metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.94D14, C14.512- 1+4, C4⋊C4.271D14, C42⋊D7⋊2C2, C28.6Q8⋊6C2, D14⋊2Q8⋊12C2, C4.95(C4○D28), C42⋊C2⋊13D7, (C4×C28).24C22, (C2×C14).73C24, C22⋊C4.97D14, C28.3Q8⋊12C2, Dic7⋊3Q8⋊12C2, D14.16(C4○D4), C28.197(C4○D4), C28.48D4⋊29C2, (C2×C28).148C23, D14⋊C4.96C22, D14.D4.1C2, (C22×C4).194D14, C23.D14⋊3C2, C4⋊Dic7.34C22, C23.85(C22×D7), Dic7⋊C4.97C22, (C2×Dic7).26C23, (C4×Dic7).69C22, C22.102(C23×D7), C2.9(D4.10D14), C23.D7.96C22, (C22×C28).231C22, (C22×C14).143C23, C7⋊2(C22.46C24), (C22×D7).166C23, (C2×Dic14).143C22, (D7×C4⋊C4)⋊12C2, C2.12(D7×C4○D4), (C4×C7⋊D4).5C2, C2.32(C2×C4○D28), C14.30(C2×C4○D4), (C2×C4×D7).60C22, (C7×C42⋊C2)⋊15C2, (C7×C4⋊C4).309C22, (C2×C4).275(C22×D7), (C2×C7⋊D4).103C22, (C7×C22⋊C4).113C22, SmallGroup(448,982)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.94D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=ab2, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 852 in 214 conjugacy classes, 97 normal (43 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×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C22.46C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×C7⋊D4, C22×C28, C28.6Q8, C42⋊D7, C23.D14, D14.D4, Dic7⋊3Q8, C28.3Q8, D7×C4⋊C4, D14⋊2Q8, C28.48D4, C4×C7⋊D4, C7×C42⋊C2, C42.94D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.46C24, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, D4.10D14, C42.94D14
►On 224 points
Generators in S224
(1 132 148 65)(2 119 149 80)(3 134 150 67)(4 121 151 82)(5 136 152 69)(6 123 153 84)(7 138 154 71)(8 125 155 58)(9 140 156 73)(10 127 157 60)(11 114 158 75)(12 129 159 62)(13 116 160 77)(14 131 161 64)(15 118 162 79)(16 133 163 66)(17 120 164 81)(18 135 165 68)(19 122 166 83)(20 137 167 70)(21 124 168 57)(22 139 141 72)(23 126 142 59)(24 113 143 74)(25 128 144 61)(26 115 145 76)(27 130 146 63)(28 117 147 78)(29 197 100 174)(30 212 101 189)(31 199 102 176)(32 214 103 191)(33 201 104 178)(34 216 105 193)(35 203 106 180)(36 218 107 195)(37 205 108 182)(38 220 109 169)(39 207 110 184)(40 222 111 171)(41 209 112 186)(42 224 85 173)(43 211 86 188)(44 198 87 175)(45 213 88 190)(46 200 89 177)(47 215 90 192)(48 202 91 179)(49 217 92 194)(50 204 93 181)(51 219 94 196)(52 206 95 183)(53 221 96 170)(54 208 97 185)(55 223 98 172)(56 210 99 187)
(1 33 15 47)(2 34 16 48)(3 35 17 49)(4 36 18 50)(5 37 19 51)(6 38 20 52)(7 39 21 53)(8 40 22 54)(9 41 23 55)(10 42 24 56)(11 43 25 29)(12 44 26 30)(13 45 27 31)(14 46 28 32)(57 170 71 184)(58 171 72 185)(59 172 73 186)(60 173 74 187)(61 174 75 188)(62 175 76 189)(63 176 77 190)(64 177 78 191)(65 178 79 192)(66 179 80 193)(67 180 81 194)(68 181 82 195)(69 182 83 196)(70 183 84 169)(85 143 99 157)(86 144 100 158)(87 145 101 159)(88 146 102 160)(89 147 103 161)(90 148 104 162)(91 149 105 163)(92 150 106 164)(93 151 107 165)(94 152 108 166)(95 153 109 167)(96 154 110 168)(97 155 111 141)(98 156 112 142)(113 210 127 224)(114 211 128 197)(115 212 129 198)(116 213 130 199)(117 214 131 200)(118 215 132 201)(119 216 133 202)(120 217 134 203)(121 218 135 204)(122 219 136 205)(123 220 137 206)(124 221 138 207)(125 222 139 208)(126 223 140 209)
(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 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 93 43 107)(30 106 44 92)(31 91 45 105)(32 104 46 90)(33 89 47 103)(34 102 48 88)(35 87 49 101)(36 100 50 86)(37 85 51 99)(38 98 52 112)(39 111 53 97)(40 96 54 110)(41 109 55 95)(42 94 56 108)(57 58 71 72)(59 84 73 70)(60 69 74 83)(61 82 75 68)(62 67 76 81)(63 80 77 66)(64 65 78 79)(113 122 127 136)(114 135 128 121)(115 120 129 134)(116 133 130 119)(117 118 131 132)(123 140 137 126)(124 125 138 139)(141 154 155 168)(142 167 156 153)(143 152 157 166)(144 165 158 151)(145 150 159 164)(146 163 160 149)(147 148 161 162)(169 209 183 223)(170 222 184 208)(171 207 185 221)(172 220 186 206)(173 205 187 219)(174 218 188 204)(175 203 189 217)(176 216 190 202)(177 201 191 215)(178 214 192 200)(179 199 193 213)(180 212 194 198)(181 197 195 211)(182 210 196 224)
G:=sub<Sym(224)| (1,132,148,65)(2,119,149,80)(3,134,150,67)(4,121,151,82)(5,136,152,69)(6,123,153,84)(7,138,154,71)(8,125,155,58)(9,140,156,73)(10,127,157,60)(11,114,158,75)(12,129,159,62)(13,116,160,77)(14,131,161,64)(15,118,162,79)(16,133,163,66)(17,120,164,81)(18,135,165,68)(19,122,166,83)(20,137,167,70)(21,124,168,57)(22,139,141,72)(23,126,142,59)(24,113,143,74)(25,128,144,61)(26,115,145,76)(27,130,146,63)(28,117,147,78)(29,197,100,174)(30,212,101,189)(31,199,102,176)(32,214,103,191)(33,201,104,178)(34,216,105,193)(35,203,106,180)(36,218,107,195)(37,205,108,182)(38,220,109,169)(39,207,110,184)(40,222,111,171)(41,209,112,186)(42,224,85,173)(43,211,86,188)(44,198,87,175)(45,213,88,190)(46,200,89,177)(47,215,90,192)(48,202,91,179)(49,217,92,194)(50,204,93,181)(51,219,94,196)(52,206,95,183)(53,221,96,170)(54,208,97,185)(55,223,98,172)(56,210,99,187), (1,33,15,47)(2,34,16,48)(3,35,17,49)(4,36,18,50)(5,37,19,51)(6,38,20,52)(7,39,21,53)(8,40,22,54)(9,41,23,55)(10,42,24,56)(11,43,25,29)(12,44,26,30)(13,45,27,31)(14,46,28,32)(57,170,71,184)(58,171,72,185)(59,172,73,186)(60,173,74,187)(61,174,75,188)(62,175,76,189)(63,176,77,190)(64,177,78,191)(65,178,79,192)(66,179,80,193)(67,180,81,194)(68,181,82,195)(69,182,83,196)(70,183,84,169)(85,143,99,157)(86,144,100,158)(87,145,101,159)(88,146,102,160)(89,147,103,161)(90,148,104,162)(91,149,105,163)(92,150,106,164)(93,151,107,165)(94,152,108,166)(95,153,109,167)(96,154,110,168)(97,155,111,141)(98,156,112,142)(113,210,127,224)(114,211,128,197)(115,212,129,198)(116,213,130,199)(117,214,131,200)(118,215,132,201)(119,216,133,202)(120,217,134,203)(121,218,135,204)(122,219,136,205)(123,220,137,206)(124,221,138,207)(125,222,139,208)(126,223,140,209), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,93,43,107)(30,106,44,92)(31,91,45,105)(32,104,46,90)(33,89,47,103)(34,102,48,88)(35,87,49,101)(36,100,50,86)(37,85,51,99)(38,98,52,112)(39,111,53,97)(40,96,54,110)(41,109,55,95)(42,94,56,108)(57,58,71,72)(59,84,73,70)(60,69,74,83)(61,82,75,68)(62,67,76,81)(63,80,77,66)(64,65,78,79)(113,122,127,136)(114,135,128,121)(115,120,129,134)(116,133,130,119)(117,118,131,132)(123,140,137,126)(124,125,138,139)(141,154,155,168)(142,167,156,153)(143,152,157,166)(144,165,158,151)(145,150,159,164)(146,163,160,149)(147,148,161,162)(169,209,183,223)(170,222,184,208)(171,207,185,221)(172,220,186,206)(173,205,187,219)(174,218,188,204)(175,203,189,217)(176,216,190,202)(177,201,191,215)(178,214,192,200)(179,199,193,213)(180,212,194,198)(181,197,195,211)(182,210,196,224)>;
G:=Group( (1,132,148,65)(2,119,149,80)(3,134,150,67)(4,121,151,82)(5,136,152,69)(6,123,153,84)(7,138,154,71)(8,125,155,58)(9,140,156,73)(10,127,157,60)(11,114,158,75)(12,129,159,62)(13,116,160,77)(14,131,161,64)(15,118,162,79)(16,133,163,66)(17,120,164,81)(18,135,165,68)(19,122,166,83)(20,137,167,70)(21,124,168,57)(22,139,141,72)(23,126,142,59)(24,113,143,74)(25,128,144,61)(26,115,145,76)(27,130,146,63)(28,117,147,78)(29,197,100,174)(30,212,101,189)(31,199,102,176)(32,214,103,191)(33,201,104,178)(34,216,105,193)(35,203,106,180)(36,218,107,195)(37,205,108,182)(38,220,109,169)(39,207,110,184)(40,222,111,171)(41,209,112,186)(42,224,85,173)(43,211,86,188)(44,198,87,175)(45,213,88,190)(46,200,89,177)(47,215,90,192)(48,202,91,179)(49,217,92,194)(50,204,93,181)(51,219,94,196)(52,206,95,183)(53,221,96,170)(54,208,97,185)(55,223,98,172)(56,210,99,187), (1,33,15,47)(2,34,16,48)(3,35,17,49)(4,36,18,50)(5,37,19,51)(6,38,20,52)(7,39,21,53)(8,40,22,54)(9,41,23,55)(10,42,24,56)(11,43,25,29)(12,44,26,30)(13,45,27,31)(14,46,28,32)(57,170,71,184)(58,171,72,185)(59,172,73,186)(60,173,74,187)(61,174,75,188)(62,175,76,189)(63,176,77,190)(64,177,78,191)(65,178,79,192)(66,179,80,193)(67,180,81,194)(68,181,82,195)(69,182,83,196)(70,183,84,169)(85,143,99,157)(86,144,100,158)(87,145,101,159)(88,146,102,160)(89,147,103,161)(90,148,104,162)(91,149,105,163)(92,150,106,164)(93,151,107,165)(94,152,108,166)(95,153,109,167)(96,154,110,168)(97,155,111,141)(98,156,112,142)(113,210,127,224)(114,211,128,197)(115,212,129,198)(116,213,130,199)(117,214,131,200)(118,215,132,201)(119,216,133,202)(120,217,134,203)(121,218,135,204)(122,219,136,205)(123,220,137,206)(124,221,138,207)(125,222,139,208)(126,223,140,209), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,93,43,107)(30,106,44,92)(31,91,45,105)(32,104,46,90)(33,89,47,103)(34,102,48,88)(35,87,49,101)(36,100,50,86)(37,85,51,99)(38,98,52,112)(39,111,53,97)(40,96,54,110)(41,109,55,95)(42,94,56,108)(57,58,71,72)(59,84,73,70)(60,69,74,83)(61,82,75,68)(62,67,76,81)(63,80,77,66)(64,65,78,79)(113,122,127,136)(114,135,128,121)(115,120,129,134)(116,133,130,119)(117,118,131,132)(123,140,137,126)(124,125,138,139)(141,154,155,168)(142,167,156,153)(143,152,157,166)(144,165,158,151)(145,150,159,164)(146,163,160,149)(147,148,161,162)(169,209,183,223)(170,222,184,208)(171,207,185,221)(172,220,186,206)(173,205,187,219)(174,218,188,204)(175,203,189,217)(176,216,190,202)(177,201,191,215)(178,214,192,200)(179,199,193,213)(180,212,194,198)(181,197,195,211)(182,210,196,224) );
G=PermutationGroup([[(1,132,148,65),(2,119,149,80),(3,134,150,67),(4,121,151,82),(5,136,152,69),(6,123,153,84),(7,138,154,71),(8,125,155,58),(9,140,156,73),(10,127,157,60),(11,114,158,75),(12,129,159,62),(13,116,160,77),(14,131,161,64),(15,118,162,79),(16,133,163,66),(17,120,164,81),(18,135,165,68),(19,122,166,83),(20,137,167,70),(21,124,168,57),(22,139,141,72),(23,126,142,59),(24,113,143,74),(25,128,144,61),(26,115,145,76),(27,130,146,63),(28,117,147,78),(29,197,100,174),(30,212,101,189),(31,199,102,176),(32,214,103,191),(33,201,104,178),(34,216,105,193),(35,203,106,180),(36,218,107,195),(37,205,108,182),(38,220,109,169),(39,207,110,184),(40,222,111,171),(41,209,112,186),(42,224,85,173),(43,211,86,188),(44,198,87,175),(45,213,88,190),(46,200,89,177),(47,215,90,192),(48,202,91,179),(49,217,92,194),(50,204,93,181),(51,219,94,196),(52,206,95,183),(53,221,96,170),(54,208,97,185),(55,223,98,172),(56,210,99,187)], [(1,33,15,47),(2,34,16,48),(3,35,17,49),(4,36,18,50),(5,37,19,51),(6,38,20,52),(7,39,21,53),(8,40,22,54),(9,41,23,55),(10,42,24,56),(11,43,25,29),(12,44,26,30),(13,45,27,31),(14,46,28,32),(57,170,71,184),(58,171,72,185),(59,172,73,186),(60,173,74,187),(61,174,75,188),(62,175,76,189),(63,176,77,190),(64,177,78,191),(65,178,79,192),(66,179,80,193),(67,180,81,194),(68,181,82,195),(69,182,83,196),(70,183,84,169),(85,143,99,157),(86,144,100,158),(87,145,101,159),(88,146,102,160),(89,147,103,161),(90,148,104,162),(91,149,105,163),(92,150,106,164),(93,151,107,165),(94,152,108,166),(95,153,109,167),(96,154,110,168),(97,155,111,141),(98,156,112,142),(113,210,127,224),(114,211,128,197),(115,212,129,198),(116,213,130,199),(117,214,131,200),(118,215,132,201),(119,216,133,202),(120,217,134,203),(121,218,135,204),(122,219,136,205),(123,220,137,206),(124,221,138,207),(125,222,139,208),(126,223,140,209)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,93,43,107),(30,106,44,92),(31,91,45,105),(32,104,46,90),(33,89,47,103),(34,102,48,88),(35,87,49,101),(36,100,50,86),(37,85,51,99),(38,98,52,112),(39,111,53,97),(40,96,54,110),(41,109,55,95),(42,94,56,108),(57,58,71,72),(59,84,73,70),(60,69,74,83),(61,82,75,68),(62,67,76,81),(63,80,77,66),(64,65,78,79),(113,122,127,136),(114,135,128,121),(115,120,129,134),(116,133,130,119),(117,118,131,132),(123,140,137,126),(124,125,138,139),(141,154,155,168),(142,167,156,153),(143,152,157,166),(144,165,158,151),(145,150,159,164),(146,163,160,149),(147,148,161,162),(169,209,183,223),(170,222,184,208),(171,207,185,221),(172,220,186,206),(173,205,187,219),(174,218,188,204),(175,203,189,217),(176,216,190,202),(177,201,191,215),(178,214,192,200),(179,199,193,213),(180,212,194,198),(181,197,195,211),(182,210,196,224)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 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 | D4.10D14 |
| kernel | C42.94D14 | C28.6Q8 | C42⋊D7 | C23.D14 | D14.D4 | Dic7⋊3Q8 | C28.3Q8 | D7×C4⋊C4 | D14⋊2Q8 | C28.48D4 | C4×C7⋊D4 | 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 C42.94D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 1 | 17 |
| 25 | 22 | 0 | 0 | 0 | 0 |
| 27 | 4 | 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 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 19 | 0 | 0 |
| 0 | 0 | 15 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 7 |
| 0 | 0 | 0 | 0 | 24 | 18 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 1 | 0 | 0 |
| 0 | 0 | 14 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 7 |
| 0 | 0 | 0 | 0 | 24 | 18 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,1,0,0,0,0,2,17],[25,27,0,0,0,0,22,4,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,15,0,0,0,0,19,25,0,0,0,0,0,0,11,24,0,0,0,0,7,18],[1,3,0,0,0,0,0,28,0,0,0,0,0,0,25,14,0,0,0,0,1,4,0,0,0,0,0,0,11,24,0,0,0,0,7,18] >;
C42.94D14 in GAP, Magma, Sage, TeX
C_4^2._{94}D_{14} % in TeX
G:=Group("C4^2.94D14"); // GroupNames label
G:=SmallGroup(448,982);
// by ID
G=gap.SmallGroup(448,982);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,675,136,18822]);
// 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,d*c*d^-1=c^13>;
// generators/relations