metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.233D14, (C2×C28).449D4, C4.90(C4○D28), C14.83(C4○D8), C28.Q8⋊28C2, C14.Q16⋊27C2, C4.Dic14⋊28C2, (C22×C14).72D4, C42⋊C2.5D7, C28.178(C4○D4), (C2×C28).326C23, C28.55D4.5C2, (C22×C4).108D14, C7⋊6(C23.20D4), C23.19(C7⋊D4), C28.48D4.11C2, C2.8(D4.8D14), C2.6(D4.9D14), C4⋊Dic7.134C22, C14.105(C8.C22), (C22×C28).146C22, (C2×Dic14).98C22, C14.65(C22.D4), C2.16(C23.23D14), (C2×C7⋊C8).86C22, (C2×C14).455(C2×D4), (C2×C4).214(C7⋊D4), (C7×C4⋊C4).264C22, (C7×C42⋊C2).5C2, (C2×C4).426(C22×D7), C22.144(C2×C7⋊D4), SmallGroup(448,530)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.233D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, bab-1=dad-1=a-1, ac=ca, bc=cb, dbd-1=ab, dcd-1=a2b2c13 >
Subgroups: 372 in 96 conjugacy classes, 39 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C22⋊C8, Q8⋊C4, C4.Q8, C2.D8, C42⋊C2, C22⋊Q8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.20D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, C28.Q8, C4.Dic14, C14.Q16, C28.55D4, C28.48D4, C7×C42⋊C2, C4⋊C4.233D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C22.D4, C4○D8, C8.C22, C7⋊D4, C22×D7, C23.20D4, C4○D28, C2×C7⋊D4, C23.23D14, D4.8D14, D4.9D14, C4⋊C4.233D14
►On 224 points
Generators in S224
(1 46 15 32)(2 47 16 33)(3 48 17 34)(4 49 18 35)(5 50 19 36)(6 51 20 37)(7 52 21 38)(8 53 22 39)(9 54 23 40)(10 55 24 41)(11 56 25 42)(12 29 26 43)(13 30 27 44)(14 31 28 45)(57 138 71 124)(58 139 72 125)(59 140 73 126)(60 113 74 127)(61 114 75 128)(62 115 76 129)(63 116 77 130)(64 117 78 131)(65 118 79 132)(66 119 80 133)(67 120 81 134)(68 121 82 135)(69 122 83 136)(70 123 84 137)(85 92 99 106)(86 93 100 107)(87 94 101 108)(88 95 102 109)(89 96 103 110)(90 97 104 111)(91 98 105 112)(141 148 155 162)(142 149 156 163)(143 150 157 164)(144 151 158 165)(145 152 159 166)(146 153 160 167)(147 154 161 168)(169 190 183 176)(170 191 184 177)(171 192 185 178)(172 193 186 179)(173 194 187 180)(174 195 188 181)(175 196 189 182)(197 218 211 204)(198 219 212 205)(199 220 213 206)(200 221 214 207)(201 222 215 208)(202 223 216 209)(203 224 217 210)
(1 123 39 63)(2 124 40 64)(3 125 41 65)(4 126 42 66)(5 127 43 67)(6 128 44 68)(7 129 45 69)(8 130 46 70)(9 131 47 71)(10 132 48 72)(11 133 49 73)(12 134 50 74)(13 135 51 75)(14 136 52 76)(15 137 53 77)(16 138 54 78)(17 139 55 79)(18 140 56 80)(19 113 29 81)(20 114 30 82)(21 115 31 83)(22 116 32 84)(23 117 33 57)(24 118 34 58)(25 119 35 59)(26 120 36 60)(27 121 37 61)(28 122 38 62)(85 218 148 192)(86 219 149 193)(87 220 150 194)(88 221 151 195)(89 222 152 196)(90 223 153 169)(91 224 154 170)(92 197 155 171)(93 198 156 172)(94 199 157 173)(95 200 158 174)(96 201 159 175)(97 202 160 176)(98 203 161 177)(99 204 162 178)(100 205 163 179)(101 206 164 180)(102 207 165 181)(103 208 166 182)(104 209 167 183)(105 210 168 184)(106 211 141 185)(107 212 142 186)(108 213 143 187)(109 214 144 188)(110 215 145 189)(111 216 146 190)(112 217 147 191)
(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 98 15 112)(2 160 16 146)(3 96 17 110)(4 158 18 144)(5 94 19 108)(6 156 20 142)(7 92 21 106)(8 154 22 168)(9 90 23 104)(10 152 24 166)(11 88 25 102)(12 150 26 164)(13 86 27 100)(14 148 28 162)(29 143 43 157)(30 107 44 93)(31 141 45 155)(32 105 46 91)(33 167 47 153)(34 103 48 89)(35 165 49 151)(36 101 50 87)(37 163 51 149)(38 99 52 85)(39 161 53 147)(40 97 54 111)(41 159 55 145)(42 95 56 109)(57 190 71 176)(58 215 72 201)(59 188 73 174)(60 213 74 199)(61 186 75 172)(62 211 76 197)(63 184 77 170)(64 209 78 223)(65 182 79 196)(66 207 80 221)(67 180 81 194)(68 205 82 219)(69 178 83 192)(70 203 84 217)(113 220 127 206)(114 193 128 179)(115 218 129 204)(116 191 130 177)(117 216 131 202)(118 189 132 175)(119 214 133 200)(120 187 134 173)(121 212 135 198)(122 185 136 171)(123 210 137 224)(124 183 138 169)(125 208 139 222)(126 181 140 195)
G:=sub<Sym(224)| (1,46,15,32)(2,47,16,33)(3,48,17,34)(4,49,18,35)(5,50,19,36)(6,51,20,37)(7,52,21,38)(8,53,22,39)(9,54,23,40)(10,55,24,41)(11,56,25,42)(12,29,26,43)(13,30,27,44)(14,31,28,45)(57,138,71,124)(58,139,72,125)(59,140,73,126)(60,113,74,127)(61,114,75,128)(62,115,76,129)(63,116,77,130)(64,117,78,131)(65,118,79,132)(66,119,80,133)(67,120,81,134)(68,121,82,135)(69,122,83,136)(70,123,84,137)(85,92,99,106)(86,93,100,107)(87,94,101,108)(88,95,102,109)(89,96,103,110)(90,97,104,111)(91,98,105,112)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,218,211,204)(198,219,212,205)(199,220,213,206)(200,221,214,207)(201,222,215,208)(202,223,216,209)(203,224,217,210), (1,123,39,63)(2,124,40,64)(3,125,41,65)(4,126,42,66)(5,127,43,67)(6,128,44,68)(7,129,45,69)(8,130,46,70)(9,131,47,71)(10,132,48,72)(11,133,49,73)(12,134,50,74)(13,135,51,75)(14,136,52,76)(15,137,53,77)(16,138,54,78)(17,139,55,79)(18,140,56,80)(19,113,29,81)(20,114,30,82)(21,115,31,83)(22,116,32,84)(23,117,33,57)(24,118,34,58)(25,119,35,59)(26,120,36,60)(27,121,37,61)(28,122,38,62)(85,218,148,192)(86,219,149,193)(87,220,150,194)(88,221,151,195)(89,222,152,196)(90,223,153,169)(91,224,154,170)(92,197,155,171)(93,198,156,172)(94,199,157,173)(95,200,158,174)(96,201,159,175)(97,202,160,176)(98,203,161,177)(99,204,162,178)(100,205,163,179)(101,206,164,180)(102,207,165,181)(103,208,166,182)(104,209,167,183)(105,210,168,184)(106,211,141,185)(107,212,142,186)(108,213,143,187)(109,214,144,188)(110,215,145,189)(111,216,146,190)(112,217,147,191), (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), (1,98,15,112)(2,160,16,146)(3,96,17,110)(4,158,18,144)(5,94,19,108)(6,156,20,142)(7,92,21,106)(8,154,22,168)(9,90,23,104)(10,152,24,166)(11,88,25,102)(12,150,26,164)(13,86,27,100)(14,148,28,162)(29,143,43,157)(30,107,44,93)(31,141,45,155)(32,105,46,91)(33,167,47,153)(34,103,48,89)(35,165,49,151)(36,101,50,87)(37,163,51,149)(38,99,52,85)(39,161,53,147)(40,97,54,111)(41,159,55,145)(42,95,56,109)(57,190,71,176)(58,215,72,201)(59,188,73,174)(60,213,74,199)(61,186,75,172)(62,211,76,197)(63,184,77,170)(64,209,78,223)(65,182,79,196)(66,207,80,221)(67,180,81,194)(68,205,82,219)(69,178,83,192)(70,203,84,217)(113,220,127,206)(114,193,128,179)(115,218,129,204)(116,191,130,177)(117,216,131,202)(118,189,132,175)(119,214,133,200)(120,187,134,173)(121,212,135,198)(122,185,136,171)(123,210,137,224)(124,183,138,169)(125,208,139,222)(126,181,140,195)>;
G:=Group( (1,46,15,32)(2,47,16,33)(3,48,17,34)(4,49,18,35)(5,50,19,36)(6,51,20,37)(7,52,21,38)(8,53,22,39)(9,54,23,40)(10,55,24,41)(11,56,25,42)(12,29,26,43)(13,30,27,44)(14,31,28,45)(57,138,71,124)(58,139,72,125)(59,140,73,126)(60,113,74,127)(61,114,75,128)(62,115,76,129)(63,116,77,130)(64,117,78,131)(65,118,79,132)(66,119,80,133)(67,120,81,134)(68,121,82,135)(69,122,83,136)(70,123,84,137)(85,92,99,106)(86,93,100,107)(87,94,101,108)(88,95,102,109)(89,96,103,110)(90,97,104,111)(91,98,105,112)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,218,211,204)(198,219,212,205)(199,220,213,206)(200,221,214,207)(201,222,215,208)(202,223,216,209)(203,224,217,210), (1,123,39,63)(2,124,40,64)(3,125,41,65)(4,126,42,66)(5,127,43,67)(6,128,44,68)(7,129,45,69)(8,130,46,70)(9,131,47,71)(10,132,48,72)(11,133,49,73)(12,134,50,74)(13,135,51,75)(14,136,52,76)(15,137,53,77)(16,138,54,78)(17,139,55,79)(18,140,56,80)(19,113,29,81)(20,114,30,82)(21,115,31,83)(22,116,32,84)(23,117,33,57)(24,118,34,58)(25,119,35,59)(26,120,36,60)(27,121,37,61)(28,122,38,62)(85,218,148,192)(86,219,149,193)(87,220,150,194)(88,221,151,195)(89,222,152,196)(90,223,153,169)(91,224,154,170)(92,197,155,171)(93,198,156,172)(94,199,157,173)(95,200,158,174)(96,201,159,175)(97,202,160,176)(98,203,161,177)(99,204,162,178)(100,205,163,179)(101,206,164,180)(102,207,165,181)(103,208,166,182)(104,209,167,183)(105,210,168,184)(106,211,141,185)(107,212,142,186)(108,213,143,187)(109,214,144,188)(110,215,145,189)(111,216,146,190)(112,217,147,191), (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), (1,98,15,112)(2,160,16,146)(3,96,17,110)(4,158,18,144)(5,94,19,108)(6,156,20,142)(7,92,21,106)(8,154,22,168)(9,90,23,104)(10,152,24,166)(11,88,25,102)(12,150,26,164)(13,86,27,100)(14,148,28,162)(29,143,43,157)(30,107,44,93)(31,141,45,155)(32,105,46,91)(33,167,47,153)(34,103,48,89)(35,165,49,151)(36,101,50,87)(37,163,51,149)(38,99,52,85)(39,161,53,147)(40,97,54,111)(41,159,55,145)(42,95,56,109)(57,190,71,176)(58,215,72,201)(59,188,73,174)(60,213,74,199)(61,186,75,172)(62,211,76,197)(63,184,77,170)(64,209,78,223)(65,182,79,196)(66,207,80,221)(67,180,81,194)(68,205,82,219)(69,178,83,192)(70,203,84,217)(113,220,127,206)(114,193,128,179)(115,218,129,204)(116,191,130,177)(117,216,131,202)(118,189,132,175)(119,214,133,200)(120,187,134,173)(121,212,135,198)(122,185,136,171)(123,210,137,224)(124,183,138,169)(125,208,139,222)(126,181,140,195) );
G=PermutationGroup([[(1,46,15,32),(2,47,16,33),(3,48,17,34),(4,49,18,35),(5,50,19,36),(6,51,20,37),(7,52,21,38),(8,53,22,39),(9,54,23,40),(10,55,24,41),(11,56,25,42),(12,29,26,43),(13,30,27,44),(14,31,28,45),(57,138,71,124),(58,139,72,125),(59,140,73,126),(60,113,74,127),(61,114,75,128),(62,115,76,129),(63,116,77,130),(64,117,78,131),(65,118,79,132),(66,119,80,133),(67,120,81,134),(68,121,82,135),(69,122,83,136),(70,123,84,137),(85,92,99,106),(86,93,100,107),(87,94,101,108),(88,95,102,109),(89,96,103,110),(90,97,104,111),(91,98,105,112),(141,148,155,162),(142,149,156,163),(143,150,157,164),(144,151,158,165),(145,152,159,166),(146,153,160,167),(147,154,161,168),(169,190,183,176),(170,191,184,177),(171,192,185,178),(172,193,186,179),(173,194,187,180),(174,195,188,181),(175,196,189,182),(197,218,211,204),(198,219,212,205),(199,220,213,206),(200,221,214,207),(201,222,215,208),(202,223,216,209),(203,224,217,210)], [(1,123,39,63),(2,124,40,64),(3,125,41,65),(4,126,42,66),(5,127,43,67),(6,128,44,68),(7,129,45,69),(8,130,46,70),(9,131,47,71),(10,132,48,72),(11,133,49,73),(12,134,50,74),(13,135,51,75),(14,136,52,76),(15,137,53,77),(16,138,54,78),(17,139,55,79),(18,140,56,80),(19,113,29,81),(20,114,30,82),(21,115,31,83),(22,116,32,84),(23,117,33,57),(24,118,34,58),(25,119,35,59),(26,120,36,60),(27,121,37,61),(28,122,38,62),(85,218,148,192),(86,219,149,193),(87,220,150,194),(88,221,151,195),(89,222,152,196),(90,223,153,169),(91,224,154,170),(92,197,155,171),(93,198,156,172),(94,199,157,173),(95,200,158,174),(96,201,159,175),(97,202,160,176),(98,203,161,177),(99,204,162,178),(100,205,163,179),(101,206,164,180),(102,207,165,181),(103,208,166,182),(104,209,167,183),(105,210,168,184),(106,211,141,185),(107,212,142,186),(108,213,143,187),(109,214,144,188),(110,215,145,189),(111,216,146,190),(112,217,147,191)], [(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)], [(1,98,15,112),(2,160,16,146),(3,96,17,110),(4,158,18,144),(5,94,19,108),(6,156,20,142),(7,92,21,106),(8,154,22,168),(9,90,23,104),(10,152,24,166),(11,88,25,102),(12,150,26,164),(13,86,27,100),(14,148,28,162),(29,143,43,157),(30,107,44,93),(31,141,45,155),(32,105,46,91),(33,167,47,153),(34,103,48,89),(35,165,49,151),(36,101,50,87),(37,163,51,149),(38,99,52,85),(39,161,53,147),(40,97,54,111),(41,159,55,145),(42,95,56,109),(57,190,71,176),(58,215,72,201),(59,188,73,174),(60,213,74,199),(61,186,75,172),(62,211,76,197),(63,184,77,170),(64,209,78,223),(65,182,79,196),(66,207,80,221),(67,180,81,194),(68,205,82,219),(69,178,83,192),(70,203,84,217),(113,220,127,206),(114,193,128,179),(115,218,129,204),(116,191,130,177),(117,216,131,202),(118,189,132,175),(119,214,133,200),(120,187,134,173),(121,212,135,198),(122,185,136,171),(123,210,137,224),(124,183,138,169),(125,208,139,222),(126,181,140,195)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 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 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 56 | 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 | D4.8D14 | D4.9D14 |
| kernel | C4⋊C4.233D14 | C28.Q8 | C4.Dic14 | C14.Q16 | C28.55D4 | C28.48D4 | 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⋊C4.233D14 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 98 | 15 |
| 15 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 1 | 111 |
| 0 | 0 | 1 | 112 |
| 109 | 0 | 0 | 0 |
| 0 | 85 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 0 | 28 | 0 | 0 |
| 109 | 0 | 0 | 0 |
| 0 | 0 | 44 | 25 |
| 0 | 0 | 31 | 69 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,98,98,0,0,0,15],[15,0,0,0,0,98,0,0,0,0,1,1,0,0,111,112],[109,0,0,0,0,85,0,0,0,0,98,0,0,0,0,98],[0,109,0,0,28,0,0,0,0,0,44,31,0,0,25,69] >;
C4⋊C4.233D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{233}D_{14} % in TeX
G:=Group("C4:C4.233D14"); // GroupNames label
G:=SmallGroup(448,530);
// by ID
G=gap.SmallGroup(448,530);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,253,232,254,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^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