metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.136D14, C14.1132+ 1+4, (C4×Q8)⋊18D7, (C4×D28)⋊42C2, (Q8×C28)⋊20C2, C4⋊C4.303D14, D28⋊C4⋊18C2, (C4×Dic14)⋊42C2, C4.19(C4○D28), C28⋊4D4.10C2, C4.D28⋊21C2, (C2×Q8).184D14, D14.5D4⋊10C2, C28.123(C4○D4), C28.23D4⋊10C2, (C2×C14).129C24, (C2×C28).592C23, (C4×C28).181C22, C4.51(Q8⋊2D7), (C2×D28).29C22, C2.25(D4⋊8D14), D14⋊C4.145C22, C4⋊Dic7.401C22, (Q8×C14).229C22, (C4×Dic7).88C22, (C2×Dic7).59C23, (C22×D7).51C23, C22.150(C23×D7), Dic7⋊C4.116C22, C7⋊2(C22.53C24), (C2×Dic14).244C22, C14.58(C2×C4○D4), C2.68(C2×C4○D28), C2.14(C2×Q8⋊2D7), (C2×C4×D7).207C22, (C7×C4⋊C4).357C22, (C2×C4).291(C22×D7), SmallGroup(448,1038)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.136D14
G = < a,b,c,d | a4=b4=d2=1, c14=a2, ab=ba, cac-1=dad=a-1b2, bc=cb, dbd=b-1, dcd=a2c13 >
Subgroups: 1220 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, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C4×D4, C4×Q8, C4×Q8, C22.D4, C4.4D4, C4⋊1D4, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.53C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C4×Dic14, C4×D28, C28⋊4D4, C4.D28, D28⋊C4, D14.5D4, C28.23D4, Q8×C28, C42.136D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.53C24, C4○D28, Q8⋊2D7, C23×D7, C2×C4○D28, C2×Q8⋊2D7, D4⋊8D14, C42.136D14
►On 224 points
Generators in S224
(1 147 15 161)(2 38 16 52)(3 149 17 163)(4 40 18 54)(5 151 19 165)(6 42 20 56)(7 153 21 167)(8 44 22 30)(9 155 23 141)(10 46 24 32)(11 157 25 143)(12 48 26 34)(13 159 27 145)(14 50 28 36)(29 171 43 185)(31 173 45 187)(33 175 47 189)(35 177 49 191)(37 179 51 193)(39 181 53 195)(41 183 55 169)(57 132 71 118)(58 223 72 209)(59 134 73 120)(60 197 74 211)(61 136 75 122)(62 199 76 213)(63 138 77 124)(64 201 78 215)(65 140 79 126)(66 203 80 217)(67 114 81 128)(68 205 82 219)(69 116 83 130)(70 207 84 221)(85 198 99 212)(86 137 100 123)(87 200 101 214)(88 139 102 125)(89 202 103 216)(90 113 104 127)(91 204 105 218)(92 115 106 129)(93 206 107 220)(94 117 108 131)(95 208 109 222)(96 119 110 133)(97 210 111 224)(98 121 112 135)(142 174 156 188)(144 176 158 190)(146 178 160 192)(148 180 162 194)(150 182 164 196)(152 184 166 170)(154 186 168 172)
(1 105 179 67)(2 106 180 68)(3 107 181 69)(4 108 182 70)(5 109 183 71)(6 110 184 72)(7 111 185 73)(8 112 186 74)(9 85 187 75)(10 86 188 76)(11 87 189 77)(12 88 190 78)(13 89 191 79)(14 90 192 80)(15 91 193 81)(16 92 194 82)(17 93 195 83)(18 94 196 84)(19 95 169 57)(20 96 170 58)(21 97 171 59)(22 98 172 60)(23 99 173 61)(24 100 174 62)(25 101 175 63)(26 102 176 64)(27 103 177 65)(28 104 178 66)(29 120 153 224)(30 121 154 197)(31 122 155 198)(32 123 156 199)(33 124 157 200)(34 125 158 201)(35 126 159 202)(36 127 160 203)(37 128 161 204)(38 129 162 205)(39 130 163 206)(40 131 164 207)(41 132 165 208)(42 133 166 209)(43 134 167 210)(44 135 168 211)(45 136 141 212)(46 137 142 213)(47 138 143 214)(48 139 144 215)(49 140 145 216)(50 113 146 217)(51 114 147 218)(52 115 148 219)(53 116 149 220)(54 117 150 221)(55 118 151 222)(56 119 152 223)
(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 59)(2 58)(3 57)(4 84)(5 83)(6 82)(7 81)(8 80)(9 79)(10 78)(11 77)(12 76)(13 75)(14 74)(15 73)(16 72)(17 71)(18 70)(19 69)(20 68)(21 67)(22 66)(23 65)(24 64)(25 63)(26 62)(27 61)(28 60)(29 114)(30 113)(31 140)(32 139)(33 138)(34 137)(35 136)(36 135)(37 134)(38 133)(39 132)(40 131)(41 130)(42 129)(43 128)(44 127)(45 126)(46 125)(47 124)(48 123)(49 122)(50 121)(51 120)(52 119)(53 118)(54 117)(55 116)(56 115)(85 191)(86 190)(87 189)(88 188)(89 187)(90 186)(91 185)(92 184)(93 183)(94 182)(95 181)(96 180)(97 179)(98 178)(99 177)(100 176)(101 175)(102 174)(103 173)(104 172)(105 171)(106 170)(107 169)(108 196)(109 195)(110 194)(111 193)(112 192)(141 202)(142 201)(143 200)(144 199)(145 198)(146 197)(147 224)(148 223)(149 222)(150 221)(151 220)(152 219)(153 218)(154 217)(155 216)(156 215)(157 214)(158 213)(159 212)(160 211)(161 210)(162 209)(163 208)(164 207)(165 206)(166 205)(167 204)(168 203)
G:=sub<Sym(224)| (1,147,15,161)(2,38,16,52)(3,149,17,163)(4,40,18,54)(5,151,19,165)(6,42,20,56)(7,153,21,167)(8,44,22,30)(9,155,23,141)(10,46,24,32)(11,157,25,143)(12,48,26,34)(13,159,27,145)(14,50,28,36)(29,171,43,185)(31,173,45,187)(33,175,47,189)(35,177,49,191)(37,179,51,193)(39,181,53,195)(41,183,55,169)(57,132,71,118)(58,223,72,209)(59,134,73,120)(60,197,74,211)(61,136,75,122)(62,199,76,213)(63,138,77,124)(64,201,78,215)(65,140,79,126)(66,203,80,217)(67,114,81,128)(68,205,82,219)(69,116,83,130)(70,207,84,221)(85,198,99,212)(86,137,100,123)(87,200,101,214)(88,139,102,125)(89,202,103,216)(90,113,104,127)(91,204,105,218)(92,115,106,129)(93,206,107,220)(94,117,108,131)(95,208,109,222)(96,119,110,133)(97,210,111,224)(98,121,112,135)(142,174,156,188)(144,176,158,190)(146,178,160,192)(148,180,162,194)(150,182,164,196)(152,184,166,170)(154,186,168,172), (1,105,179,67)(2,106,180,68)(3,107,181,69)(4,108,182,70)(5,109,183,71)(6,110,184,72)(7,111,185,73)(8,112,186,74)(9,85,187,75)(10,86,188,76)(11,87,189,77)(12,88,190,78)(13,89,191,79)(14,90,192,80)(15,91,193,81)(16,92,194,82)(17,93,195,83)(18,94,196,84)(19,95,169,57)(20,96,170,58)(21,97,171,59)(22,98,172,60)(23,99,173,61)(24,100,174,62)(25,101,175,63)(26,102,176,64)(27,103,177,65)(28,104,178,66)(29,120,153,224)(30,121,154,197)(31,122,155,198)(32,123,156,199)(33,124,157,200)(34,125,158,201)(35,126,159,202)(36,127,160,203)(37,128,161,204)(38,129,162,205)(39,130,163,206)(40,131,164,207)(41,132,165,208)(42,133,166,209)(43,134,167,210)(44,135,168,211)(45,136,141,212)(46,137,142,213)(47,138,143,214)(48,139,144,215)(49,140,145,216)(50,113,146,217)(51,114,147,218)(52,115,148,219)(53,116,149,220)(54,117,150,221)(55,118,151,222)(56,119,152,223), (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), (1,59)(2,58)(3,57)(4,84)(5,83)(6,82)(7,81)(8,80)(9,79)(10,78)(11,77)(12,76)(13,75)(14,74)(15,73)(16,72)(17,71)(18,70)(19,69)(20,68)(21,67)(22,66)(23,65)(24,64)(25,63)(26,62)(27,61)(28,60)(29,114)(30,113)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(85,191)(86,190)(87,189)(88,188)(89,187)(90,186)(91,185)(92,184)(93,183)(94,182)(95,181)(96,180)(97,179)(98,178)(99,177)(100,176)(101,175)(102,174)(103,173)(104,172)(105,171)(106,170)(107,169)(108,196)(109,195)(110,194)(111,193)(112,192)(141,202)(142,201)(143,200)(144,199)(145,198)(146,197)(147,224)(148,223)(149,222)(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)(158,213)(159,212)(160,211)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)>;
G:=Group( (1,147,15,161)(2,38,16,52)(3,149,17,163)(4,40,18,54)(5,151,19,165)(6,42,20,56)(7,153,21,167)(8,44,22,30)(9,155,23,141)(10,46,24,32)(11,157,25,143)(12,48,26,34)(13,159,27,145)(14,50,28,36)(29,171,43,185)(31,173,45,187)(33,175,47,189)(35,177,49,191)(37,179,51,193)(39,181,53,195)(41,183,55,169)(57,132,71,118)(58,223,72,209)(59,134,73,120)(60,197,74,211)(61,136,75,122)(62,199,76,213)(63,138,77,124)(64,201,78,215)(65,140,79,126)(66,203,80,217)(67,114,81,128)(68,205,82,219)(69,116,83,130)(70,207,84,221)(85,198,99,212)(86,137,100,123)(87,200,101,214)(88,139,102,125)(89,202,103,216)(90,113,104,127)(91,204,105,218)(92,115,106,129)(93,206,107,220)(94,117,108,131)(95,208,109,222)(96,119,110,133)(97,210,111,224)(98,121,112,135)(142,174,156,188)(144,176,158,190)(146,178,160,192)(148,180,162,194)(150,182,164,196)(152,184,166,170)(154,186,168,172), (1,105,179,67)(2,106,180,68)(3,107,181,69)(4,108,182,70)(5,109,183,71)(6,110,184,72)(7,111,185,73)(8,112,186,74)(9,85,187,75)(10,86,188,76)(11,87,189,77)(12,88,190,78)(13,89,191,79)(14,90,192,80)(15,91,193,81)(16,92,194,82)(17,93,195,83)(18,94,196,84)(19,95,169,57)(20,96,170,58)(21,97,171,59)(22,98,172,60)(23,99,173,61)(24,100,174,62)(25,101,175,63)(26,102,176,64)(27,103,177,65)(28,104,178,66)(29,120,153,224)(30,121,154,197)(31,122,155,198)(32,123,156,199)(33,124,157,200)(34,125,158,201)(35,126,159,202)(36,127,160,203)(37,128,161,204)(38,129,162,205)(39,130,163,206)(40,131,164,207)(41,132,165,208)(42,133,166,209)(43,134,167,210)(44,135,168,211)(45,136,141,212)(46,137,142,213)(47,138,143,214)(48,139,144,215)(49,140,145,216)(50,113,146,217)(51,114,147,218)(52,115,148,219)(53,116,149,220)(54,117,150,221)(55,118,151,222)(56,119,152,223), (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), (1,59)(2,58)(3,57)(4,84)(5,83)(6,82)(7,81)(8,80)(9,79)(10,78)(11,77)(12,76)(13,75)(14,74)(15,73)(16,72)(17,71)(18,70)(19,69)(20,68)(21,67)(22,66)(23,65)(24,64)(25,63)(26,62)(27,61)(28,60)(29,114)(30,113)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(85,191)(86,190)(87,189)(88,188)(89,187)(90,186)(91,185)(92,184)(93,183)(94,182)(95,181)(96,180)(97,179)(98,178)(99,177)(100,176)(101,175)(102,174)(103,173)(104,172)(105,171)(106,170)(107,169)(108,196)(109,195)(110,194)(111,193)(112,192)(141,202)(142,201)(143,200)(144,199)(145,198)(146,197)(147,224)(148,223)(149,222)(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)(158,213)(159,212)(160,211)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203) );
G=PermutationGroup([[(1,147,15,161),(2,38,16,52),(3,149,17,163),(4,40,18,54),(5,151,19,165),(6,42,20,56),(7,153,21,167),(8,44,22,30),(9,155,23,141),(10,46,24,32),(11,157,25,143),(12,48,26,34),(13,159,27,145),(14,50,28,36),(29,171,43,185),(31,173,45,187),(33,175,47,189),(35,177,49,191),(37,179,51,193),(39,181,53,195),(41,183,55,169),(57,132,71,118),(58,223,72,209),(59,134,73,120),(60,197,74,211),(61,136,75,122),(62,199,76,213),(63,138,77,124),(64,201,78,215),(65,140,79,126),(66,203,80,217),(67,114,81,128),(68,205,82,219),(69,116,83,130),(70,207,84,221),(85,198,99,212),(86,137,100,123),(87,200,101,214),(88,139,102,125),(89,202,103,216),(90,113,104,127),(91,204,105,218),(92,115,106,129),(93,206,107,220),(94,117,108,131),(95,208,109,222),(96,119,110,133),(97,210,111,224),(98,121,112,135),(142,174,156,188),(144,176,158,190),(146,178,160,192),(148,180,162,194),(150,182,164,196),(152,184,166,170),(154,186,168,172)], [(1,105,179,67),(2,106,180,68),(3,107,181,69),(4,108,182,70),(5,109,183,71),(6,110,184,72),(7,111,185,73),(8,112,186,74),(9,85,187,75),(10,86,188,76),(11,87,189,77),(12,88,190,78),(13,89,191,79),(14,90,192,80),(15,91,193,81),(16,92,194,82),(17,93,195,83),(18,94,196,84),(19,95,169,57),(20,96,170,58),(21,97,171,59),(22,98,172,60),(23,99,173,61),(24,100,174,62),(25,101,175,63),(26,102,176,64),(27,103,177,65),(28,104,178,66),(29,120,153,224),(30,121,154,197),(31,122,155,198),(32,123,156,199),(33,124,157,200),(34,125,158,201),(35,126,159,202),(36,127,160,203),(37,128,161,204),(38,129,162,205),(39,130,163,206),(40,131,164,207),(41,132,165,208),(42,133,166,209),(43,134,167,210),(44,135,168,211),(45,136,141,212),(46,137,142,213),(47,138,143,214),(48,139,144,215),(49,140,145,216),(50,113,146,217),(51,114,147,218),(52,115,148,219),(53,116,149,220),(54,117,150,221),(55,118,151,222),(56,119,152,223)], [(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)], [(1,59),(2,58),(3,57),(4,84),(5,83),(6,82),(7,81),(8,80),(9,79),(10,78),(11,77),(12,76),(13,75),(14,74),(15,73),(16,72),(17,71),(18,70),(19,69),(20,68),(21,67),(22,66),(23,65),(24,64),(25,63),(26,62),(27,61),(28,60),(29,114),(30,113),(31,140),(32,139),(33,138),(34,137),(35,136),(36,135),(37,134),(38,133),(39,132),(40,131),(41,130),(42,129),(43,128),(44,127),(45,126),(46,125),(47,124),(48,123),(49,122),(50,121),(51,120),(52,119),(53,118),(54,117),(55,116),(56,115),(85,191),(86,190),(87,189),(88,188),(89,187),(90,186),(91,185),(92,184),(93,183),(94,182),(95,181),(96,180),(97,179),(98,178),(99,177),(100,176),(101,175),(102,174),(103,173),(104,172),(105,171),(106,170),(107,169),(108,196),(109,195),(110,194),(111,193),(112,192),(141,202),(142,201),(143,200),(144,199),(145,198),(146,197),(147,224),(148,223),(149,222),(150,221),(151,220),(152,219),(153,218),(154,217),(155,216),(156,215),(157,214),(158,213),(159,212),(160,211),(161,210),(162,209),(163,208),(164,207),(165,206),(166,205),(167,204),(168,203)]])
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 | 28A | ··· | 28L | 28M | ··· | 28AV |
| 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 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | C4○D28 | 2+ 1+4 | Q8⋊2D7 | D4⋊8D14 |
| kernel | C42.136D14 | C4×Dic14 | C4×D28 | C28⋊4D4 | C4.D28 | D28⋊C4 | D14.5D4 | C28.23D4 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 8 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.136D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 24 | 0 | 0 | 0 | 0 |
| 12 | 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 | 28 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 24 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 3 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,2,17],[1,12,0,0,0,0,24,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,17,0,0,0,0,5,1,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,28,12,0,0,0,0,24,1],[28,0,0,0,0,0,5,1,0,0,0,0,0,0,8,3,0,0,0,0,8,21,0,0,0,0,0,0,28,12,0,0,0,0,0,1] >;
C42.136D14 in GAP, Magma, Sage, TeX
C_4^2._{136}D_{14} % in TeX
G:=Group("C4^2.136D14"); // GroupNames label
G:=SmallGroup(448,1038);
// by ID
G=gap.SmallGroup(448,1038);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,184,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=a^2,a*b=b*a,c*a*c^-1=d*a*d=a^-1*b^2,b*c=c*b,d*b*d=b^-1,d*c*d=a^2*c^13>;
// generators/relations