metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.117D14, C14.1062+ 1+4, (C4×D4)⋊25D7, (D4×C28)⋊27C2, (C4×D28)⋊34C2, C28⋊2D4⋊11C2, C28⋊7D4⋊20C2, C4⋊C4.320D14, C28⋊2Q8⋊26C2, (C2×D4).224D14, C4.66(C4○D28), C28.114(C4○D4), (C4×C28).161C22, (C2×C28).165C23, (C2×C14).107C24, D14⋊C4.55C22, C22⋊C4.119D14, (C22×C4).215D14, C2.19(D4⋊8D14), C4.118(D4⋊2D7), Dic7.D4⋊11C2, (D4×C14).266C22, (C2×D28).214C22, C23.21D14⋊9C2, C4⋊Dic7.302C22, (C22×D7).41C23, C23.104(C22×D7), C22.132(C23×D7), (C22×C14).177C23, (C22×C28).111C22, C7⋊2(C22.49C24), (C2×Dic7).209C23, (C2×Dic14).28C22, (C4×Dic7).206C22, C23.D7.108C22, C4⋊C4⋊7D7⋊16C2, C2.56(C2×C4○D28), C14.49(C2×C4○D4), (C2×C4×D7).68C22, C2.24(C2×D4⋊2D7), (C7×C4⋊C4).335C22, (C2×C4).163(C22×D7), (C2×C7⋊D4).20C22, (C7×C22⋊C4).130C22, SmallGroup(448,1016)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.117D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=a2b2c-1 >
Subgroups: 1076 in 236 conjugacy classes, 99 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, 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, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C4.4D4, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.49C24, C4×Dic7, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, D4×C14, C28⋊2Q8, C4×D28, Dic7.D4, C4⋊C4⋊7D7, C23.21D14, C28⋊7D4, C28⋊2D4, D4×C28, C42.117D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.49C24, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D4⋊8D14, C42.117D14
►On 224 points
Generators in S224
(1 148 80 194)(2 195 81 149)(3 150 82 196)(4 183 83 151)(5 152 84 184)(6 185 71 153)(7 154 72 186)(8 187 73 141)(9 142 74 188)(10 189 75 143)(11 144 76 190)(12 191 77 145)(13 146 78 192)(14 193 79 147)(15 204 139 33)(16 34 140 205)(17 206 127 35)(18 36 128 207)(19 208 129 37)(20 38 130 209)(21 210 131 39)(22 40 132 197)(23 198 133 41)(24 42 134 199)(25 200 135 29)(26 30 136 201)(27 202 137 31)(28 32 138 203)(43 167 170 213)(44 214 171 168)(45 155 172 215)(46 216 173 156)(47 157 174 217)(48 218 175 158)(49 159 176 219)(50 220 177 160)(51 161 178 221)(52 222 179 162)(53 163 180 223)(54 224 181 164)(55 165 182 211)(56 212 169 166)(57 93 104 126)(58 113 105 94)(59 95 106 114)(60 115 107 96)(61 97 108 116)(62 117 109 98)(63 85 110 118)(64 119 111 86)(65 87 112 120)(66 121 99 88)(67 89 100 122)(68 123 101 90)(69 91 102 124)(70 125 103 92)
(1 112 200 215)(2 99 201 216)(3 100 202 217)(4 101 203 218)(5 102 204 219)(6 103 205 220)(7 104 206 221)(8 105 207 222)(9 106 208 223)(10 107 209 224)(11 108 210 211)(12 109 197 212)(13 110 198 213)(14 111 199 214)(15 176 184 91)(16 177 185 92)(17 178 186 93)(18 179 187 94)(19 180 188 95)(20 181 189 96)(21 182 190 97)(22 169 191 98)(23 170 192 85)(24 171 193 86)(25 172 194 87)(26 173 195 88)(27 174 196 89)(28 175 183 90)(29 155 80 65)(30 156 81 66)(31 157 82 67)(32 158 83 68)(33 159 84 69)(34 160 71 70)(35 161 72 57)(36 162 73 58)(37 163 74 59)(38 164 75 60)(39 165 76 61)(40 166 77 62)(41 167 78 63)(42 168 79 64)(43 146 118 133)(44 147 119 134)(45 148 120 135)(46 149 121 136)(47 150 122 137)(48 151 123 138)(49 152 124 139)(50 153 125 140)(51 154 126 127)(52 141 113 128)(53 142 114 129)(54 143 115 130)(55 144 116 131)(56 145 117 132)
(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)
(1 214 29 64)(2 63 30 213)(3 212 31 62)(4 61 32 211)(5 224 33 60)(6 59 34 223)(7 222 35 58)(8 57 36 221)(9 220 37 70)(10 69 38 219)(11 218 39 68)(12 67 40 217)(13 216 41 66)(14 65 42 215)(15 96 152 54)(16 53 153 95)(17 94 154 52)(18 51 141 93)(19 92 142 50)(20 49 143 91)(21 90 144 48)(22 47 145 89)(23 88 146 46)(24 45 147 87)(25 86 148 44)(26 43 149 85)(27 98 150 56)(28 55 151 97)(71 106 205 163)(72 162 206 105)(73 104 207 161)(74 160 208 103)(75 102 209 159)(76 158 210 101)(77 100 197 157)(78 156 198 99)(79 112 199 155)(80 168 200 111)(81 110 201 167)(82 166 202 109)(83 108 203 165)(84 164 204 107)(113 186 179 127)(114 140 180 185)(115 184 181 139)(116 138 182 183)(117 196 169 137)(118 136 170 195)(119 194 171 135)(120 134 172 193)(121 192 173 133)(122 132 174 191)(123 190 175 131)(124 130 176 189)(125 188 177 129)(126 128 178 187)
G:=sub<Sym(224)| (1,148,80,194)(2,195,81,149)(3,150,82,196)(4,183,83,151)(5,152,84,184)(6,185,71,153)(7,154,72,186)(8,187,73,141)(9,142,74,188)(10,189,75,143)(11,144,76,190)(12,191,77,145)(13,146,78,192)(14,193,79,147)(15,204,139,33)(16,34,140,205)(17,206,127,35)(18,36,128,207)(19,208,129,37)(20,38,130,209)(21,210,131,39)(22,40,132,197)(23,198,133,41)(24,42,134,199)(25,200,135,29)(26,30,136,201)(27,202,137,31)(28,32,138,203)(43,167,170,213)(44,214,171,168)(45,155,172,215)(46,216,173,156)(47,157,174,217)(48,218,175,158)(49,159,176,219)(50,220,177,160)(51,161,178,221)(52,222,179,162)(53,163,180,223)(54,224,181,164)(55,165,182,211)(56,212,169,166)(57,93,104,126)(58,113,105,94)(59,95,106,114)(60,115,107,96)(61,97,108,116)(62,117,109,98)(63,85,110,118)(64,119,111,86)(65,87,112,120)(66,121,99,88)(67,89,100,122)(68,123,101,90)(69,91,102,124)(70,125,103,92), (1,112,200,215)(2,99,201,216)(3,100,202,217)(4,101,203,218)(5,102,204,219)(6,103,205,220)(7,104,206,221)(8,105,207,222)(9,106,208,223)(10,107,209,224)(11,108,210,211)(12,109,197,212)(13,110,198,213)(14,111,199,214)(15,176,184,91)(16,177,185,92)(17,178,186,93)(18,179,187,94)(19,180,188,95)(20,181,189,96)(21,182,190,97)(22,169,191,98)(23,170,192,85)(24,171,193,86)(25,172,194,87)(26,173,195,88)(27,174,196,89)(28,175,183,90)(29,155,80,65)(30,156,81,66)(31,157,82,67)(32,158,83,68)(33,159,84,69)(34,160,71,70)(35,161,72,57)(36,162,73,58)(37,163,74,59)(38,164,75,60)(39,165,76,61)(40,166,77,62)(41,167,78,63)(42,168,79,64)(43,146,118,133)(44,147,119,134)(45,148,120,135)(46,149,121,136)(47,150,122,137)(48,151,123,138)(49,152,124,139)(50,153,125,140)(51,154,126,127)(52,141,113,128)(53,142,114,129)(54,143,115,130)(55,144,116,131)(56,145,117,132), (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), (1,214,29,64)(2,63,30,213)(3,212,31,62)(4,61,32,211)(5,224,33,60)(6,59,34,223)(7,222,35,58)(8,57,36,221)(9,220,37,70)(10,69,38,219)(11,218,39,68)(12,67,40,217)(13,216,41,66)(14,65,42,215)(15,96,152,54)(16,53,153,95)(17,94,154,52)(18,51,141,93)(19,92,142,50)(20,49,143,91)(21,90,144,48)(22,47,145,89)(23,88,146,46)(24,45,147,87)(25,86,148,44)(26,43,149,85)(27,98,150,56)(28,55,151,97)(71,106,205,163)(72,162,206,105)(73,104,207,161)(74,160,208,103)(75,102,209,159)(76,158,210,101)(77,100,197,157)(78,156,198,99)(79,112,199,155)(80,168,200,111)(81,110,201,167)(82,166,202,109)(83,108,203,165)(84,164,204,107)(113,186,179,127)(114,140,180,185)(115,184,181,139)(116,138,182,183)(117,196,169,137)(118,136,170,195)(119,194,171,135)(120,134,172,193)(121,192,173,133)(122,132,174,191)(123,190,175,131)(124,130,176,189)(125,188,177,129)(126,128,178,187)>;
G:=Group( (1,148,80,194)(2,195,81,149)(3,150,82,196)(4,183,83,151)(5,152,84,184)(6,185,71,153)(7,154,72,186)(8,187,73,141)(9,142,74,188)(10,189,75,143)(11,144,76,190)(12,191,77,145)(13,146,78,192)(14,193,79,147)(15,204,139,33)(16,34,140,205)(17,206,127,35)(18,36,128,207)(19,208,129,37)(20,38,130,209)(21,210,131,39)(22,40,132,197)(23,198,133,41)(24,42,134,199)(25,200,135,29)(26,30,136,201)(27,202,137,31)(28,32,138,203)(43,167,170,213)(44,214,171,168)(45,155,172,215)(46,216,173,156)(47,157,174,217)(48,218,175,158)(49,159,176,219)(50,220,177,160)(51,161,178,221)(52,222,179,162)(53,163,180,223)(54,224,181,164)(55,165,182,211)(56,212,169,166)(57,93,104,126)(58,113,105,94)(59,95,106,114)(60,115,107,96)(61,97,108,116)(62,117,109,98)(63,85,110,118)(64,119,111,86)(65,87,112,120)(66,121,99,88)(67,89,100,122)(68,123,101,90)(69,91,102,124)(70,125,103,92), (1,112,200,215)(2,99,201,216)(3,100,202,217)(4,101,203,218)(5,102,204,219)(6,103,205,220)(7,104,206,221)(8,105,207,222)(9,106,208,223)(10,107,209,224)(11,108,210,211)(12,109,197,212)(13,110,198,213)(14,111,199,214)(15,176,184,91)(16,177,185,92)(17,178,186,93)(18,179,187,94)(19,180,188,95)(20,181,189,96)(21,182,190,97)(22,169,191,98)(23,170,192,85)(24,171,193,86)(25,172,194,87)(26,173,195,88)(27,174,196,89)(28,175,183,90)(29,155,80,65)(30,156,81,66)(31,157,82,67)(32,158,83,68)(33,159,84,69)(34,160,71,70)(35,161,72,57)(36,162,73,58)(37,163,74,59)(38,164,75,60)(39,165,76,61)(40,166,77,62)(41,167,78,63)(42,168,79,64)(43,146,118,133)(44,147,119,134)(45,148,120,135)(46,149,121,136)(47,150,122,137)(48,151,123,138)(49,152,124,139)(50,153,125,140)(51,154,126,127)(52,141,113,128)(53,142,114,129)(54,143,115,130)(55,144,116,131)(56,145,117,132), (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), (1,214,29,64)(2,63,30,213)(3,212,31,62)(4,61,32,211)(5,224,33,60)(6,59,34,223)(7,222,35,58)(8,57,36,221)(9,220,37,70)(10,69,38,219)(11,218,39,68)(12,67,40,217)(13,216,41,66)(14,65,42,215)(15,96,152,54)(16,53,153,95)(17,94,154,52)(18,51,141,93)(19,92,142,50)(20,49,143,91)(21,90,144,48)(22,47,145,89)(23,88,146,46)(24,45,147,87)(25,86,148,44)(26,43,149,85)(27,98,150,56)(28,55,151,97)(71,106,205,163)(72,162,206,105)(73,104,207,161)(74,160,208,103)(75,102,209,159)(76,158,210,101)(77,100,197,157)(78,156,198,99)(79,112,199,155)(80,168,200,111)(81,110,201,167)(82,166,202,109)(83,108,203,165)(84,164,204,107)(113,186,179,127)(114,140,180,185)(115,184,181,139)(116,138,182,183)(117,196,169,137)(118,136,170,195)(119,194,171,135)(120,134,172,193)(121,192,173,133)(122,132,174,191)(123,190,175,131)(124,130,176,189)(125,188,177,129)(126,128,178,187) );
G=PermutationGroup([[(1,148,80,194),(2,195,81,149),(3,150,82,196),(4,183,83,151),(5,152,84,184),(6,185,71,153),(7,154,72,186),(8,187,73,141),(9,142,74,188),(10,189,75,143),(11,144,76,190),(12,191,77,145),(13,146,78,192),(14,193,79,147),(15,204,139,33),(16,34,140,205),(17,206,127,35),(18,36,128,207),(19,208,129,37),(20,38,130,209),(21,210,131,39),(22,40,132,197),(23,198,133,41),(24,42,134,199),(25,200,135,29),(26,30,136,201),(27,202,137,31),(28,32,138,203),(43,167,170,213),(44,214,171,168),(45,155,172,215),(46,216,173,156),(47,157,174,217),(48,218,175,158),(49,159,176,219),(50,220,177,160),(51,161,178,221),(52,222,179,162),(53,163,180,223),(54,224,181,164),(55,165,182,211),(56,212,169,166),(57,93,104,126),(58,113,105,94),(59,95,106,114),(60,115,107,96),(61,97,108,116),(62,117,109,98),(63,85,110,118),(64,119,111,86),(65,87,112,120),(66,121,99,88),(67,89,100,122),(68,123,101,90),(69,91,102,124),(70,125,103,92)], [(1,112,200,215),(2,99,201,216),(3,100,202,217),(4,101,203,218),(5,102,204,219),(6,103,205,220),(7,104,206,221),(8,105,207,222),(9,106,208,223),(10,107,209,224),(11,108,210,211),(12,109,197,212),(13,110,198,213),(14,111,199,214),(15,176,184,91),(16,177,185,92),(17,178,186,93),(18,179,187,94),(19,180,188,95),(20,181,189,96),(21,182,190,97),(22,169,191,98),(23,170,192,85),(24,171,193,86),(25,172,194,87),(26,173,195,88),(27,174,196,89),(28,175,183,90),(29,155,80,65),(30,156,81,66),(31,157,82,67),(32,158,83,68),(33,159,84,69),(34,160,71,70),(35,161,72,57),(36,162,73,58),(37,163,74,59),(38,164,75,60),(39,165,76,61),(40,166,77,62),(41,167,78,63),(42,168,79,64),(43,146,118,133),(44,147,119,134),(45,148,120,135),(46,149,121,136),(47,150,122,137),(48,151,123,138),(49,152,124,139),(50,153,125,140),(51,154,126,127),(52,141,113,128),(53,142,114,129),(54,143,115,130),(55,144,116,131),(56,145,117,132)], [(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)], [(1,214,29,64),(2,63,30,213),(3,212,31,62),(4,61,32,211),(5,224,33,60),(6,59,34,223),(7,222,35,58),(8,57,36,221),(9,220,37,70),(10,69,38,219),(11,218,39,68),(12,67,40,217),(13,216,41,66),(14,65,42,215),(15,96,152,54),(16,53,153,95),(17,94,154,52),(18,51,141,93),(19,92,142,50),(20,49,143,91),(21,90,144,48),(22,47,145,89),(23,88,146,46),(24,45,147,87),(25,86,148,44),(26,43,149,85),(27,98,150,56),(28,55,151,97),(71,106,205,163),(72,162,206,105),(73,104,207,161),(74,160,208,103),(75,102,209,159),(76,158,210,101),(77,100,197,157),(78,156,198,99),(79,112,199,155),(80,168,200,111),(81,110,201,167),(82,166,202,109),(83,108,203,165),(84,164,204,107),(113,186,179,127),(114,140,180,185),(115,184,181,139),(116,138,182,183),(117,196,169,137),(118,136,170,195),(119,194,171,135),(120,134,172,193),(121,192,173,133),(122,132,174,191),(123,190,175,131),(124,130,176,189),(125,188,177,129),(126,128,178,187)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 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 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊2D7 | D4⋊8D14 |
| kernel | C42.117D14 | C28⋊2Q8 | C4×D28 | Dic7.D4 | C4⋊C4⋊7D7 | C23.21D14 | C28⋊7D4 | C28⋊2D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 2 | 1 | 3 | 8 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.117D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 9 | 12 |
| 28 | 12 | 0 | 0 | 0 | 0 |
| 24 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 12 | 1 | 0 | 0 | 0 | 0 |
| 2 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 24 |
| 0 | 0 | 0 | 0 | 16 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 27 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 21 | 0 | 0 |
| 0 | 0 | 26 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 24 |
| 0 | 0 | 0 | 0 | 28 | 20 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,9,0,0,0,0,0,12],[28,24,0,0,0,0,12,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[12,2,0,0,0,0,1,17,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,9,16,0,0,0,0,24,20],[17,27,0,0,0,0,0,12,0,0,0,0,0,0,21,26,0,0,0,0,21,8,0,0,0,0,0,0,9,28,0,0,0,0,24,20] >;
C42.117D14 in GAP, Magma, Sage, TeX
C_4^2._{117}D_{14} % in TeX
G:=Group("C4^2.117D14"); // GroupNames label
G:=SmallGroup(448,1016);
// by ID
G=gap.SmallGroup(448,1016);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,758,219,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*b^2*c^-1>;
// generators/relations