metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.236D14, (C2×C28).450D4, C42⋊C2⋊3D7, C14.D8⋊28C2, C14.86(C4○D8), C4.91(C4○D28), C28⋊7D4.11C2, C28.Q8⋊29C2, C28.55D4⋊6C2, C4.Dic14⋊29C2, (C22×C14).76D4, C28.179(C4○D4), C2.6(D4⋊D14), (C2×C28).330C23, (C2×D28).92C22, (C22×C4).111D14, C7⋊6(C23.19D4), C23.20(C7⋊D4), C14.106(C8⋊C22), C2.9(D4.8D14), C4⋊Dic7.135C22, (C22×C28).152C22, C14.66(C22.D4), C2.17(C23.23D14), (C2×C7⋊C8).87C22, (C7×C42⋊C2)⋊3C2, (C2×C14).459(C2×D4), (C2×C4).215(C7⋊D4), (C7×C4⋊C4).267C22, (C2×C4).430(C22×D7), C22.145(C2×C7⋊D4), SmallGroup(448,537)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.236D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=b2, bab-1=dad-1=a-1, ac=ca, bc=cb, dbd-1=ab, dcd-1=a2b2c13 >
Subgroups: 564 in 106 conjugacy classes, 39 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, C4.Q8, C2.D8, C42⋊C2, C4⋊D4, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.19D4, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, C28.Q8, C4.Dic14, C14.D8, C28.55D4, C28⋊7D4, C7×C42⋊C2, C4⋊C4.236D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C22.D4, C4○D8, C8⋊C22, C7⋊D4, C22×D7, C23.19D4, C4○D28, C2×C7⋊D4, C23.23D14, D4⋊D14, D4.8D14, C4⋊C4.236D14
►On 224 points
Generators in S224
(1 133 15 119)(2 134 16 120)(3 135 17 121)(4 136 18 122)(5 137 19 123)(6 138 20 124)(7 139 21 125)(8 140 22 126)(9 113 23 127)(10 114 24 128)(11 115 25 129)(12 116 26 130)(13 117 27 131)(14 118 28 132)(29 50 43 36)(30 51 44 37)(31 52 45 38)(32 53 46 39)(33 54 47 40)(34 55 48 41)(35 56 49 42)(57 159 71 145)(58 160 72 146)(59 161 73 147)(60 162 74 148)(61 163 75 149)(62 164 76 150)(63 165 77 151)(64 166 78 152)(65 167 79 153)(66 168 80 154)(67 141 81 155)(68 142 82 156)(69 143 83 157)(70 144 84 158)(85 106 99 92)(86 107 100 93)(87 108 101 94)(88 109 102 95)(89 110 103 96)(90 111 104 97)(91 112 105 98)(169 176 183 190)(170 177 184 191)(171 178 185 192)(172 179 186 193)(173 180 187 194)(174 181 188 195)(175 182 189 196)(197 204 211 218)(198 205 212 219)(199 206 213 220)(200 207 214 221)(201 208 215 222)(202 209 216 223)(203 210 217 224)
(1 142 126 61)(2 143 127 62)(3 144 128 63)(4 145 129 64)(5 146 130 65)(6 147 131 66)(7 148 132 67)(8 149 133 68)(9 150 134 69)(10 151 135 70)(11 152 136 71)(12 153 137 72)(13 154 138 73)(14 155 139 74)(15 156 140 75)(16 157 113 76)(17 158 114 77)(18 159 115 78)(19 160 116 79)(20 161 117 80)(21 162 118 81)(22 163 119 82)(23 164 120 83)(24 165 121 84)(25 166 122 57)(26 167 123 58)(27 168 124 59)(28 141 125 60)(29 177 102 221)(30 178 103 222)(31 179 104 223)(32 180 105 224)(33 181 106 197)(34 182 107 198)(35 183 108 199)(36 184 109 200)(37 185 110 201)(38 186 111 202)(39 187 112 203)(40 188 85 204)(41 189 86 205)(42 190 87 206)(43 191 88 207)(44 192 89 208)(45 193 90 209)(46 194 91 210)(47 195 92 211)(48 196 93 212)(49 169 94 213)(50 170 95 214)(51 171 96 215)(52 172 97 216)(53 173 98 217)(54 174 99 218)(55 175 100 219)(56 176 101 220)
(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)
(1 208 126 192)(2 191 127 207)(3 206 128 190)(4 189 129 205)(5 204 130 188)(6 187 131 203)(7 202 132 186)(8 185 133 201)(9 200 134 184)(10 183 135 199)(11 198 136 182)(12 181 137 197)(13 224 138 180)(14 179 139 223)(15 222 140 178)(16 177 113 221)(17 220 114 176)(18 175 115 219)(19 218 116 174)(20 173 117 217)(21 216 118 172)(22 171 119 215)(23 214 120 170)(24 169 121 213)(25 212 122 196)(26 195 123 211)(27 210 124 194)(28 193 125 209)(29 83 102 164)(30 163 103 82)(31 81 104 162)(32 161 105 80)(33 79 106 160)(34 159 107 78)(35 77 108 158)(36 157 109 76)(37 75 110 156)(38 155 111 74)(39 73 112 154)(40 153 85 72)(41 71 86 152)(42 151 87 70)(43 69 88 150)(44 149 89 68)(45 67 90 148)(46 147 91 66)(47 65 92 146)(48 145 93 64)(49 63 94 144)(50 143 95 62)(51 61 96 142)(52 141 97 60)(53 59 98 168)(54 167 99 58)(55 57 100 166)(56 165 101 84)
G:=sub<Sym(224)| (1,133,15,119)(2,134,16,120)(3,135,17,121)(4,136,18,122)(5,137,19,123)(6,138,20,124)(7,139,21,125)(8,140,22,126)(9,113,23,127)(10,114,24,128)(11,115,25,129)(12,116,26,130)(13,117,27,131)(14,118,28,132)(29,50,43,36)(30,51,44,37)(31,52,45,38)(32,53,46,39)(33,54,47,40)(34,55,48,41)(35,56,49,42)(57,159,71,145)(58,160,72,146)(59,161,73,147)(60,162,74,148)(61,163,75,149)(62,164,76,150)(63,165,77,151)(64,166,78,152)(65,167,79,153)(66,168,80,154)(67,141,81,155)(68,142,82,156)(69,143,83,157)(70,144,84,158)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(169,176,183,190)(170,177,184,191)(171,178,185,192)(172,179,186,193)(173,180,187,194)(174,181,188,195)(175,182,189,196)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,142,126,61)(2,143,127,62)(3,144,128,63)(4,145,129,64)(5,146,130,65)(6,147,131,66)(7,148,132,67)(8,149,133,68)(9,150,134,69)(10,151,135,70)(11,152,136,71)(12,153,137,72)(13,154,138,73)(14,155,139,74)(15,156,140,75)(16,157,113,76)(17,158,114,77)(18,159,115,78)(19,160,116,79)(20,161,117,80)(21,162,118,81)(22,163,119,82)(23,164,120,83)(24,165,121,84)(25,166,122,57)(26,167,123,58)(27,168,124,59)(28,141,125,60)(29,177,102,221)(30,178,103,222)(31,179,104,223)(32,180,105,224)(33,181,106,197)(34,182,107,198)(35,183,108,199)(36,184,109,200)(37,185,110,201)(38,186,111,202)(39,187,112,203)(40,188,85,204)(41,189,86,205)(42,190,87,206)(43,191,88,207)(44,192,89,208)(45,193,90,209)(46,194,91,210)(47,195,92,211)(48,196,93,212)(49,169,94,213)(50,170,95,214)(51,171,96,215)(52,172,97,216)(53,173,98,217)(54,174,99,218)(55,175,100,219)(56,176,101,220), (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), (1,208,126,192)(2,191,127,207)(3,206,128,190)(4,189,129,205)(5,204,130,188)(6,187,131,203)(7,202,132,186)(8,185,133,201)(9,200,134,184)(10,183,135,199)(11,198,136,182)(12,181,137,197)(13,224,138,180)(14,179,139,223)(15,222,140,178)(16,177,113,221)(17,220,114,176)(18,175,115,219)(19,218,116,174)(20,173,117,217)(21,216,118,172)(22,171,119,215)(23,214,120,170)(24,169,121,213)(25,212,122,196)(26,195,123,211)(27,210,124,194)(28,193,125,209)(29,83,102,164)(30,163,103,82)(31,81,104,162)(32,161,105,80)(33,79,106,160)(34,159,107,78)(35,77,108,158)(36,157,109,76)(37,75,110,156)(38,155,111,74)(39,73,112,154)(40,153,85,72)(41,71,86,152)(42,151,87,70)(43,69,88,150)(44,149,89,68)(45,67,90,148)(46,147,91,66)(47,65,92,146)(48,145,93,64)(49,63,94,144)(50,143,95,62)(51,61,96,142)(52,141,97,60)(53,59,98,168)(54,167,99,58)(55,57,100,166)(56,165,101,84)>;
G:=Group( (1,133,15,119)(2,134,16,120)(3,135,17,121)(4,136,18,122)(5,137,19,123)(6,138,20,124)(7,139,21,125)(8,140,22,126)(9,113,23,127)(10,114,24,128)(11,115,25,129)(12,116,26,130)(13,117,27,131)(14,118,28,132)(29,50,43,36)(30,51,44,37)(31,52,45,38)(32,53,46,39)(33,54,47,40)(34,55,48,41)(35,56,49,42)(57,159,71,145)(58,160,72,146)(59,161,73,147)(60,162,74,148)(61,163,75,149)(62,164,76,150)(63,165,77,151)(64,166,78,152)(65,167,79,153)(66,168,80,154)(67,141,81,155)(68,142,82,156)(69,143,83,157)(70,144,84,158)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(169,176,183,190)(170,177,184,191)(171,178,185,192)(172,179,186,193)(173,180,187,194)(174,181,188,195)(175,182,189,196)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,142,126,61)(2,143,127,62)(3,144,128,63)(4,145,129,64)(5,146,130,65)(6,147,131,66)(7,148,132,67)(8,149,133,68)(9,150,134,69)(10,151,135,70)(11,152,136,71)(12,153,137,72)(13,154,138,73)(14,155,139,74)(15,156,140,75)(16,157,113,76)(17,158,114,77)(18,159,115,78)(19,160,116,79)(20,161,117,80)(21,162,118,81)(22,163,119,82)(23,164,120,83)(24,165,121,84)(25,166,122,57)(26,167,123,58)(27,168,124,59)(28,141,125,60)(29,177,102,221)(30,178,103,222)(31,179,104,223)(32,180,105,224)(33,181,106,197)(34,182,107,198)(35,183,108,199)(36,184,109,200)(37,185,110,201)(38,186,111,202)(39,187,112,203)(40,188,85,204)(41,189,86,205)(42,190,87,206)(43,191,88,207)(44,192,89,208)(45,193,90,209)(46,194,91,210)(47,195,92,211)(48,196,93,212)(49,169,94,213)(50,170,95,214)(51,171,96,215)(52,172,97,216)(53,173,98,217)(54,174,99,218)(55,175,100,219)(56,176,101,220), (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), (1,208,126,192)(2,191,127,207)(3,206,128,190)(4,189,129,205)(5,204,130,188)(6,187,131,203)(7,202,132,186)(8,185,133,201)(9,200,134,184)(10,183,135,199)(11,198,136,182)(12,181,137,197)(13,224,138,180)(14,179,139,223)(15,222,140,178)(16,177,113,221)(17,220,114,176)(18,175,115,219)(19,218,116,174)(20,173,117,217)(21,216,118,172)(22,171,119,215)(23,214,120,170)(24,169,121,213)(25,212,122,196)(26,195,123,211)(27,210,124,194)(28,193,125,209)(29,83,102,164)(30,163,103,82)(31,81,104,162)(32,161,105,80)(33,79,106,160)(34,159,107,78)(35,77,108,158)(36,157,109,76)(37,75,110,156)(38,155,111,74)(39,73,112,154)(40,153,85,72)(41,71,86,152)(42,151,87,70)(43,69,88,150)(44,149,89,68)(45,67,90,148)(46,147,91,66)(47,65,92,146)(48,145,93,64)(49,63,94,144)(50,143,95,62)(51,61,96,142)(52,141,97,60)(53,59,98,168)(54,167,99,58)(55,57,100,166)(56,165,101,84) );
G=PermutationGroup([[(1,133,15,119),(2,134,16,120),(3,135,17,121),(4,136,18,122),(5,137,19,123),(6,138,20,124),(7,139,21,125),(8,140,22,126),(9,113,23,127),(10,114,24,128),(11,115,25,129),(12,116,26,130),(13,117,27,131),(14,118,28,132),(29,50,43,36),(30,51,44,37),(31,52,45,38),(32,53,46,39),(33,54,47,40),(34,55,48,41),(35,56,49,42),(57,159,71,145),(58,160,72,146),(59,161,73,147),(60,162,74,148),(61,163,75,149),(62,164,76,150),(63,165,77,151),(64,166,78,152),(65,167,79,153),(66,168,80,154),(67,141,81,155),(68,142,82,156),(69,143,83,157),(70,144,84,158),(85,106,99,92),(86,107,100,93),(87,108,101,94),(88,109,102,95),(89,110,103,96),(90,111,104,97),(91,112,105,98),(169,176,183,190),(170,177,184,191),(171,178,185,192),(172,179,186,193),(173,180,187,194),(174,181,188,195),(175,182,189,196),(197,204,211,218),(198,205,212,219),(199,206,213,220),(200,207,214,221),(201,208,215,222),(202,209,216,223),(203,210,217,224)], [(1,142,126,61),(2,143,127,62),(3,144,128,63),(4,145,129,64),(5,146,130,65),(6,147,131,66),(7,148,132,67),(8,149,133,68),(9,150,134,69),(10,151,135,70),(11,152,136,71),(12,153,137,72),(13,154,138,73),(14,155,139,74),(15,156,140,75),(16,157,113,76),(17,158,114,77),(18,159,115,78),(19,160,116,79),(20,161,117,80),(21,162,118,81),(22,163,119,82),(23,164,120,83),(24,165,121,84),(25,166,122,57),(26,167,123,58),(27,168,124,59),(28,141,125,60),(29,177,102,221),(30,178,103,222),(31,179,104,223),(32,180,105,224),(33,181,106,197),(34,182,107,198),(35,183,108,199),(36,184,109,200),(37,185,110,201),(38,186,111,202),(39,187,112,203),(40,188,85,204),(41,189,86,205),(42,190,87,206),(43,191,88,207),(44,192,89,208),(45,193,90,209),(46,194,91,210),(47,195,92,211),(48,196,93,212),(49,169,94,213),(50,170,95,214),(51,171,96,215),(52,172,97,216),(53,173,98,217),(54,174,99,218),(55,175,100,219),(56,176,101,220)], [(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)], [(1,208,126,192),(2,191,127,207),(3,206,128,190),(4,189,129,205),(5,204,130,188),(6,187,131,203),(7,202,132,186),(8,185,133,201),(9,200,134,184),(10,183,135,199),(11,198,136,182),(12,181,137,197),(13,224,138,180),(14,179,139,223),(15,222,140,178),(16,177,113,221),(17,220,114,176),(18,175,115,219),(19,218,116,174),(20,173,117,217),(21,216,118,172),(22,171,119,215),(23,214,120,170),(24,169,121,213),(25,212,122,196),(26,195,123,211),(27,210,124,194),(28,193,125,209),(29,83,102,164),(30,163,103,82),(31,81,104,162),(32,161,105,80),(33,79,106,160),(34,159,107,78),(35,77,108,158),(36,157,109,76),(37,75,110,156),(38,155,111,74),(39,73,112,154),(40,153,85,72),(41,71,86,152),(42,151,87,70),(43,69,88,150),(44,149,89,68),(45,67,90,148),(46,147,91,66),(47,65,92,146),(48,145,93,64),(49,63,94,144),(50,143,95,62),(51,61,96,142),(52,141,97,60),(53,59,98,168),(54,167,99,58),(55,57,100,166),(56,165,101,84)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 56 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | C7⋊D4 | C7⋊D4 | C4○D28 | C8⋊C22 | D4⋊D14 | D4.8D14 |
| kernel | C4⋊C4.236D14 | C28.Q8 | C4.Dic14 | C14.D8 | C28.55D4 | C28⋊7D4 | C7×C42⋊C2 | C2×C28 | C22×C14 | C42⋊C2 | C28 | C4⋊C4 | C22×C4 | C14 | C2×C4 | C23 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 6 | 3 | 4 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of C4⋊C4.236D14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 21 | 15 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 1 | 66 |
| 0 | 0 | 89 | 112 |
| 85 | 0 | 0 | 0 |
| 0 | 109 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 0 | 4 | 0 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 0 | 44 | 79 |
| 0 | 0 | 47 | 69 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,98,21,0,0,0,15],[15,0,0,0,0,15,0,0,0,0,1,89,0,0,66,112],[85,0,0,0,0,109,0,0,0,0,98,0,0,0,0,98],[0,28,0,0,4,0,0,0,0,0,44,47,0,0,79,69] >;
C4⋊C4.236D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{236}D_{14} % in TeX
G:=Group("C4:C4.236D14"); // GroupNames label
G:=SmallGroup(448,537);
// by ID
G=gap.SmallGroup(448,537);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,254,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,b*c=c*b,d*b*d^-1=a*b,d*c*d^-1=a^2*b^2*c^13>;
// generators/relations