),(87,110,101,96),(88,95,102,109),(89,108,103,94),(90,93,104,107),(91,106,105,92),(113,171,127,185),(114,184,128,170),(115,169,129,183),(116,182,130,196),(117,195,131,181),(118,180,132,194),(119,193,133,179),(120,178,134,192),(121,191,135,177),(122,176,136,190),(123,189,137,175),(124,174,138,188),(125,187,139,173),(126,172,140,186),(197,216,211,202),(198,201,212,215),(199,214,213,200),(203,210,217,224),(204,223,218,209),(205,208,219,222),(206,221,220,207)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.95D14 | C4×D28 | C42⋊2D7 | D14.D4 | D14⋊D4 | C28.3Q8 | D7×C4⋊C4 | D28⋊C4 | C4⋊D28 | C4×C7⋊D4 | C28⋊7D4 | C7×C42⋊C2 | C42⋊C2 | C28 | D14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 6 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.95D14 ►in GL4(𝔽29) generated by
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 27 | 12 |
| 11 | 16 | 0 | 0 |
| 7 | 18 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 18 | 21 | 0 | 0 |
| 11 | 0 | 0 | 0 |
| 0 | 0 | 10 | 25 |
| 0 | 0 | 18 | 19 |
| 1 | 0 | 0 | 0 |
| 24 | 28 | 0 | 0 |
| 0 | 0 | 19 | 4 |
| 0 | 0 | 11 | 10 |
G:=sub<GL(4,GF(29))| [12,0,0,0,0,12,0,0,0,0,17,27,0,0,0,12],[11,7,0,0,16,18,0,0,0,0,12,0,0,0,0,12],[18,11,0,0,21,0,0,0,0,0,10,18,0,0,25,19],[1,24,0,0,0,28,0,0,0,0,19,11,0,0,4,10] >;
C42.95D14 in GAP, Magma, Sage, TeX
C_4^2._{95}D_{14} % in TeX
G:=Group("C4^2.95D14"); // GroupNames label
G:=SmallGroup(448,983);
// by ID
G=gap.SmallGroup(448,983);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations