metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.228D14, (C2×C28).284D4, C14.D8⋊26C2, C4.87(C4○D28), C28.55D4⋊5C2, C28⋊7D4.10C2, C4.Dic14⋊25C2, C14.67(C2×SD16), (C2×C14).41SD16, (C22×C4).95D14, C22.8(Q8⋊D7), C28.175(C4○D4), C14.84(C8⋊C22), (C2×C28).321C23, (C2×D28).91C22, (C22×C14).186D4, C7⋊4(C23.46D4), C23.78(C7⋊D4), C2.6(D4.D14), C4⋊Dic7.131C22, (C22×C28).136C22, C2.9(C23.23D14), C14.59(C22.D4), (C2×C4⋊C4)⋊4D7, (C14×C4⋊C4)⋊4C2, C2.5(C2×Q8⋊D7), (C2×C7⋊C8).82C22, (C2×C14).441(C2×D4), (C2×C4).32(C7⋊D4), (C7×C4⋊C4).259C22, (C2×C4).421(C22×D7), C22.131(C2×C7⋊D4), SmallGroup(448,502)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.228D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, bab-1=dad-1=a-1, ac=ca, bc=cb, dbd-1=ab, dcd-1=a2b2c-1 >
Subgroups: 580 in 114 conjugacy classes, 43 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, C4.Q8, C2×C4⋊C4, C4⋊D4, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.46D4, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, C22×C28, C4.Dic14, C14.D8, C28.55D4, C28⋊7D4, C14×C4⋊C4, C4⋊C4.228D14
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C22.D4, C2×SD16, C8⋊C22, C7⋊D4, C22×D7, C23.46D4, Q8⋊D7, C4○D28, C2×C7⋊D4, C23.23D14, D4.D14, C2×Q8⋊D7, C4⋊C4.228D14
►On 224 points
Generators in S224
(1 43 12 51)(2 44 13 52)(3 45 14 53)(4 46 8 54)(5 47 9 55)(6 48 10 56)(7 49 11 50)(15 29 22 36)(16 30 23 37)(17 31 24 38)(18 32 25 39)(19 33 26 40)(20 34 27 41)(21 35 28 42)(57 106 64 99)(58 107 65 100)(59 108 66 101)(60 109 67 102)(61 110 68 103)(62 111 69 104)(63 112 70 105)(71 92 78 85)(72 93 79 86)(73 94 80 87)(74 95 81 88)(75 96 82 89)(76 97 83 90)(77 98 84 91)(113 171 154 164)(114 172 141 165)(115 173 142 166)(116 174 143 167)(117 175 144 168)(118 176 145 155)(119 177 146 156)(120 178 147 157)(121 179 148 158)(122 180 149 159)(123 181 150 160)(124 182 151 161)(125 169 152 162)(126 170 153 163)(127 197 211 191)(128 198 212 192)(129 199 213 193)(130 200 214 194)(131 201 215 195)(132 202 216 196)(133 203 217 183)(134 204 218 184)(135 205 219 185)(136 206 220 186)(137 207 221 187)(138 208 222 188)(139 209 223 189)(140 210 224 190)
(1 78 26 57)(2 79 27 58)(3 80 28 59)(4 81 22 60)(5 82 23 61)(6 83 24 62)(7 84 25 63)(8 74 15 67)(9 75 16 68)(10 76 17 69)(11 77 18 70)(12 71 19 64)(13 72 20 65)(14 73 21 66)(29 109 54 88)(30 110 55 89)(31 111 56 90)(32 112 50 91)(33 106 51 85)(34 107 52 86)(35 108 53 87)(36 102 46 95)(37 103 47 96)(38 104 48 97)(39 105 49 98)(40 99 43 92)(41 100 44 93)(42 101 45 94)(113 187 147 200)(114 188 148 201)(115 189 149 202)(116 190 150 203)(117 191 151 204)(118 192 152 205)(119 193 153 206)(120 194 154 207)(121 195 141 208)(122 196 142 209)(123 183 143 210)(124 184 144 197)(125 185 145 198)(126 186 146 199)(127 182 218 168)(128 169 219 155)(129 170 220 156)(130 171 221 157)(131 172 222 158)(132 173 223 159)(133 174 224 160)(134 175 211 161)(135 176 212 162)(136 177 213 163)(137 178 214 164)(138 179 215 165)(139 180 216 166)(140 181 217 167)
(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)
(1 155 19 162)(2 161 20 168)(3 167 21 160)(4 159 15 166)(5 165 16 158)(6 157 17 164)(7 163 18 156)(8 180 22 173)(9 172 23 179)(10 178 24 171)(11 170 25 177)(12 176 26 169)(13 182 27 175)(14 174 28 181)(29 142 46 149)(30 148 47 141)(31 154 48 147)(32 146 49 153)(33 152 43 145)(34 144 44 151)(35 150 45 143)(36 115 54 122)(37 121 55 114)(38 113 56 120)(39 119 50 126)(40 125 51 118)(41 117 52 124)(42 123 53 116)(57 205 71 198)(58 197 72 204)(59 203 73 210)(60 209 74 202)(61 201 75 208)(62 207 76 200)(63 199 77 206)(64 185 78 192)(65 191 79 184)(66 183 80 190)(67 189 81 196)(68 195 82 188)(69 187 83 194)(70 193 84 186)(85 212 99 219)(86 218 100 211)(87 224 101 217)(88 216 102 223)(89 222 103 215)(90 214 104 221)(91 220 105 213)(92 128 106 135)(93 134 107 127)(94 140 108 133)(95 132 109 139)(96 138 110 131)(97 130 111 137)(98 136 112 129)
G:=sub<Sym(224)| (1,43,12,51)(2,44,13,52)(3,45,14,53)(4,46,8,54)(5,47,9,55)(6,48,10,56)(7,49,11,50)(15,29,22,36)(16,30,23,37)(17,31,24,38)(18,32,25,39)(19,33,26,40)(20,34,27,41)(21,35,28,42)(57,106,64,99)(58,107,65,100)(59,108,66,101)(60,109,67,102)(61,110,68,103)(62,111,69,104)(63,112,70,105)(71,92,78,85)(72,93,79,86)(73,94,80,87)(74,95,81,88)(75,96,82,89)(76,97,83,90)(77,98,84,91)(113,171,154,164)(114,172,141,165)(115,173,142,166)(116,174,143,167)(117,175,144,168)(118,176,145,155)(119,177,146,156)(120,178,147,157)(121,179,148,158)(122,180,149,159)(123,181,150,160)(124,182,151,161)(125,169,152,162)(126,170,153,163)(127,197,211,191)(128,198,212,192)(129,199,213,193)(130,200,214,194)(131,201,215,195)(132,202,216,196)(133,203,217,183)(134,204,218,184)(135,205,219,185)(136,206,220,186)(137,207,221,187)(138,208,222,188)(139,209,223,189)(140,210,224,190), (1,78,26,57)(2,79,27,58)(3,80,28,59)(4,81,22,60)(5,82,23,61)(6,83,24,62)(7,84,25,63)(8,74,15,67)(9,75,16,68)(10,76,17,69)(11,77,18,70)(12,71,19,64)(13,72,20,65)(14,73,21,66)(29,109,54,88)(30,110,55,89)(31,111,56,90)(32,112,50,91)(33,106,51,85)(34,107,52,86)(35,108,53,87)(36,102,46,95)(37,103,47,96)(38,104,48,97)(39,105,49,98)(40,99,43,92)(41,100,44,93)(42,101,45,94)(113,187,147,200)(114,188,148,201)(115,189,149,202)(116,190,150,203)(117,191,151,204)(118,192,152,205)(119,193,153,206)(120,194,154,207)(121,195,141,208)(122,196,142,209)(123,183,143,210)(124,184,144,197)(125,185,145,198)(126,186,146,199)(127,182,218,168)(128,169,219,155)(129,170,220,156)(130,171,221,157)(131,172,222,158)(132,173,223,159)(133,174,224,160)(134,175,211,161)(135,176,212,162)(136,177,213,163)(137,178,214,164)(138,179,215,165)(139,180,216,166)(140,181,217,167), (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), (1,155,19,162)(2,161,20,168)(3,167,21,160)(4,159,15,166)(5,165,16,158)(6,157,17,164)(7,163,18,156)(8,180,22,173)(9,172,23,179)(10,178,24,171)(11,170,25,177)(12,176,26,169)(13,182,27,175)(14,174,28,181)(29,142,46,149)(30,148,47,141)(31,154,48,147)(32,146,49,153)(33,152,43,145)(34,144,44,151)(35,150,45,143)(36,115,54,122)(37,121,55,114)(38,113,56,120)(39,119,50,126)(40,125,51,118)(41,117,52,124)(42,123,53,116)(57,205,71,198)(58,197,72,204)(59,203,73,210)(60,209,74,202)(61,201,75,208)(62,207,76,200)(63,199,77,206)(64,185,78,192)(65,191,79,184)(66,183,80,190)(67,189,81,196)(68,195,82,188)(69,187,83,194)(70,193,84,186)(85,212,99,219)(86,218,100,211)(87,224,101,217)(88,216,102,223)(89,222,103,215)(90,214,104,221)(91,220,105,213)(92,128,106,135)(93,134,107,127)(94,140,108,133)(95,132,109,139)(96,138,110,131)(97,130,111,137)(98,136,112,129)>;
G:=Group( (1,43,12,51)(2,44,13,52)(3,45,14,53)(4,46,8,54)(5,47,9,55)(6,48,10,56)(7,49,11,50)(15,29,22,36)(16,30,23,37)(17,31,24,38)(18,32,25,39)(19,33,26,40)(20,34,27,41)(21,35,28,42)(57,106,64,99)(58,107,65,100)(59,108,66,101)(60,109,67,102)(61,110,68,103)(62,111,69,104)(63,112,70,105)(71,92,78,85)(72,93,79,86)(73,94,80,87)(74,95,81,88)(75,96,82,89)(76,97,83,90)(77,98,84,91)(113,171,154,164)(114,172,141,165)(115,173,142,166)(116,174,143,167)(117,175,144,168)(118,176,145,155)(119,177,146,156)(120,178,147,157)(121,179,148,158)(122,180,149,159)(123,181,150,160)(124,182,151,161)(125,169,152,162)(126,170,153,163)(127,197,211,191)(128,198,212,192)(129,199,213,193)(130,200,214,194)(131,201,215,195)(132,202,216,196)(133,203,217,183)(134,204,218,184)(135,205,219,185)(136,206,220,186)(137,207,221,187)(138,208,222,188)(139,209,223,189)(140,210,224,190), (1,78,26,57)(2,79,27,58)(3,80,28,59)(4,81,22,60)(5,82,23,61)(6,83,24,62)(7,84,25,63)(8,74,15,67)(9,75,16,68)(10,76,17,69)(11,77,18,70)(12,71,19,64)(13,72,20,65)(14,73,21,66)(29,109,54,88)(30,110,55,89)(31,111,56,90)(32,112,50,91)(33,106,51,85)(34,107,52,86)(35,108,53,87)(36,102,46,95)(37,103,47,96)(38,104,48,97)(39,105,49,98)(40,99,43,92)(41,100,44,93)(42,101,45,94)(113,187,147,200)(114,188,148,201)(115,189,149,202)(116,190,150,203)(117,191,151,204)(118,192,152,205)(119,193,153,206)(120,194,154,207)(121,195,141,208)(122,196,142,209)(123,183,143,210)(124,184,144,197)(125,185,145,198)(126,186,146,199)(127,182,218,168)(128,169,219,155)(129,170,220,156)(130,171,221,157)(131,172,222,158)(132,173,223,159)(133,174,224,160)(134,175,211,161)(135,176,212,162)(136,177,213,163)(137,178,214,164)(138,179,215,165)(139,180,216,166)(140,181,217,167), (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), (1,155,19,162)(2,161,20,168)(3,167,21,160)(4,159,15,166)(5,165,16,158)(6,157,17,164)(7,163,18,156)(8,180,22,173)(9,172,23,179)(10,178,24,171)(11,170,25,177)(12,176,26,169)(13,182,27,175)(14,174,28,181)(29,142,46,149)(30,148,47,141)(31,154,48,147)(32,146,49,153)(33,152,43,145)(34,144,44,151)(35,150,45,143)(36,115,54,122)(37,121,55,114)(38,113,56,120)(39,119,50,126)(40,125,51,118)(41,117,52,124)(42,123,53,116)(57,205,71,198)(58,197,72,204)(59,203,73,210)(60,209,74,202)(61,201,75,208)(62,207,76,200)(63,199,77,206)(64,185,78,192)(65,191,79,184)(66,183,80,190)(67,189,81,196)(68,195,82,188)(69,187,83,194)(70,193,84,186)(85,212,99,219)(86,218,100,211)(87,224,101,217)(88,216,102,223)(89,222,103,215)(90,214,104,221)(91,220,105,213)(92,128,106,135)(93,134,107,127)(94,140,108,133)(95,132,109,139)(96,138,110,131)(97,130,111,137)(98,136,112,129) );
G=PermutationGroup([[(1,43,12,51),(2,44,13,52),(3,45,14,53),(4,46,8,54),(5,47,9,55),(6,48,10,56),(7,49,11,50),(15,29,22,36),(16,30,23,37),(17,31,24,38),(18,32,25,39),(19,33,26,40),(20,34,27,41),(21,35,28,42),(57,106,64,99),(58,107,65,100),(59,108,66,101),(60,109,67,102),(61,110,68,103),(62,111,69,104),(63,112,70,105),(71,92,78,85),(72,93,79,86),(73,94,80,87),(74,95,81,88),(75,96,82,89),(76,97,83,90),(77,98,84,91),(113,171,154,164),(114,172,141,165),(115,173,142,166),(116,174,143,167),(117,175,144,168),(118,176,145,155),(119,177,146,156),(120,178,147,157),(121,179,148,158),(122,180,149,159),(123,181,150,160),(124,182,151,161),(125,169,152,162),(126,170,153,163),(127,197,211,191),(128,198,212,192),(129,199,213,193),(130,200,214,194),(131,201,215,195),(132,202,216,196),(133,203,217,183),(134,204,218,184),(135,205,219,185),(136,206,220,186),(137,207,221,187),(138,208,222,188),(139,209,223,189),(140,210,224,190)], [(1,78,26,57),(2,79,27,58),(3,80,28,59),(4,81,22,60),(5,82,23,61),(6,83,24,62),(7,84,25,63),(8,74,15,67),(9,75,16,68),(10,76,17,69),(11,77,18,70),(12,71,19,64),(13,72,20,65),(14,73,21,66),(29,109,54,88),(30,110,55,89),(31,111,56,90),(32,112,50,91),(33,106,51,85),(34,107,52,86),(35,108,53,87),(36,102,46,95),(37,103,47,96),(38,104,48,97),(39,105,49,98),(40,99,43,92),(41,100,44,93),(42,101,45,94),(113,187,147,200),(114,188,148,201),(115,189,149,202),(116,190,150,203),(117,191,151,204),(118,192,152,205),(119,193,153,206),(120,194,154,207),(121,195,141,208),(122,196,142,209),(123,183,143,210),(124,184,144,197),(125,185,145,198),(126,186,146,199),(127,182,218,168),(128,169,219,155),(129,170,220,156),(130,171,221,157),(131,172,222,158),(132,173,223,159),(133,174,224,160),(134,175,211,161),(135,176,212,162),(136,177,213,163),(137,178,214,164),(138,179,215,165),(139,180,216,166),(140,181,217,167)], [(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)], [(1,155,19,162),(2,161,20,168),(3,167,21,160),(4,159,15,166),(5,165,16,158),(6,157,17,164),(7,163,18,156),(8,180,22,173),(9,172,23,179),(10,178,24,171),(11,170,25,177),(12,176,26,169),(13,182,27,175),(14,174,28,181),(29,142,46,149),(30,148,47,141),(31,154,48,147),(32,146,49,153),(33,152,43,145),(34,144,44,151),(35,150,45,143),(36,115,54,122),(37,121,55,114),(38,113,56,120),(39,119,50,126),(40,125,51,118),(41,117,52,124),(42,123,53,116),(57,205,71,198),(58,197,72,204),(59,203,73,210),(60,209,74,202),(61,201,75,208),(62,207,76,200),(63,199,77,206),(64,185,78,192),(65,191,79,184),(66,183,80,190),(67,189,81,196),(68,195,82,188),(69,187,83,194),(70,193,84,186),(85,212,99,219),(86,218,100,211),(87,224,101,217),(88,216,102,223),(89,222,103,215),(90,214,104,221),(91,220,105,213),(92,128,106,135),(93,134,107,127),(94,140,108,133),(95,132,109,139),(96,138,110,131),(97,130,111,137),(98,136,112,129)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 56 | 2 | 2 | 4 | ··· | 4 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 |
79 irreducible representations
| dim | 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 | D4 | D4 | D7 | C4○D4 | SD16 | D14 | D14 | C7⋊D4 | C7⋊D4 | C4○D28 | C8⋊C22 | Q8⋊D7 | D4.D14 |
| kernel | C4⋊C4.228D14 | C4.Dic14 | C14.D8 | C28.55D4 | C28⋊7D4 | C14×C4⋊C4 | C2×C28 | C22×C14 | C2×C4⋊C4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C23 | C4 | C14 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 3 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of C4⋊C4.228D14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 107 |
| 0 | 0 | 38 | 112 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 88 | 107 |
| 0 | 0 | 29 | 25 |
| 30 | 0 | 0 | 0 |
| 52 | 64 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 5 | 0 | 0 |
| 90 | 112 | 0 | 0 |
| 0 | 0 | 111 | 84 |
| 0 | 0 | 4 | 2 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,1,38,0,0,107,112],[98,0,0,0,0,98,0,0,0,0,88,29,0,0,107,25],[30,52,0,0,0,64,0,0,0,0,1,0,0,0,0,1],[1,90,0,0,5,112,0,0,0,0,111,4,0,0,84,2] >;
C4⋊C4.228D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{228}D_{14} % in TeX
G:=Group("C4:C4.228D14"); // GroupNames label
G:=SmallGroup(448,502);
// by ID
G=gap.SmallGroup(448,502);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,268,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^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^-1>;
// generators/relations