metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.70D14, C4⋊C4.76D14, (C2×C28).85D4, C42.C2⋊2D7, C28⋊4D4.7C2, C14.D8⋊41C2, C28.71(C4○D4), (C2×C28).385C23, (C4×C28).115C22, C4.13(Q8⋊2D7), C42.D7⋊11C2, C2.22(D4⋊D14), C14.123(C8⋊C22), C2.8(C28.23D4), C14.55(C4.4D4), (C2×D28).103C22, C7⋊3(C42.29C22), (C7×C42.C2)⋊2C2, (C2×C14).516(C2×D4), (C2×C4).67(C7⋊D4), (C2×C7⋊C8).127C22, (C7×C4⋊C4).123C22, (C2×C4).483(C22×D7), C22.189(C2×C7⋊D4), SmallGroup(448,601)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.70D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b-1, ab=ba, cac-1=a-1b2, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c13 >
Subgroups: 764 in 110 conjugacy classes, 39 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, C23, D7, C14, C14, C42, C4⋊C4, C4⋊C4, C2×C8, C2×D4, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, C42.C2, C4⋊1D4, C7⋊C8, D28, C2×C28, C2×C28, C2×C28, C22×D7, C42.29C22, C2×C7⋊C8, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×D28, C42.D7, C14.D8, C28⋊4D4, C7×C42.C2, C42.70D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C7⋊D4, C22×D7, C42.29C22, Q8⋊2D7, C2×C7⋊D4, C28.23D4, D4⋊D14, C42.70D14
►On 224 points
Generators in S224
(1 73 15 59)(2 120 16 134)(3 75 17 61)(4 122 18 136)(5 77 19 63)(6 124 20 138)(7 79 21 65)(8 126 22 140)(9 81 23 67)(10 128 24 114)(11 83 25 69)(12 130 26 116)(13 57 27 71)(14 132 28 118)(29 80 43 66)(30 127 44 113)(31 82 45 68)(32 129 46 115)(33 84 47 70)(34 131 48 117)(35 58 49 72)(36 133 50 119)(37 60 51 74)(38 135 52 121)(39 62 53 76)(40 137 54 123)(41 64 55 78)(42 139 56 125)(85 175 99 189)(86 197 100 211)(87 177 101 191)(88 199 102 213)(89 179 103 193)(90 201 104 215)(91 181 105 195)(92 203 106 217)(93 183 107 169)(94 205 108 219)(95 185 109 171)(96 207 110 221)(97 187 111 173)(98 209 112 223)(141 200 155 214)(142 180 156 194)(143 202 157 216)(144 182 158 196)(145 204 159 218)(146 184 160 170)(147 206 161 220)(148 186 162 172)(149 208 163 222)(150 188 164 174)(151 210 165 224)(152 190 166 176)(153 212 167 198)(154 192 168 178)
(1 85 36 151)(2 152 37 86)(3 87 38 153)(4 154 39 88)(5 89 40 155)(6 156 41 90)(7 91 42 157)(8 158 43 92)(9 93 44 159)(10 160 45 94)(11 95 46 161)(12 162 47 96)(13 97 48 163)(14 164 49 98)(15 99 50 165)(16 166 51 100)(17 101 52 167)(18 168 53 102)(19 103 54 141)(20 142 55 104)(21 105 56 143)(22 144 29 106)(23 107 30 145)(24 146 31 108)(25 109 32 147)(26 148 33 110)(27 111 34 149)(28 150 35 112)(57 187 117 222)(58 223 118 188)(59 189 119 224)(60 197 120 190)(61 191 121 198)(62 199 122 192)(63 193 123 200)(64 201 124 194)(65 195 125 202)(66 203 126 196)(67 169 127 204)(68 205 128 170)(69 171 129 206)(70 207 130 172)(71 173 131 208)(72 209 132 174)(73 175 133 210)(74 211 134 176)(75 177 135 212)(76 213 136 178)(77 179 137 214)(78 215 138 180)(79 181 139 216)(80 217 140 182)(81 183 113 218)(82 219 114 184)(83 185 115 220)(84 221 116 186)
(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 14 165 112 36 49 99 150)(2 149 100 48 37 111 166 13)(3 12 167 110 38 47 101 148)(4 147 102 46 39 109 168 11)(5 10 141 108 40 45 103 146)(6 145 104 44 41 107 142 9)(7 8 143 106 42 43 105 144)(15 28 151 98 50 35 85 164)(16 163 86 34 51 97 152 27)(17 26 153 96 52 33 87 162)(18 161 88 32 53 95 154 25)(19 24 155 94 54 31 89 160)(20 159 90 30 55 93 156 23)(21 22 157 92 56 29 91 158)(57 60 208 176 117 120 173 211)(58 210 174 119 118 175 209 59)(61 84 212 172 121 116 177 207)(62 206 178 115 122 171 213 83)(63 82 214 170 123 114 179 205)(64 204 180 113 124 169 215 81)(65 80 216 196 125 140 181 203)(66 202 182 139 126 195 217 79)(67 78 218 194 127 138 183 201)(68 200 184 137 128 193 219 77)(69 76 220 192 129 136 185 199)(70 198 186 135 130 191 221 75)(71 74 222 190 131 134 187 197)(72 224 188 133 132 189 223 73)
G:=sub<Sym(224)| (1,73,15,59)(2,120,16,134)(3,75,17,61)(4,122,18,136)(5,77,19,63)(6,124,20,138)(7,79,21,65)(8,126,22,140)(9,81,23,67)(10,128,24,114)(11,83,25,69)(12,130,26,116)(13,57,27,71)(14,132,28,118)(29,80,43,66)(30,127,44,113)(31,82,45,68)(32,129,46,115)(33,84,47,70)(34,131,48,117)(35,58,49,72)(36,133,50,119)(37,60,51,74)(38,135,52,121)(39,62,53,76)(40,137,54,123)(41,64,55,78)(42,139,56,125)(85,175,99,189)(86,197,100,211)(87,177,101,191)(88,199,102,213)(89,179,103,193)(90,201,104,215)(91,181,105,195)(92,203,106,217)(93,183,107,169)(94,205,108,219)(95,185,109,171)(96,207,110,221)(97,187,111,173)(98,209,112,223)(141,200,155,214)(142,180,156,194)(143,202,157,216)(144,182,158,196)(145,204,159,218)(146,184,160,170)(147,206,161,220)(148,186,162,172)(149,208,163,222)(150,188,164,174)(151,210,165,224)(152,190,166,176)(153,212,167,198)(154,192,168,178), (1,85,36,151)(2,152,37,86)(3,87,38,153)(4,154,39,88)(5,89,40,155)(6,156,41,90)(7,91,42,157)(8,158,43,92)(9,93,44,159)(10,160,45,94)(11,95,46,161)(12,162,47,96)(13,97,48,163)(14,164,49,98)(15,99,50,165)(16,166,51,100)(17,101,52,167)(18,168,53,102)(19,103,54,141)(20,142,55,104)(21,105,56,143)(22,144,29,106)(23,107,30,145)(24,146,31,108)(25,109,32,147)(26,148,33,110)(27,111,34,149)(28,150,35,112)(57,187,117,222)(58,223,118,188)(59,189,119,224)(60,197,120,190)(61,191,121,198)(62,199,122,192)(63,193,123,200)(64,201,124,194)(65,195,125,202)(66,203,126,196)(67,169,127,204)(68,205,128,170)(69,171,129,206)(70,207,130,172)(71,173,131,208)(72,209,132,174)(73,175,133,210)(74,211,134,176)(75,177,135,212)(76,213,136,178)(77,179,137,214)(78,215,138,180)(79,181,139,216)(80,217,140,182)(81,183,113,218)(82,219,114,184)(83,185,115,220)(84,221,116,186), (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), (1,14,165,112,36,49,99,150)(2,149,100,48,37,111,166,13)(3,12,167,110,38,47,101,148)(4,147,102,46,39,109,168,11)(5,10,141,108,40,45,103,146)(6,145,104,44,41,107,142,9)(7,8,143,106,42,43,105,144)(15,28,151,98,50,35,85,164)(16,163,86,34,51,97,152,27)(17,26,153,96,52,33,87,162)(18,161,88,32,53,95,154,25)(19,24,155,94,54,31,89,160)(20,159,90,30,55,93,156,23)(21,22,157,92,56,29,91,158)(57,60,208,176,117,120,173,211)(58,210,174,119,118,175,209,59)(61,84,212,172,121,116,177,207)(62,206,178,115,122,171,213,83)(63,82,214,170,123,114,179,205)(64,204,180,113,124,169,215,81)(65,80,216,196,125,140,181,203)(66,202,182,139,126,195,217,79)(67,78,218,194,127,138,183,201)(68,200,184,137,128,193,219,77)(69,76,220,192,129,136,185,199)(70,198,186,135,130,191,221,75)(71,74,222,190,131,134,187,197)(72,224,188,133,132,189,223,73)>;
G:=Group( (1,73,15,59)(2,120,16,134)(3,75,17,61)(4,122,18,136)(5,77,19,63)(6,124,20,138)(7,79,21,65)(8,126,22,140)(9,81,23,67)(10,128,24,114)(11,83,25,69)(12,130,26,116)(13,57,27,71)(14,132,28,118)(29,80,43,66)(30,127,44,113)(31,82,45,68)(32,129,46,115)(33,84,47,70)(34,131,48,117)(35,58,49,72)(36,133,50,119)(37,60,51,74)(38,135,52,121)(39,62,53,76)(40,137,54,123)(41,64,55,78)(42,139,56,125)(85,175,99,189)(86,197,100,211)(87,177,101,191)(88,199,102,213)(89,179,103,193)(90,201,104,215)(91,181,105,195)(92,203,106,217)(93,183,107,169)(94,205,108,219)(95,185,109,171)(96,207,110,221)(97,187,111,173)(98,209,112,223)(141,200,155,214)(142,180,156,194)(143,202,157,216)(144,182,158,196)(145,204,159,218)(146,184,160,170)(147,206,161,220)(148,186,162,172)(149,208,163,222)(150,188,164,174)(151,210,165,224)(152,190,166,176)(153,212,167,198)(154,192,168,178), (1,85,36,151)(2,152,37,86)(3,87,38,153)(4,154,39,88)(5,89,40,155)(6,156,41,90)(7,91,42,157)(8,158,43,92)(9,93,44,159)(10,160,45,94)(11,95,46,161)(12,162,47,96)(13,97,48,163)(14,164,49,98)(15,99,50,165)(16,166,51,100)(17,101,52,167)(18,168,53,102)(19,103,54,141)(20,142,55,104)(21,105,56,143)(22,144,29,106)(23,107,30,145)(24,146,31,108)(25,109,32,147)(26,148,33,110)(27,111,34,149)(28,150,35,112)(57,187,117,222)(58,223,118,188)(59,189,119,224)(60,197,120,190)(61,191,121,198)(62,199,122,192)(63,193,123,200)(64,201,124,194)(65,195,125,202)(66,203,126,196)(67,169,127,204)(68,205,128,170)(69,171,129,206)(70,207,130,172)(71,173,131,208)(72,209,132,174)(73,175,133,210)(74,211,134,176)(75,177,135,212)(76,213,136,178)(77,179,137,214)(78,215,138,180)(79,181,139,216)(80,217,140,182)(81,183,113,218)(82,219,114,184)(83,185,115,220)(84,221,116,186), (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), (1,14,165,112,36,49,99,150)(2,149,100,48,37,111,166,13)(3,12,167,110,38,47,101,148)(4,147,102,46,39,109,168,11)(5,10,141,108,40,45,103,146)(6,145,104,44,41,107,142,9)(7,8,143,106,42,43,105,144)(15,28,151,98,50,35,85,164)(16,163,86,34,51,97,152,27)(17,26,153,96,52,33,87,162)(18,161,88,32,53,95,154,25)(19,24,155,94,54,31,89,160)(20,159,90,30,55,93,156,23)(21,22,157,92,56,29,91,158)(57,60,208,176,117,120,173,211)(58,210,174,119,118,175,209,59)(61,84,212,172,121,116,177,207)(62,206,178,115,122,171,213,83)(63,82,214,170,123,114,179,205)(64,204,180,113,124,169,215,81)(65,80,216,196,125,140,181,203)(66,202,182,139,126,195,217,79)(67,78,218,194,127,138,183,201)(68,200,184,137,128,193,219,77)(69,76,220,192,129,136,185,199)(70,198,186,135,130,191,221,75)(71,74,222,190,131,134,187,197)(72,224,188,133,132,189,223,73) );
G=PermutationGroup([[(1,73,15,59),(2,120,16,134),(3,75,17,61),(4,122,18,136),(5,77,19,63),(6,124,20,138),(7,79,21,65),(8,126,22,140),(9,81,23,67),(10,128,24,114),(11,83,25,69),(12,130,26,116),(13,57,27,71),(14,132,28,118),(29,80,43,66),(30,127,44,113),(31,82,45,68),(32,129,46,115),(33,84,47,70),(34,131,48,117),(35,58,49,72),(36,133,50,119),(37,60,51,74),(38,135,52,121),(39,62,53,76),(40,137,54,123),(41,64,55,78),(42,139,56,125),(85,175,99,189),(86,197,100,211),(87,177,101,191),(88,199,102,213),(89,179,103,193),(90,201,104,215),(91,181,105,195),(92,203,106,217),(93,183,107,169),(94,205,108,219),(95,185,109,171),(96,207,110,221),(97,187,111,173),(98,209,112,223),(141,200,155,214),(142,180,156,194),(143,202,157,216),(144,182,158,196),(145,204,159,218),(146,184,160,170),(147,206,161,220),(148,186,162,172),(149,208,163,222),(150,188,164,174),(151,210,165,224),(152,190,166,176),(153,212,167,198),(154,192,168,178)], [(1,85,36,151),(2,152,37,86),(3,87,38,153),(4,154,39,88),(5,89,40,155),(6,156,41,90),(7,91,42,157),(8,158,43,92),(9,93,44,159),(10,160,45,94),(11,95,46,161),(12,162,47,96),(13,97,48,163),(14,164,49,98),(15,99,50,165),(16,166,51,100),(17,101,52,167),(18,168,53,102),(19,103,54,141),(20,142,55,104),(21,105,56,143),(22,144,29,106),(23,107,30,145),(24,146,31,108),(25,109,32,147),(26,148,33,110),(27,111,34,149),(28,150,35,112),(57,187,117,222),(58,223,118,188),(59,189,119,224),(60,197,120,190),(61,191,121,198),(62,199,122,192),(63,193,123,200),(64,201,124,194),(65,195,125,202),(66,203,126,196),(67,169,127,204),(68,205,128,170),(69,171,129,206),(70,207,130,172),(71,173,131,208),(72,209,132,174),(73,175,133,210),(74,211,134,176),(75,177,135,212),(76,213,136,178),(77,179,137,214),(78,215,138,180),(79,181,139,216),(80,217,140,182),(81,183,113,218),(82,219,114,184),(83,185,115,220),(84,221,116,186)], [(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)], [(1,14,165,112,36,49,99,150),(2,149,100,48,37,111,166,13),(3,12,167,110,38,47,101,148),(4,147,102,46,39,109,168,11),(5,10,141,108,40,45,103,146),(6,145,104,44,41,107,142,9),(7,8,143,106,42,43,105,144),(15,28,151,98,50,35,85,164),(16,163,86,34,51,97,152,27),(17,26,153,96,52,33,87,162),(18,161,88,32,53,95,154,25),(19,24,155,94,54,31,89,160),(20,159,90,30,55,93,156,23),(21,22,157,92,56,29,91,158),(57,60,208,176,117,120,173,211),(58,210,174,119,118,175,209,59),(61,84,212,172,121,116,177,207),(62,206,178,115,122,171,213,83),(63,82,214,170,123,114,179,205),(64,204,180,113,124,169,215,81),(65,80,216,196,125,140,181,203),(66,202,182,139,126,195,217,79),(67,78,218,194,127,138,183,201),(68,200,184,137,128,193,219,77),(69,76,220,192,129,136,185,199),(70,198,186,135,130,191,221,75),(71,74,222,190,131,134,187,197),(72,224,188,133,132,189,223,73)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 56 | 56 | 2 | 2 | 4 | 4 | 8 | 8 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | C8⋊C22 | Q8⋊2D7 | D4⋊D14 |
| kernel | C42.70D14 | C42.D7 | C14.D8 | C28⋊4D4 | C7×C42.C2 | C2×C28 | C42.C2 | C28 | C42 | C4⋊C4 | C2×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 12 | 2 | 6 | 12 |
Matrix representation of C42.70D14 ►in GL6(𝔽113)
| 1 | 25 | 0 | 0 | 0 | 0 |
| 18 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 55 | 38 | 0 | 0 |
| 0 | 0 | 75 | 58 | 0 | 0 |
| 0 | 0 | 0 | 0 | 55 | 38 |
| 0 | 0 | 0 | 0 | 75 | 58 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 44 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 37 | 51 | 51 | 37 |
| 0 | 0 | 62 | 44 | 76 | 45 |
| 0 | 0 | 51 | 37 | 76 | 62 |
| 0 | 0 | 76 | 45 | 51 | 69 |
| 15 | 36 | 0 | 0 | 0 | 0 |
| 44 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 51 | 37 | 76 | 62 |
| 0 | 0 | 44 | 62 | 68 | 37 |
| 0 | 0 | 37 | 51 | 51 | 37 |
| 0 | 0 | 45 | 76 | 44 | 62 |
G:=sub<GL(6,GF(113))| [1,18,0,0,0,0,25,112,0,0,0,0,0,0,55,75,0,0,0,0,38,58,0,0,0,0,0,0,55,75,0,0,0,0,38,58],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,1,0,0,0,0,0,0,1,0,0],[15,44,0,0,0,0,0,98,0,0,0,0,0,0,37,62,51,76,0,0,51,44,37,45,0,0,51,76,76,51,0,0,37,45,62,69],[15,44,0,0,0,0,36,98,0,0,0,0,0,0,51,44,37,45,0,0,37,62,51,76,0,0,76,68,51,44,0,0,62,37,37,62] >;
C42.70D14 in GAP, Magma, Sage, TeX
C_4^2._{70}D_{14} % in TeX
G:=Group("C4^2.70D14"); // GroupNames label
G:=SmallGroup(448,601);
// by ID
G=gap.SmallGroup(448,601);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,555,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^2*b^-1,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^13>;
// generators/relations