metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.216D14, C4⋊C4.77D14, C42.C2⋊3D7, (C2×C28).276D4, C28.72(C4○D4), C14.Q16⋊41C2, C4.D28.7C2, C14.D8.13C2, C14.110(C4○D8), (C2×C28).386C23, (C4×C28).116C22, C4.14(Q8⋊2D7), C14.56(C4.4D4), C2.9(C28.23D4), (C2×D28).104C22, C2.29(D4.8D14), C7⋊5(C42.78C22), (C2×Dic14).109C22, (C4×C7⋊C8)⋊13C2, (C7×C42.C2)⋊3C2, (C2×C14).517(C2×D4), (C2×C7⋊C8).255C22, (C2×C4).112(C7⋊D4), (C7×C4⋊C4).124C22, (C2×C4).484(C22×D7), C22.190(C2×C7⋊D4), SmallGroup(448,602)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.216D14
G = < a,b,c,d | a4=b4=1, c14=a2b2, d2=a2b, ab=ba, cac-1=a-1b2, ad=da, cbc-1=b-1, bd=db, dcd-1=b-1c13 >
Subgroups: 508 in 96 conjugacy classes, 39 normal (17 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C4×C8, D4⋊C4, Q8⋊C4, C4.4D4, C42.C2, C7⋊C8, Dic14, D28, C2×Dic7, C2×C28, C2×C28, C2×C28, C22×D7, C42.78C22, C2×C7⋊C8, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×D28, C4×C7⋊C8, C14.D8, C14.Q16, C4.D28, C7×C42.C2, C42.216D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C4○D8, C7⋊D4, C22×D7, C42.78C22, Q8⋊2D7, C2×C7⋊D4, C28.23D4, D4.8D14, C42.216D14
►On 224 points
Generators in S224
(1 202 106 35)(2 217 107 50)(3 204 108 37)(4 219 109 52)(5 206 110 39)(6 221 111 54)(7 208 112 41)(8 223 85 56)(9 210 86 43)(10 197 87 30)(11 212 88 45)(12 199 89 32)(13 214 90 47)(14 201 91 34)(15 216 92 49)(16 203 93 36)(17 218 94 51)(18 205 95 38)(19 220 96 53)(20 207 97 40)(21 222 98 55)(22 209 99 42)(23 224 100 29)(24 211 101 44)(25 198 102 31)(26 213 103 46)(27 200 104 33)(28 215 105 48)(57 122 187 166)(58 137 188 153)(59 124 189 168)(60 139 190 155)(61 126 191 142)(62 113 192 157)(63 128 193 144)(64 115 194 159)(65 130 195 146)(66 117 196 161)(67 132 169 148)(68 119 170 163)(69 134 171 150)(70 121 172 165)(71 136 173 152)(72 123 174 167)(73 138 175 154)(74 125 176 141)(75 140 177 156)(76 127 178 143)(77 114 179 158)(78 129 180 145)(79 116 181 160)(80 131 182 147)(81 118 183 162)(82 133 184 149)(83 120 185 164)(84 135 186 151)
(1 133 92 163)(2 164 93 134)(3 135 94 165)(4 166 95 136)(5 137 96 167)(6 168 97 138)(7 139 98 141)(8 142 99 140)(9 113 100 143)(10 144 101 114)(11 115 102 145)(12 146 103 116)(13 117 104 147)(14 148 105 118)(15 119 106 149)(16 150 107 120)(17 121 108 151)(18 152 109 122)(19 123 110 153)(20 154 111 124)(21 125 112 155)(22 156 85 126)(23 127 86 157)(24 158 87 128)(25 129 88 159)(26 160 89 130)(27 131 90 161)(28 162 91 132)(29 76 210 192)(30 193 211 77)(31 78 212 194)(32 195 213 79)(33 80 214 196)(34 169 215 81)(35 82 216 170)(36 171 217 83)(37 84 218 172)(38 173 219 57)(39 58 220 174)(40 175 221 59)(41 60 222 176)(42 177 223 61)(43 62 224 178)(44 179 197 63)(45 64 198 180)(46 181 199 65)(47 66 200 182)(48 183 201 67)(49 68 202 184)(50 185 203 69)(51 70 204 186)(52 187 205 71)(53 72 206 188)(54 189 207 73)(55 74 208 190)(56 191 209 75)
(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 14 149 132 92 105 119 162)(2 161 120 104 93 131 150 13)(3 12 151 130 94 103 121 160)(4 159 122 102 95 129 152 11)(5 10 153 128 96 101 123 158)(6 157 124 100 97 127 154 9)(7 8 155 126 98 99 125 156)(15 28 163 118 106 91 133 148)(16 147 134 90 107 117 164 27)(17 26 165 116 108 89 135 146)(18 145 136 88 109 115 166 25)(19 24 167 114 110 87 137 144)(20 143 138 86 111 113 168 23)(21 22 141 140 112 85 139 142)(29 40 178 73 210 221 62 189)(30 188 63 220 211 72 179 39)(31 38 180 71 212 219 64 187)(32 186 65 218 213 70 181 37)(33 36 182 69 214 217 66 185)(34 184 67 216 215 68 183 35)(41 56 190 61 222 209 74 177)(42 176 75 208 223 60 191 55)(43 54 192 59 224 207 76 175)(44 174 77 206 197 58 193 53)(45 52 194 57 198 205 78 173)(46 172 79 204 199 84 195 51)(47 50 196 83 200 203 80 171)(48 170 81 202 201 82 169 49)
G:=sub<Sym(224)| (1,202,106,35)(2,217,107,50)(3,204,108,37)(4,219,109,52)(5,206,110,39)(6,221,111,54)(7,208,112,41)(8,223,85,56)(9,210,86,43)(10,197,87,30)(11,212,88,45)(12,199,89,32)(13,214,90,47)(14,201,91,34)(15,216,92,49)(16,203,93,36)(17,218,94,51)(18,205,95,38)(19,220,96,53)(20,207,97,40)(21,222,98,55)(22,209,99,42)(23,224,100,29)(24,211,101,44)(25,198,102,31)(26,213,103,46)(27,200,104,33)(28,215,105,48)(57,122,187,166)(58,137,188,153)(59,124,189,168)(60,139,190,155)(61,126,191,142)(62,113,192,157)(63,128,193,144)(64,115,194,159)(65,130,195,146)(66,117,196,161)(67,132,169,148)(68,119,170,163)(69,134,171,150)(70,121,172,165)(71,136,173,152)(72,123,174,167)(73,138,175,154)(74,125,176,141)(75,140,177,156)(76,127,178,143)(77,114,179,158)(78,129,180,145)(79,116,181,160)(80,131,182,147)(81,118,183,162)(82,133,184,149)(83,120,185,164)(84,135,186,151), (1,133,92,163)(2,164,93,134)(3,135,94,165)(4,166,95,136)(5,137,96,167)(6,168,97,138)(7,139,98,141)(8,142,99,140)(9,113,100,143)(10,144,101,114)(11,115,102,145)(12,146,103,116)(13,117,104,147)(14,148,105,118)(15,119,106,149)(16,150,107,120)(17,121,108,151)(18,152,109,122)(19,123,110,153)(20,154,111,124)(21,125,112,155)(22,156,85,126)(23,127,86,157)(24,158,87,128)(25,129,88,159)(26,160,89,130)(27,131,90,161)(28,162,91,132)(29,76,210,192)(30,193,211,77)(31,78,212,194)(32,195,213,79)(33,80,214,196)(34,169,215,81)(35,82,216,170)(36,171,217,83)(37,84,218,172)(38,173,219,57)(39,58,220,174)(40,175,221,59)(41,60,222,176)(42,177,223,61)(43,62,224,178)(44,179,197,63)(45,64,198,180)(46,181,199,65)(47,66,200,182)(48,183,201,67)(49,68,202,184)(50,185,203,69)(51,70,204,186)(52,187,205,71)(53,72,206,188)(54,189,207,73)(55,74,208,190)(56,191,209,75), (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), (1,14,149,132,92,105,119,162)(2,161,120,104,93,131,150,13)(3,12,151,130,94,103,121,160)(4,159,122,102,95,129,152,11)(5,10,153,128,96,101,123,158)(6,157,124,100,97,127,154,9)(7,8,155,126,98,99,125,156)(15,28,163,118,106,91,133,148)(16,147,134,90,107,117,164,27)(17,26,165,116,108,89,135,146)(18,145,136,88,109,115,166,25)(19,24,167,114,110,87,137,144)(20,143,138,86,111,113,168,23)(21,22,141,140,112,85,139,142)(29,40,178,73,210,221,62,189)(30,188,63,220,211,72,179,39)(31,38,180,71,212,219,64,187)(32,186,65,218,213,70,181,37)(33,36,182,69,214,217,66,185)(34,184,67,216,215,68,183,35)(41,56,190,61,222,209,74,177)(42,176,75,208,223,60,191,55)(43,54,192,59,224,207,76,175)(44,174,77,206,197,58,193,53)(45,52,194,57,198,205,78,173)(46,172,79,204,199,84,195,51)(47,50,196,83,200,203,80,171)(48,170,81,202,201,82,169,49)>;
G:=Group( (1,202,106,35)(2,217,107,50)(3,204,108,37)(4,219,109,52)(5,206,110,39)(6,221,111,54)(7,208,112,41)(8,223,85,56)(9,210,86,43)(10,197,87,30)(11,212,88,45)(12,199,89,32)(13,214,90,47)(14,201,91,34)(15,216,92,49)(16,203,93,36)(17,218,94,51)(18,205,95,38)(19,220,96,53)(20,207,97,40)(21,222,98,55)(22,209,99,42)(23,224,100,29)(24,211,101,44)(25,198,102,31)(26,213,103,46)(27,200,104,33)(28,215,105,48)(57,122,187,166)(58,137,188,153)(59,124,189,168)(60,139,190,155)(61,126,191,142)(62,113,192,157)(63,128,193,144)(64,115,194,159)(65,130,195,146)(66,117,196,161)(67,132,169,148)(68,119,170,163)(69,134,171,150)(70,121,172,165)(71,136,173,152)(72,123,174,167)(73,138,175,154)(74,125,176,141)(75,140,177,156)(76,127,178,143)(77,114,179,158)(78,129,180,145)(79,116,181,160)(80,131,182,147)(81,118,183,162)(82,133,184,149)(83,120,185,164)(84,135,186,151), (1,133,92,163)(2,164,93,134)(3,135,94,165)(4,166,95,136)(5,137,96,167)(6,168,97,138)(7,139,98,141)(8,142,99,140)(9,113,100,143)(10,144,101,114)(11,115,102,145)(12,146,103,116)(13,117,104,147)(14,148,105,118)(15,119,106,149)(16,150,107,120)(17,121,108,151)(18,152,109,122)(19,123,110,153)(20,154,111,124)(21,125,112,155)(22,156,85,126)(23,127,86,157)(24,158,87,128)(25,129,88,159)(26,160,89,130)(27,131,90,161)(28,162,91,132)(29,76,210,192)(30,193,211,77)(31,78,212,194)(32,195,213,79)(33,80,214,196)(34,169,215,81)(35,82,216,170)(36,171,217,83)(37,84,218,172)(38,173,219,57)(39,58,220,174)(40,175,221,59)(41,60,222,176)(42,177,223,61)(43,62,224,178)(44,179,197,63)(45,64,198,180)(46,181,199,65)(47,66,200,182)(48,183,201,67)(49,68,202,184)(50,185,203,69)(51,70,204,186)(52,187,205,71)(53,72,206,188)(54,189,207,73)(55,74,208,190)(56,191,209,75), (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), (1,14,149,132,92,105,119,162)(2,161,120,104,93,131,150,13)(3,12,151,130,94,103,121,160)(4,159,122,102,95,129,152,11)(5,10,153,128,96,101,123,158)(6,157,124,100,97,127,154,9)(7,8,155,126,98,99,125,156)(15,28,163,118,106,91,133,148)(16,147,134,90,107,117,164,27)(17,26,165,116,108,89,135,146)(18,145,136,88,109,115,166,25)(19,24,167,114,110,87,137,144)(20,143,138,86,111,113,168,23)(21,22,141,140,112,85,139,142)(29,40,178,73,210,221,62,189)(30,188,63,220,211,72,179,39)(31,38,180,71,212,219,64,187)(32,186,65,218,213,70,181,37)(33,36,182,69,214,217,66,185)(34,184,67,216,215,68,183,35)(41,56,190,61,222,209,74,177)(42,176,75,208,223,60,191,55)(43,54,192,59,224,207,76,175)(44,174,77,206,197,58,193,53)(45,52,194,57,198,205,78,173)(46,172,79,204,199,84,195,51)(47,50,196,83,200,203,80,171)(48,170,81,202,201,82,169,49) );
G=PermutationGroup([[(1,202,106,35),(2,217,107,50),(3,204,108,37),(4,219,109,52),(5,206,110,39),(6,221,111,54),(7,208,112,41),(8,223,85,56),(9,210,86,43),(10,197,87,30),(11,212,88,45),(12,199,89,32),(13,214,90,47),(14,201,91,34),(15,216,92,49),(16,203,93,36),(17,218,94,51),(18,205,95,38),(19,220,96,53),(20,207,97,40),(21,222,98,55),(22,209,99,42),(23,224,100,29),(24,211,101,44),(25,198,102,31),(26,213,103,46),(27,200,104,33),(28,215,105,48),(57,122,187,166),(58,137,188,153),(59,124,189,168),(60,139,190,155),(61,126,191,142),(62,113,192,157),(63,128,193,144),(64,115,194,159),(65,130,195,146),(66,117,196,161),(67,132,169,148),(68,119,170,163),(69,134,171,150),(70,121,172,165),(71,136,173,152),(72,123,174,167),(73,138,175,154),(74,125,176,141),(75,140,177,156),(76,127,178,143),(77,114,179,158),(78,129,180,145),(79,116,181,160),(80,131,182,147),(81,118,183,162),(82,133,184,149),(83,120,185,164),(84,135,186,151)], [(1,133,92,163),(2,164,93,134),(3,135,94,165),(4,166,95,136),(5,137,96,167),(6,168,97,138),(7,139,98,141),(8,142,99,140),(9,113,100,143),(10,144,101,114),(11,115,102,145),(12,146,103,116),(13,117,104,147),(14,148,105,118),(15,119,106,149),(16,150,107,120),(17,121,108,151),(18,152,109,122),(19,123,110,153),(20,154,111,124),(21,125,112,155),(22,156,85,126),(23,127,86,157),(24,158,87,128),(25,129,88,159),(26,160,89,130),(27,131,90,161),(28,162,91,132),(29,76,210,192),(30,193,211,77),(31,78,212,194),(32,195,213,79),(33,80,214,196),(34,169,215,81),(35,82,216,170),(36,171,217,83),(37,84,218,172),(38,173,219,57),(39,58,220,174),(40,175,221,59),(41,60,222,176),(42,177,223,61),(43,62,224,178),(44,179,197,63),(45,64,198,180),(46,181,199,65),(47,66,200,182),(48,183,201,67),(49,68,202,184),(50,185,203,69),(51,70,204,186),(52,187,205,71),(53,72,206,188),(54,189,207,73),(55,74,208,190),(56,191,209,75)], [(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)], [(1,14,149,132,92,105,119,162),(2,161,120,104,93,131,150,13),(3,12,151,130,94,103,121,160),(4,159,122,102,95,129,152,11),(5,10,153,128,96,101,123,158),(6,157,124,100,97,127,154,9),(7,8,155,126,98,99,125,156),(15,28,163,118,106,91,133,148),(16,147,134,90,107,117,164,27),(17,26,165,116,108,89,135,146),(18,145,136,88,109,115,166,25),(19,24,167,114,110,87,137,144),(20,143,138,86,111,113,168,23),(21,22,141,140,112,85,139,142),(29,40,178,73,210,221,62,189),(30,188,63,220,211,72,179,39),(31,38,180,71,212,219,64,187),(32,186,65,218,213,70,181,37),(33,36,182,69,214,217,66,185),(34,184,67,216,215,68,183,35),(41,56,190,61,222,209,74,177),(42,176,75,208,223,60,191,55),(43,54,192,59,224,207,76,175),(44,174,77,206,197,58,193,53),(45,52,194,57,198,205,78,173),(46,172,79,204,199,84,195,51),(47,50,196,83,200,203,80,171),(48,170,81,202,201,82,169,49)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | ··· | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | ··· | 2 | 8 | 8 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | C7⋊D4 | Q8⋊2D7 | D4.8D14 |
| kernel | C42.216D14 | C4×C7⋊C8 | C14.D8 | C14.Q16 | C4.D28 | C7×C42.C2 | C2×C28 | C42.C2 | C28 | C42 | C4⋊C4 | C14 | C2×C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 8 | 12 | 6 | 12 |
Matrix representation of C42.216D14 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 98 | 0 | 0 |
| 0 | 0 | 15 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 0 | 0 | 98 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 36 |
| 0 | 0 | 0 | 0 | 69 | 112 |
| 31 | 54 | 0 | 0 | 0 | 0 |
| 59 | 59 | 0 | 0 | 0 | 0 |
| 0 | 0 | 100 | 100 | 0 | 0 |
| 0 | 0 | 100 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 62 | 99 |
| 0 | 0 | 0 | 0 | 105 | 51 |
| 12 | 22 | 0 | 0 | 0 | 0 |
| 91 | 101 | 0 | 0 | 0 | 0 |
| 0 | 0 | 100 | 13 | 0 | 0 |
| 0 | 0 | 100 | 100 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 |
| 0 | 0 | 0 | 0 | 8 | 62 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,15,0,0,0,0,98,0,0,0,0,0,0,0,98,0,0,0,0,0,0,98],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,112,0,0,0,0,1,0,0,0,0,0,0,0,1,69,0,0,0,0,36,112],[31,59,0,0,0,0,54,59,0,0,0,0,0,0,100,100,0,0,0,0,100,13,0,0,0,0,0,0,62,105,0,0,0,0,99,51],[12,91,0,0,0,0,22,101,0,0,0,0,0,0,100,100,0,0,0,0,13,100,0,0,0,0,0,0,0,8,0,0,0,0,14,62] >;
C42.216D14 in GAP, Magma, Sage, TeX
C_4^2._{216}D_{14} % in TeX
G:=Group("C4^2.216D14"); // GroupNames label
G:=SmallGroup(448,602);
// by ID
G=gap.SmallGroup(448,602);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,219,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^2,d^2=a^2*b,a*b=b*a,c*a*c^-1=a^-1*b^2,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^13>;
// generators/relations