metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.178D14, C14.402- 1+4, C14.842+ 1+4, C4⋊Q8⋊16D7, C4⋊C4.126D14, (C2×Q8).88D14, D28⋊C4⋊44C2, D14⋊2Q8⋊46C2, D14⋊3Q8⋊38C2, C4.D28⋊27C2, C4⋊D28.13C2, C42⋊D7⋊26C2, Dic7⋊3Q8⋊43C2, D14.5D4⋊47C2, C28.140(C4○D4), C28.23D4⋊27C2, (C4×C28).218C22, (C2×C14).277C24, (C2×C28).639C23, C4.23(Q8⋊2D7), C2.88(D4⋊6D14), D14⋊C4.156C22, (C2×D28).173C22, C4⋊Dic7.255C22, (Q8×C14).144C22, C22.298(C23×D7), Dic7⋊C4.169C22, (C4×Dic7).166C22, (C2×Dic7).274C23, (C22×D7).122C23, C2.41(Q8.10D14), C7⋊11(C22.36C24), (C2×Dic14).192C22, (C7×C4⋊Q8)⋊19C2, C4⋊C4⋊D7⋊47C2, C14.124(C2×C4○D4), C2.32(C2×Q8⋊2D7), (C2×C4×D7).150C22, (C7×C4⋊C4).220C22, (C2×C4).602(C22×D7), SmallGroup(448,1186)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.178D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1036 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22.36C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8×C14, C42⋊D7, C4.D28, Dic7⋊3Q8, D28⋊C4, D14.5D4, C4⋊D28, D14⋊2Q8, C4⋊C4⋊D7, D14⋊3Q8, C28.23D4, C7×C4⋊Q8, C42.178D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, Q8⋊2D7, C23×D7, D4⋊6D14, C2×Q8⋊2D7, Q8.10D14, C42.178D14
►On 224 points
Generators in S224
(1 80 15 66)(2 67 16 81)(3 82 17 68)(4 69 18 83)(5 84 19 70)(6 71 20 57)(7 58 21 72)(8 73 22 59)(9 60 23 74)(10 75 24 61)(11 62 25 76)(12 77 26 63)(13 64 27 78)(14 79 28 65)(29 219 43 205)(30 206 44 220)(31 221 45 207)(32 208 46 222)(33 223 47 209)(34 210 48 224)(35 197 49 211)(36 212 50 198)(37 199 51 213)(38 214 52 200)(39 201 53 215)(40 216 54 202)(41 203 55 217)(42 218 56 204)(85 114 99 128)(86 129 100 115)(87 116 101 130)(88 131 102 117)(89 118 103 132)(90 133 104 119)(91 120 105 134)(92 135 106 121)(93 122 107 136)(94 137 108 123)(95 124 109 138)(96 139 110 125)(97 126 111 140)(98 113 112 127)(141 190 155 176)(142 177 156 191)(143 192 157 178)(144 179 158 193)(145 194 159 180)(146 181 160 195)(147 196 161 182)(148 183 162 169)(149 170 163 184)(150 185 164 171)(151 172 165 186)(152 187 166 173)(153 174 167 188)(154 189 168 175)
(1 147 122 220)(2 221 123 148)(3 149 124 222)(4 223 125 150)(5 151 126 224)(6 197 127 152)(7 153 128 198)(8 199 129 154)(9 155 130 200)(10 201 131 156)(11 157 132 202)(12 203 133 158)(13 159 134 204)(14 205 135 160)(15 161 136 206)(16 207 137 162)(17 163 138 208)(18 209 139 164)(19 165 140 210)(20 211 113 166)(21 167 114 212)(22 213 115 168)(23 141 116 214)(24 215 117 142)(25 143 118 216)(26 217 119 144)(27 145 120 218)(28 219 121 146)(29 106 195 79)(30 80 196 107)(31 108 169 81)(32 82 170 109)(33 110 171 83)(34 84 172 111)(35 112 173 57)(36 58 174 85)(37 86 175 59)(38 60 176 87)(39 88 177 61)(40 62 178 89)(41 90 179 63)(42 64 180 91)(43 92 181 65)(44 66 182 93)(45 94 183 67)(46 68 184 95)(47 96 185 69)(48 70 186 97)(49 98 187 71)(50 72 188 99)(51 100 189 73)(52 74 190 101)(53 102 191 75)(54 76 192 103)(55 104 193 77)(56 78 194 105)
(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 29 15 43)(2 42 16 56)(3 55 17 41)(4 40 18 54)(5 53 19 39)(6 38 20 52)(7 51 21 37)(8 36 22 50)(9 49 23 35)(10 34 24 48)(11 47 25 33)(12 32 26 46)(13 45 27 31)(14 30 28 44)(57 141 71 155)(58 154 72 168)(59 167 73 153)(60 152 74 166)(61 165 75 151)(62 150 76 164)(63 163 77 149)(64 148 78 162)(65 161 79 147)(66 146 80 160)(67 159 81 145)(68 144 82 158)(69 157 83 143)(70 142 84 156)(85 199 99 213)(86 212 100 198)(87 197 101 211)(88 210 102 224)(89 223 103 209)(90 208 104 222)(91 221 105 207)(92 206 106 220)(93 219 107 205)(94 204 108 218)(95 217 109 203)(96 202 110 216)(97 215 111 201)(98 200 112 214)(113 190 127 176)(114 175 128 189)(115 188 129 174)(116 173 130 187)(117 186 131 172)(118 171 132 185)(119 184 133 170)(120 169 134 183)(121 182 135 196)(122 195 136 181)(123 180 137 194)(124 193 138 179)(125 178 139 192)(126 191 140 177)
G:=sub<Sym(224)| (1,80,15,66)(2,67,16,81)(3,82,17,68)(4,69,18,83)(5,84,19,70)(6,71,20,57)(7,58,21,72)(8,73,22,59)(9,60,23,74)(10,75,24,61)(11,62,25,76)(12,77,26,63)(13,64,27,78)(14,79,28,65)(29,219,43,205)(30,206,44,220)(31,221,45,207)(32,208,46,222)(33,223,47,209)(34,210,48,224)(35,197,49,211)(36,212,50,198)(37,199,51,213)(38,214,52,200)(39,201,53,215)(40,216,54,202)(41,203,55,217)(42,218,56,204)(85,114,99,128)(86,129,100,115)(87,116,101,130)(88,131,102,117)(89,118,103,132)(90,133,104,119)(91,120,105,134)(92,135,106,121)(93,122,107,136)(94,137,108,123)(95,124,109,138)(96,139,110,125)(97,126,111,140)(98,113,112,127)(141,190,155,176)(142,177,156,191)(143,192,157,178)(144,179,158,193)(145,194,159,180)(146,181,160,195)(147,196,161,182)(148,183,162,169)(149,170,163,184)(150,185,164,171)(151,172,165,186)(152,187,166,173)(153,174,167,188)(154,189,168,175), (1,147,122,220)(2,221,123,148)(3,149,124,222)(4,223,125,150)(5,151,126,224)(6,197,127,152)(7,153,128,198)(8,199,129,154)(9,155,130,200)(10,201,131,156)(11,157,132,202)(12,203,133,158)(13,159,134,204)(14,205,135,160)(15,161,136,206)(16,207,137,162)(17,163,138,208)(18,209,139,164)(19,165,140,210)(20,211,113,166)(21,167,114,212)(22,213,115,168)(23,141,116,214)(24,215,117,142)(25,143,118,216)(26,217,119,144)(27,145,120,218)(28,219,121,146)(29,106,195,79)(30,80,196,107)(31,108,169,81)(32,82,170,109)(33,110,171,83)(34,84,172,111)(35,112,173,57)(36,58,174,85)(37,86,175,59)(38,60,176,87)(39,88,177,61)(40,62,178,89)(41,90,179,63)(42,64,180,91)(43,92,181,65)(44,66,182,93)(45,94,183,67)(46,68,184,95)(47,96,185,69)(48,70,186,97)(49,98,187,71)(50,72,188,99)(51,100,189,73)(52,74,190,101)(53,102,191,75)(54,76,192,103)(55,104,193,77)(56,78,194,105), (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), (1,29,15,43)(2,42,16,56)(3,55,17,41)(4,40,18,54)(5,53,19,39)(6,38,20,52)(7,51,21,37)(8,36,22,50)(9,49,23,35)(10,34,24,48)(11,47,25,33)(12,32,26,46)(13,45,27,31)(14,30,28,44)(57,141,71,155)(58,154,72,168)(59,167,73,153)(60,152,74,166)(61,165,75,151)(62,150,76,164)(63,163,77,149)(64,148,78,162)(65,161,79,147)(66,146,80,160)(67,159,81,145)(68,144,82,158)(69,157,83,143)(70,142,84,156)(85,199,99,213)(86,212,100,198)(87,197,101,211)(88,210,102,224)(89,223,103,209)(90,208,104,222)(91,221,105,207)(92,206,106,220)(93,219,107,205)(94,204,108,218)(95,217,109,203)(96,202,110,216)(97,215,111,201)(98,200,112,214)(113,190,127,176)(114,175,128,189)(115,188,129,174)(116,173,130,187)(117,186,131,172)(118,171,132,185)(119,184,133,170)(120,169,134,183)(121,182,135,196)(122,195,136,181)(123,180,137,194)(124,193,138,179)(125,178,139,192)(126,191,140,177)>;
G:=Group( (1,80,15,66)(2,67,16,81)(3,82,17,68)(4,69,18,83)(5,84,19,70)(6,71,20,57)(7,58,21,72)(8,73,22,59)(9,60,23,74)(10,75,24,61)(11,62,25,76)(12,77,26,63)(13,64,27,78)(14,79,28,65)(29,219,43,205)(30,206,44,220)(31,221,45,207)(32,208,46,222)(33,223,47,209)(34,210,48,224)(35,197,49,211)(36,212,50,198)(37,199,51,213)(38,214,52,200)(39,201,53,215)(40,216,54,202)(41,203,55,217)(42,218,56,204)(85,114,99,128)(86,129,100,115)(87,116,101,130)(88,131,102,117)(89,118,103,132)(90,133,104,119)(91,120,105,134)(92,135,106,121)(93,122,107,136)(94,137,108,123)(95,124,109,138)(96,139,110,125)(97,126,111,140)(98,113,112,127)(141,190,155,176)(142,177,156,191)(143,192,157,178)(144,179,158,193)(145,194,159,180)(146,181,160,195)(147,196,161,182)(148,183,162,169)(149,170,163,184)(150,185,164,171)(151,172,165,186)(152,187,166,173)(153,174,167,188)(154,189,168,175), (1,147,122,220)(2,221,123,148)(3,149,124,222)(4,223,125,150)(5,151,126,224)(6,197,127,152)(7,153,128,198)(8,199,129,154)(9,155,130,200)(10,201,131,156)(11,157,132,202)(12,203,133,158)(13,159,134,204)(14,205,135,160)(15,161,136,206)(16,207,137,162)(17,163,138,208)(18,209,139,164)(19,165,140,210)(20,211,113,166)(21,167,114,212)(22,213,115,168)(23,141,116,214)(24,215,117,142)(25,143,118,216)(26,217,119,144)(27,145,120,218)(28,219,121,146)(29,106,195,79)(30,80,196,107)(31,108,169,81)(32,82,170,109)(33,110,171,83)(34,84,172,111)(35,112,173,57)(36,58,174,85)(37,86,175,59)(38,60,176,87)(39,88,177,61)(40,62,178,89)(41,90,179,63)(42,64,180,91)(43,92,181,65)(44,66,182,93)(45,94,183,67)(46,68,184,95)(47,96,185,69)(48,70,186,97)(49,98,187,71)(50,72,188,99)(51,100,189,73)(52,74,190,101)(53,102,191,75)(54,76,192,103)(55,104,193,77)(56,78,194,105), (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), (1,29,15,43)(2,42,16,56)(3,55,17,41)(4,40,18,54)(5,53,19,39)(6,38,20,52)(7,51,21,37)(8,36,22,50)(9,49,23,35)(10,34,24,48)(11,47,25,33)(12,32,26,46)(13,45,27,31)(14,30,28,44)(57,141,71,155)(58,154,72,168)(59,167,73,153)(60,152,74,166)(61,165,75,151)(62,150,76,164)(63,163,77,149)(64,148,78,162)(65,161,79,147)(66,146,80,160)(67,159,81,145)(68,144,82,158)(69,157,83,143)(70,142,84,156)(85,199,99,213)(86,212,100,198)(87,197,101,211)(88,210,102,224)(89,223,103,209)(90,208,104,222)(91,221,105,207)(92,206,106,220)(93,219,107,205)(94,204,108,218)(95,217,109,203)(96,202,110,216)(97,215,111,201)(98,200,112,214)(113,190,127,176)(114,175,128,189)(115,188,129,174)(116,173,130,187)(117,186,131,172)(118,171,132,185)(119,184,133,170)(120,169,134,183)(121,182,135,196)(122,195,136,181)(123,180,137,194)(124,193,138,179)(125,178,139,192)(126,191,140,177) );
G=PermutationGroup([[(1,80,15,66),(2,67,16,81),(3,82,17,68),(4,69,18,83),(5,84,19,70),(6,71,20,57),(7,58,21,72),(8,73,22,59),(9,60,23,74),(10,75,24,61),(11,62,25,76),(12,77,26,63),(13,64,27,78),(14,79,28,65),(29,219,43,205),(30,206,44,220),(31,221,45,207),(32,208,46,222),(33,223,47,209),(34,210,48,224),(35,197,49,211),(36,212,50,198),(37,199,51,213),(38,214,52,200),(39,201,53,215),(40,216,54,202),(41,203,55,217),(42,218,56,204),(85,114,99,128),(86,129,100,115),(87,116,101,130),(88,131,102,117),(89,118,103,132),(90,133,104,119),(91,120,105,134),(92,135,106,121),(93,122,107,136),(94,137,108,123),(95,124,109,138),(96,139,110,125),(97,126,111,140),(98,113,112,127),(141,190,155,176),(142,177,156,191),(143,192,157,178),(144,179,158,193),(145,194,159,180),(146,181,160,195),(147,196,161,182),(148,183,162,169),(149,170,163,184),(150,185,164,171),(151,172,165,186),(152,187,166,173),(153,174,167,188),(154,189,168,175)], [(1,147,122,220),(2,221,123,148),(3,149,124,222),(4,223,125,150),(5,151,126,224),(6,197,127,152),(7,153,128,198),(8,199,129,154),(9,155,130,200),(10,201,131,156),(11,157,132,202),(12,203,133,158),(13,159,134,204),(14,205,135,160),(15,161,136,206),(16,207,137,162),(17,163,138,208),(18,209,139,164),(19,165,140,210),(20,211,113,166),(21,167,114,212),(22,213,115,168),(23,141,116,214),(24,215,117,142),(25,143,118,216),(26,217,119,144),(27,145,120,218),(28,219,121,146),(29,106,195,79),(30,80,196,107),(31,108,169,81),(32,82,170,109),(33,110,171,83),(34,84,172,111),(35,112,173,57),(36,58,174,85),(37,86,175,59),(38,60,176,87),(39,88,177,61),(40,62,178,89),(41,90,179,63),(42,64,180,91),(43,92,181,65),(44,66,182,93),(45,94,183,67),(46,68,184,95),(47,96,185,69),(48,70,186,97),(49,98,187,71),(50,72,188,99),(51,100,189,73),(52,74,190,101),(53,102,191,75),(54,76,192,103),(55,104,193,77),(56,78,194,105)], [(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)], [(1,29,15,43),(2,42,16,56),(3,55,17,41),(4,40,18,54),(5,53,19,39),(6,38,20,52),(7,51,21,37),(8,36,22,50),(9,49,23,35),(10,34,24,48),(11,47,25,33),(12,32,26,46),(13,45,27,31),(14,30,28,44),(57,141,71,155),(58,154,72,168),(59,167,73,153),(60,152,74,166),(61,165,75,151),(62,150,76,164),(63,163,77,149),(64,148,78,162),(65,161,79,147),(66,146,80,160),(67,159,81,145),(68,144,82,158),(69,157,83,143),(70,142,84,156),(85,199,99,213),(86,212,100,198),(87,197,101,211),(88,210,102,224),(89,223,103,209),(90,208,104,222),(91,221,105,207),(92,206,106,220),(93,219,107,205),(94,204,108,218),(95,217,109,203),(96,202,110,216),(97,215,111,201),(98,200,112,214),(113,190,127,176),(114,175,128,189),(115,188,129,174),(116,173,130,187),(117,186,131,172),(118,171,132,185),(119,184,133,170),(120,169,134,183),(121,182,135,196),(122,195,136,181),(123,180,137,194),(124,193,138,179),(125,178,139,192),(126,191,140,177)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8⋊2D7 | D4⋊6D14 | Q8.10D14 |
| kernel | C42.178D14 | C42⋊D7 | C4.D28 | Dic7⋊3Q8 | D28⋊C4 | D14.5D4 | C4⋊D28 | D14⋊2Q8 | C4⋊C4⋊D7 | D14⋊3Q8 | C28.23D4 | C7×C4⋊Q8 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 1 | 3 | 4 | 3 | 12 | 6 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.178D14 ►in GL8(𝔽29)
| 28 | 0 | 10 | 13 | 0 | 0 | 0 | 0 |
| 0 | 28 | 26 | 13 | 0 | 0 | 0 | 0 |
| 11 | 18 | 1 | 0 | 0 | 0 | 0 | 0 |
| 7 | 4 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 18 | 27 |
| 0 | 0 | 0 | 0 | 25 | 28 | 2 | 11 |
| 1 | 0 | 19 | 16 | 0 | 0 | 0 | 0 |
| 0 | 1 | 3 | 16 | 0 | 0 | 0 | 0 |
| 18 | 11 | 28 | 0 | 0 | 0 | 0 | 0 |
| 22 | 25 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 15 | 0 | 11 |
| 0 | 0 | 0 | 0 | 21 | 18 | 18 | 14 |
| 0 | 0 | 0 | 0 | 6 | 16 | 9 | 14 |
| 0 | 0 | 0 | 0 | 13 | 0 | 15 | 20 |
| 23 | 3 | 11 | 10 | 0 | 0 | 0 | 0 |
| 27 | 25 | 8 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 22 | 8 | 9 |
| 0 | 0 | 0 | 0 | 28 | 16 | 18 | 1 |
| 0 | 0 | 0 | 0 | 18 | 19 | 12 | 7 |
| 0 | 0 | 0 | 0 | 27 | 0 | 26 | 12 |
| 25 | 26 | 2 | 4 | 0 | 0 | 0 | 0 |
| 5 | 4 | 20 | 28 | 0 | 0 | 0 | 0 |
| 12 | 19 | 12 | 16 | 0 | 0 | 0 | 0 |
| 8 | 5 | 11 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 12 | 26 | 20 |
| 0 | 0 | 0 | 0 | 19 | 2 | 3 | 27 |
| 0 | 0 | 0 | 0 | 4 | 22 | 13 | 8 |
| 0 | 0 | 0 | 0 | 27 | 18 | 23 | 26 |
G:=sub<GL(8,GF(29))| [28,0,11,7,0,0,0,0,0,28,18,4,0,0,0,0,10,26,1,0,0,0,0,0,13,13,0,1,0,0,0,0,0,0,0,0,3,4,1,25,0,0,0,0,27,26,0,28,0,0,0,0,0,0,18,2,0,0,0,0,0,0,27,11],[1,0,18,22,0,0,0,0,0,1,11,25,0,0,0,0,19,3,28,0,0,0,0,0,16,16,0,28,0,0,0,0,0,0,0,0,11,21,6,13,0,0,0,0,15,18,16,0,0,0,0,0,0,18,9,15,0,0,0,0,11,14,14,20],[23,27,0,0,0,0,0,0,3,25,0,0,0,0,0,0,11,8,27,18,0,0,0,0,10,20,26,12,0,0,0,0,0,0,0,0,18,28,18,27,0,0,0,0,22,16,19,0,0,0,0,0,8,18,12,26,0,0,0,0,9,1,7,12],[25,5,12,8,0,0,0,0,26,4,19,5,0,0,0,0,2,20,12,11,0,0,0,0,4,28,16,17,0,0,0,0,0,0,0,0,17,19,4,27,0,0,0,0,12,2,22,18,0,0,0,0,26,3,13,23,0,0,0,0,20,27,8,26] >;
C42.178D14 in GAP, Magma, Sage, TeX
C_4^2._{178}D_{14} % in TeX
G:=Group("C4^2.178D14"); // GroupNames label
G:=SmallGroup(448,1186);
// by ID
G=gap.SmallGroup(448,1186);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,100,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations