metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.116D14, C14.1052+ 1+4, (C4×D4)⋊24D7, (D4×C28)⋊26C2, (C4×D28)⋊33C2, C4⋊D28⋊16C2, C28⋊D4⋊10C2, C28⋊2D4⋊10C2, C28⋊7D4⋊12C2, C4⋊C4.287D14, D14⋊D4⋊11C2, D14.D4⋊9C2, (C2×D4).223D14, C4.46(C4○D28), C42⋊D7⋊15C2, C28.3Q8⋊16C2, C28.113(C4○D4), (C2×C28).164C23, (C2×C14).106C24, (C4×C28).160C22, D14⋊C4.88C22, C22⋊C4.118D14, (C22×C4).214D14, Dic7⋊C4.7C22, C2.24(D4⋊6D14), C2.18(D4⋊8D14), (D4×C14).265C22, (C2×D28).260C22, C23.23D14⋊4C2, C4⋊Dic7.364C22, (C22×C28).83C22, (C2×Dic7).47C23, (C4×Dic7).78C22, (C22×D7).40C23, C23.103(C22×D7), C22.131(C23×D7), C23.D7.16C22, (C22×C14).176C23, C7⋊2(C22.34C24), C14.48(C2×C4○D4), C2.55(C2×C4○D28), (C2×C4×D7).203C22, (C7×C4⋊C4).334C22, (C2×C4).581(C22×D7), (C2×C7⋊D4).19C22, (C7×C22⋊C4).129C22, SmallGroup(448,1015)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.116D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, bc=cb, dbd-1=a2b-1, dcd-1=a2c-1 >
Subgroups: 1236 in 240 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C22.D4, C42.C2, C4⋊1D4, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22.34C24, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C2×C7⋊D4, C22×C28, D4×C14, C42⋊D7, C4×D28, D14.D4, D14⋊D4, C28.3Q8, C4⋊D28, C23.23D14, C28⋊7D4, C28⋊2D4, C28⋊D4, D4×C28, C42.116D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.34C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D4⋊8D14, C42.116D14
►On 224 points
Generators in S224
(1 180 143 157)(2 184 144 132)(3 182 145 159)(4 186 146 134)(5 170 147 161)(6 188 148 136)(7 172 149 163)(8 190 150 138)(9 174 151 165)(10 192 152 140)(11 176 153 167)(12 194 154 128)(13 178 141 155)(14 196 142 130)(15 103 116 86)(16 217 117 46)(17 105 118 88)(18 219 119 48)(19 107 120 90)(20 221 121 50)(21 109 122 92)(22 223 123 52)(23 111 124 94)(24 211 125 54)(25 99 126 96)(26 213 113 56)(27 101 114 98)(28 215 115 44)(29 156 77 179)(30 131 78 183)(31 158 79 181)(32 133 80 185)(33 160 81 169)(34 135 82 187)(35 162 83 171)(36 137 84 189)(37 164 71 173)(38 139 72 191)(39 166 73 175)(40 127 74 193)(41 168 75 177)(42 129 76 195)(43 207 214 62)(45 209 216 64)(47 197 218 66)(49 199 220 68)(51 201 222 70)(53 203 224 58)(55 205 212 60)(57 93 202 110)(59 95 204 112)(61 97 206 100)(63 85 208 102)(65 87 210 104)(67 89 198 106)(69 91 200 108)
(1 123 30 202)(2 124 31 203)(3 125 32 204)(4 126 33 205)(5 113 34 206)(6 114 35 207)(7 115 36 208)(8 116 37 209)(9 117 38 210)(10 118 39 197)(11 119 40 198)(12 120 41 199)(13 121 42 200)(14 122 29 201)(15 71 64 150)(16 72 65 151)(17 73 66 152)(18 74 67 153)(19 75 68 154)(20 76 69 141)(21 77 70 142)(22 78 57 143)(23 79 58 144)(24 80 59 145)(25 81 60 146)(26 82 61 147)(27 83 62 148)(28 84 63 149)(43 136 101 171)(44 137 102 172)(45 138 103 173)(46 139 104 174)(47 140 105 175)(48 127 106 176)(49 128 107 177)(50 129 108 178)(51 130 109 179)(52 131 110 180)(53 132 111 181)(54 133 112 182)(55 134 99 169)(56 135 100 170)(85 163 215 189)(86 164 216 190)(87 165 217 191)(88 166 218 192)(89 167 219 193)(90 168 220 194)(91 155 221 195)(92 156 222 196)(93 157 223 183)(94 158 224 184)(95 159 211 185)(96 160 212 186)(97 161 213 187)(98 162 214 188)
(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)
(1 208 143 63)(2 62 144 207)(3 206 145 61)(4 60 146 205)(5 204 147 59)(6 58 148 203)(7 202 149 57)(8 70 150 201)(9 200 151 69)(10 68 152 199)(11 198 153 67)(12 66 154 197)(13 210 141 65)(14 64 142 209)(15 77 116 29)(16 42 117 76)(17 75 118 41)(18 40 119 74)(19 73 120 39)(20 38 121 72)(21 71 122 37)(22 36 123 84)(23 83 124 35)(24 34 125 82)(25 81 126 33)(26 32 113 80)(27 79 114 31)(28 30 115 78)(43 158 214 181)(44 180 215 157)(45 156 216 179)(46 178 217 155)(47 168 218 177)(48 176 219 167)(49 166 220 175)(50 174 221 165)(51 164 222 173)(52 172 223 163)(53 162 224 171)(54 170 211 161)(55 160 212 169)(56 182 213 159)(85 183 102 131)(86 130 103 196)(87 195 104 129)(88 128 105 194)(89 193 106 127)(90 140 107 192)(91 191 108 139)(92 138 109 190)(93 189 110 137)(94 136 111 188)(95 187 112 135)(96 134 99 186)(97 185 100 133)(98 132 101 184)
G:=sub<Sym(224)| (1,180,143,157)(2,184,144,132)(3,182,145,159)(4,186,146,134)(5,170,147,161)(6,188,148,136)(7,172,149,163)(8,190,150,138)(9,174,151,165)(10,192,152,140)(11,176,153,167)(12,194,154,128)(13,178,141,155)(14,196,142,130)(15,103,116,86)(16,217,117,46)(17,105,118,88)(18,219,119,48)(19,107,120,90)(20,221,121,50)(21,109,122,92)(22,223,123,52)(23,111,124,94)(24,211,125,54)(25,99,126,96)(26,213,113,56)(27,101,114,98)(28,215,115,44)(29,156,77,179)(30,131,78,183)(31,158,79,181)(32,133,80,185)(33,160,81,169)(34,135,82,187)(35,162,83,171)(36,137,84,189)(37,164,71,173)(38,139,72,191)(39,166,73,175)(40,127,74,193)(41,168,75,177)(42,129,76,195)(43,207,214,62)(45,209,216,64)(47,197,218,66)(49,199,220,68)(51,201,222,70)(53,203,224,58)(55,205,212,60)(57,93,202,110)(59,95,204,112)(61,97,206,100)(63,85,208,102)(65,87,210,104)(67,89,198,106)(69,91,200,108), (1,123,30,202)(2,124,31,203)(3,125,32,204)(4,126,33,205)(5,113,34,206)(6,114,35,207)(7,115,36,208)(8,116,37,209)(9,117,38,210)(10,118,39,197)(11,119,40,198)(12,120,41,199)(13,121,42,200)(14,122,29,201)(15,71,64,150)(16,72,65,151)(17,73,66,152)(18,74,67,153)(19,75,68,154)(20,76,69,141)(21,77,70,142)(22,78,57,143)(23,79,58,144)(24,80,59,145)(25,81,60,146)(26,82,61,147)(27,83,62,148)(28,84,63,149)(43,136,101,171)(44,137,102,172)(45,138,103,173)(46,139,104,174)(47,140,105,175)(48,127,106,176)(49,128,107,177)(50,129,108,178)(51,130,109,179)(52,131,110,180)(53,132,111,181)(54,133,112,182)(55,134,99,169)(56,135,100,170)(85,163,215,189)(86,164,216,190)(87,165,217,191)(88,166,218,192)(89,167,219,193)(90,168,220,194)(91,155,221,195)(92,156,222,196)(93,157,223,183)(94,158,224,184)(95,159,211,185)(96,160,212,186)(97,161,213,187)(98,162,214,188), (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), (1,208,143,63)(2,62,144,207)(3,206,145,61)(4,60,146,205)(5,204,147,59)(6,58,148,203)(7,202,149,57)(8,70,150,201)(9,200,151,69)(10,68,152,199)(11,198,153,67)(12,66,154,197)(13,210,141,65)(14,64,142,209)(15,77,116,29)(16,42,117,76)(17,75,118,41)(18,40,119,74)(19,73,120,39)(20,38,121,72)(21,71,122,37)(22,36,123,84)(23,83,124,35)(24,34,125,82)(25,81,126,33)(26,32,113,80)(27,79,114,31)(28,30,115,78)(43,158,214,181)(44,180,215,157)(45,156,216,179)(46,178,217,155)(47,168,218,177)(48,176,219,167)(49,166,220,175)(50,174,221,165)(51,164,222,173)(52,172,223,163)(53,162,224,171)(54,170,211,161)(55,160,212,169)(56,182,213,159)(85,183,102,131)(86,130,103,196)(87,195,104,129)(88,128,105,194)(89,193,106,127)(90,140,107,192)(91,191,108,139)(92,138,109,190)(93,189,110,137)(94,136,111,188)(95,187,112,135)(96,134,99,186)(97,185,100,133)(98,132,101,184)>;
G:=Group( (1,180,143,157)(2,184,144,132)(3,182,145,159)(4,186,146,134)(5,170,147,161)(6,188,148,136)(7,172,149,163)(8,190,150,138)(9,174,151,165)(10,192,152,140)(11,176,153,167)(12,194,154,128)(13,178,141,155)(14,196,142,130)(15,103,116,86)(16,217,117,46)(17,105,118,88)(18,219,119,48)(19,107,120,90)(20,221,121,50)(21,109,122,92)(22,223,123,52)(23,111,124,94)(24,211,125,54)(25,99,126,96)(26,213,113,56)(27,101,114,98)(28,215,115,44)(29,156,77,179)(30,131,78,183)(31,158,79,181)(32,133,80,185)(33,160,81,169)(34,135,82,187)(35,162,83,171)(36,137,84,189)(37,164,71,173)(38,139,72,191)(39,166,73,175)(40,127,74,193)(41,168,75,177)(42,129,76,195)(43,207,214,62)(45,209,216,64)(47,197,218,66)(49,199,220,68)(51,201,222,70)(53,203,224,58)(55,205,212,60)(57,93,202,110)(59,95,204,112)(61,97,206,100)(63,85,208,102)(65,87,210,104)(67,89,198,106)(69,91,200,108), (1,123,30,202)(2,124,31,203)(3,125,32,204)(4,126,33,205)(5,113,34,206)(6,114,35,207)(7,115,36,208)(8,116,37,209)(9,117,38,210)(10,118,39,197)(11,119,40,198)(12,120,41,199)(13,121,42,200)(14,122,29,201)(15,71,64,150)(16,72,65,151)(17,73,66,152)(18,74,67,153)(19,75,68,154)(20,76,69,141)(21,77,70,142)(22,78,57,143)(23,79,58,144)(24,80,59,145)(25,81,60,146)(26,82,61,147)(27,83,62,148)(28,84,63,149)(43,136,101,171)(44,137,102,172)(45,138,103,173)(46,139,104,174)(47,140,105,175)(48,127,106,176)(49,128,107,177)(50,129,108,178)(51,130,109,179)(52,131,110,180)(53,132,111,181)(54,133,112,182)(55,134,99,169)(56,135,100,170)(85,163,215,189)(86,164,216,190)(87,165,217,191)(88,166,218,192)(89,167,219,193)(90,168,220,194)(91,155,221,195)(92,156,222,196)(93,157,223,183)(94,158,224,184)(95,159,211,185)(96,160,212,186)(97,161,213,187)(98,162,214,188), (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), (1,208,143,63)(2,62,144,207)(3,206,145,61)(4,60,146,205)(5,204,147,59)(6,58,148,203)(7,202,149,57)(8,70,150,201)(9,200,151,69)(10,68,152,199)(11,198,153,67)(12,66,154,197)(13,210,141,65)(14,64,142,209)(15,77,116,29)(16,42,117,76)(17,75,118,41)(18,40,119,74)(19,73,120,39)(20,38,121,72)(21,71,122,37)(22,36,123,84)(23,83,124,35)(24,34,125,82)(25,81,126,33)(26,32,113,80)(27,79,114,31)(28,30,115,78)(43,158,214,181)(44,180,215,157)(45,156,216,179)(46,178,217,155)(47,168,218,177)(48,176,219,167)(49,166,220,175)(50,174,221,165)(51,164,222,173)(52,172,223,163)(53,162,224,171)(54,170,211,161)(55,160,212,169)(56,182,213,159)(85,183,102,131)(86,130,103,196)(87,195,104,129)(88,128,105,194)(89,193,106,127)(90,140,107,192)(91,191,108,139)(92,138,109,190)(93,189,110,137)(94,136,111,188)(95,187,112,135)(96,134,99,186)(97,185,100,133)(98,132,101,184) );
G=PermutationGroup([[(1,180,143,157),(2,184,144,132),(3,182,145,159),(4,186,146,134),(5,170,147,161),(6,188,148,136),(7,172,149,163),(8,190,150,138),(9,174,151,165),(10,192,152,140),(11,176,153,167),(12,194,154,128),(13,178,141,155),(14,196,142,130),(15,103,116,86),(16,217,117,46),(17,105,118,88),(18,219,119,48),(19,107,120,90),(20,221,121,50),(21,109,122,92),(22,223,123,52),(23,111,124,94),(24,211,125,54),(25,99,126,96),(26,213,113,56),(27,101,114,98),(28,215,115,44),(29,156,77,179),(30,131,78,183),(31,158,79,181),(32,133,80,185),(33,160,81,169),(34,135,82,187),(35,162,83,171),(36,137,84,189),(37,164,71,173),(38,139,72,191),(39,166,73,175),(40,127,74,193),(41,168,75,177),(42,129,76,195),(43,207,214,62),(45,209,216,64),(47,197,218,66),(49,199,220,68),(51,201,222,70),(53,203,224,58),(55,205,212,60),(57,93,202,110),(59,95,204,112),(61,97,206,100),(63,85,208,102),(65,87,210,104),(67,89,198,106),(69,91,200,108)], [(1,123,30,202),(2,124,31,203),(3,125,32,204),(4,126,33,205),(5,113,34,206),(6,114,35,207),(7,115,36,208),(8,116,37,209),(9,117,38,210),(10,118,39,197),(11,119,40,198),(12,120,41,199),(13,121,42,200),(14,122,29,201),(15,71,64,150),(16,72,65,151),(17,73,66,152),(18,74,67,153),(19,75,68,154),(20,76,69,141),(21,77,70,142),(22,78,57,143),(23,79,58,144),(24,80,59,145),(25,81,60,146),(26,82,61,147),(27,83,62,148),(28,84,63,149),(43,136,101,171),(44,137,102,172),(45,138,103,173),(46,139,104,174),(47,140,105,175),(48,127,106,176),(49,128,107,177),(50,129,108,178),(51,130,109,179),(52,131,110,180),(53,132,111,181),(54,133,112,182),(55,134,99,169),(56,135,100,170),(85,163,215,189),(86,164,216,190),(87,165,217,191),(88,166,218,192),(89,167,219,193),(90,168,220,194),(91,155,221,195),(92,156,222,196),(93,157,223,183),(94,158,224,184),(95,159,211,185),(96,160,212,186),(97,161,213,187),(98,162,214,188)], [(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)], [(1,208,143,63),(2,62,144,207),(3,206,145,61),(4,60,146,205),(5,204,147,59),(6,58,148,203),(7,202,149,57),(8,70,150,201),(9,200,151,69),(10,68,152,199),(11,198,153,67),(12,66,154,197),(13,210,141,65),(14,64,142,209),(15,77,116,29),(16,42,117,76),(17,75,118,41),(18,40,119,74),(19,73,120,39),(20,38,121,72),(21,71,122,37),(22,36,123,84),(23,83,124,35),(24,34,125,82),(25,81,126,33),(26,32,113,80),(27,79,114,31),(28,30,115,78),(43,158,214,181),(44,180,215,157),(45,156,216,179),(46,178,217,155),(47,168,218,177),(48,176,219,167),(49,166,220,175),(50,174,221,165),(51,164,222,173),(52,172,223,163),(53,162,224,171),(54,170,211,161),(55,160,212,169),(56,182,213,159),(85,183,102,131),(86,130,103,196),(87,195,104,129),(88,128,105,194),(89,193,106,127),(90,140,107,192),(91,191,108,139),(92,138,109,190),(93,189,110,137),(94,136,111,188),(95,187,112,135),(96,134,99,186),(97,185,100,133),(98,132,101,184)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 2 | ··· | 2 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 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 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊6D14 | D4⋊8D14 |
| kernel | C42.116D14 | C42⋊D7 | C4×D28 | D14.D4 | D14⋊D4 | C28.3Q8 | C4⋊D28 | C23.23D14 | C28⋊7D4 | C28⋊2D4 | C28⋊D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 2 | 6 | 6 |
Matrix representation of C42.116D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 20 | 5 | 7 |
| 0 | 0 | 9 | 6 | 0 | 22 |
| 0 | 0 | 15 | 15 | 26 | 9 |
| 0 | 0 | 0 | 10 | 23 | 3 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 5 | 0 | 0 |
| 0 | 0 | 24 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 5 |
| 0 | 0 | 0 | 0 | 16 | 21 |
| 18 | 18 | 0 | 0 | 0 | 0 |
| 3 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 19 | 1 |
| 0 | 0 | 4 | 11 | 19 | 9 |
| 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 7 | 22 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 24 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 3 | 0 | 0 |
| 0 | 0 | 7 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 26 |
| 0 | 0 | 0 | 0 | 5 | 4 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,23,9,15,0,0,0,20,6,15,10,0,0,5,0,26,23,0,0,7,22,9,3],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,13,24,0,0,0,0,5,16,0,0,0,0,0,0,8,16,0,0,0,0,5,21],[18,3,0,0,0,0,18,11,0,0,0,0,0,0,25,4,0,0,0,0,25,11,0,0,0,0,19,19,0,7,0,0,1,9,4,22],[17,24,0,0,0,0,0,12,0,0,0,0,0,0,26,7,0,0,0,0,3,3,0,0,0,0,0,0,25,5,0,0,0,0,26,4] >;
C42.116D14 in GAP, Magma, Sage, TeX
C_4^2._{116}D_{14} % in TeX
G:=Group("C4^2.116D14"); // GroupNames label
G:=SmallGroup(448,1015);
// by ID
G=gap.SmallGroup(448,1015);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations