metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.231D14, (C2×C28).286D4, C4.89(C4○D28), C14.Q16⋊26C2, C4.Dic14⋊26C2, C14.50(C2×SD16), (C2×C14).33SD16, (C22×C4).97D14, C28.177(C4○D4), (C2×C28).324C23, C28.55D4.4C2, (C22×C14).189D4, C23.80(C7⋊D4), C7⋊4(C23.47D4), C22.8(D4.D7), C28.48D4.10C2, C2.7(C28.C23), C14.85(C8.C22), C4⋊Dic7.133C22, (C22×C28).139C22, (C2×Dic14).97C22, C14.61(C22.D4), C2.11(C23.23D14), (C2×C4⋊C4).9D7, (C14×C4⋊C4).8C2, C2.5(C2×D4.D7), (C2×C7⋊C8).84C22, (C2×C14).444(C2×D4), (C2×C4).34(C7⋊D4), (C7×C4⋊C4).262C22, (C2×C4).424(C22×D7), C22.133(C2×C7⋊D4), SmallGroup(448,505)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.231D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, bab-1=dad-1=a-1, ac=ca, bc=cb, dbd-1=a-1b, dcd-1=b2c-1 >
Subgroups: 388 in 104 conjugacy classes, 43 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C22⋊C8, Q8⋊C4, C4.Q8, C2×C4⋊C4, C22⋊Q8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.47D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C23.D7, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, C22×C28, C4.Dic14, C14.Q16, C28.55D4, C28.48D4, C14×C4⋊C4, C4⋊C4.231D14
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C22.D4, C2×SD16, C8.C22, C7⋊D4, C22×D7, C23.47D4, D4.D7, C4○D28, C2×C7⋊D4, C23.23D14, C2×D4.D7, C28.C23, C4⋊C4.231D14
►On 224 points
Generators in S224
(1 48 8 55)(2 49 9 56)(3 50 10 43)(4 51 11 44)(5 52 12 45)(6 53 13 46)(7 54 14 47)(15 32 120 199)(16 33 121 200)(17 34 122 201)(18 35 123 202)(19 36 124 203)(20 37 125 204)(21 38 126 205)(22 39 113 206)(23 40 114 207)(24 41 115 208)(25 42 116 209)(26 29 117 210)(27 30 118 197)(28 31 119 198)(57 112 64 105)(58 99 65 106)(59 100 66 107)(60 101 67 108)(61 102 68 109)(62 103 69 110)(63 104 70 111)(71 168 78 161)(72 155 79 162)(73 156 80 163)(74 157 81 164)(75 158 82 165)(76 159 83 166)(77 160 84 167)(85 171 92 178)(86 172 93 179)(87 173 94 180)(88 174 95 181)(89 175 96 182)(90 176 97 169)(91 177 98 170)(127 194 219 153)(128 195 220 154)(129 196 221 141)(130 183 222 142)(131 184 223 143)(132 185 224 144)(133 186 211 145)(134 187 212 146)(135 188 213 147)(136 189 214 148)(137 190 215 149)(138 191 216 150)(139 192 217 151)(140 193 218 152)
(1 84 112 91)(2 71 99 92)(3 72 100 93)(4 73 101 94)(5 74 102 95)(6 75 103 96)(7 76 104 97)(8 77 105 98)(9 78 106 85)(10 79 107 86)(11 80 108 87)(12 81 109 88)(13 82 110 89)(14 83 111 90)(15 133 113 218)(16 134 114 219)(17 135 115 220)(18 136 116 221)(19 137 117 222)(20 138 118 223)(21 139 119 224)(22 140 120 211)(23 127 121 212)(24 128 122 213)(25 129 123 214)(26 130 124 215)(27 131 125 216)(28 132 126 217)(29 142 203 190)(30 143 204 191)(31 144 205 192)(32 145 206 193)(33 146 207 194)(34 147 208 195)(35 148 209 196)(36 149 210 183)(37 150 197 184)(38 151 198 185)(39 152 199 186)(40 153 200 187)(41 154 201 188)(42 141 202 189)(43 155 59 179)(44 156 60 180)(45 157 61 181)(46 158 62 182)(47 159 63 169)(48 160 64 170)(49 161 65 171)(50 162 66 172)(51 163 67 173)(52 164 68 174)(53 165 69 175)(54 166 70 176)(55 167 57 177)(56 168 58 178)
(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)
(1 147 105 154)(2 194 106 187)(3 145 107 152)(4 192 108 185)(5 143 109 150)(6 190 110 183)(7 141 111 148)(8 188 112 195)(9 153 99 146)(10 186 100 193)(11 151 101 144)(12 184 102 191)(13 149 103 142)(14 196 104 189)(15 72 22 86)(16 92 23 78)(17 84 24 98)(18 90 25 76)(19 82 26 96)(20 88 27 74)(21 80 28 94)(29 175 36 158)(30 164 37 181)(31 173 38 156)(32 162 39 179)(33 171 40 168)(34 160 41 177)(35 169 42 166)(43 133 66 140)(44 217 67 224)(45 131 68 138)(46 215 69 222)(47 129 70 136)(48 213 57 220)(49 127 58 134)(50 211 59 218)(51 139 60 132)(52 223 61 216)(53 137 62 130)(54 221 63 214)(55 135 64 128)(56 219 65 212)(71 121 85 114)(73 119 87 126)(75 117 89 124)(77 115 91 122)(79 113 93 120)(81 125 95 118)(83 123 97 116)(155 206 172 199)(157 204 174 197)(159 202 176 209)(161 200 178 207)(163 198 180 205)(165 210 182 203)(167 208 170 201)
G:=sub<Sym(224)| (1,48,8,55)(2,49,9,56)(3,50,10,43)(4,51,11,44)(5,52,12,45)(6,53,13,46)(7,54,14,47)(15,32,120,199)(16,33,121,200)(17,34,122,201)(18,35,123,202)(19,36,124,203)(20,37,125,204)(21,38,126,205)(22,39,113,206)(23,40,114,207)(24,41,115,208)(25,42,116,209)(26,29,117,210)(27,30,118,197)(28,31,119,198)(57,112,64,105)(58,99,65,106)(59,100,66,107)(60,101,67,108)(61,102,68,109)(62,103,69,110)(63,104,70,111)(71,168,78,161)(72,155,79,162)(73,156,80,163)(74,157,81,164)(75,158,82,165)(76,159,83,166)(77,160,84,167)(85,171,92,178)(86,172,93,179)(87,173,94,180)(88,174,95,181)(89,175,96,182)(90,176,97,169)(91,177,98,170)(127,194,219,153)(128,195,220,154)(129,196,221,141)(130,183,222,142)(131,184,223,143)(132,185,224,144)(133,186,211,145)(134,187,212,146)(135,188,213,147)(136,189,214,148)(137,190,215,149)(138,191,216,150)(139,192,217,151)(140,193,218,152), (1,84,112,91)(2,71,99,92)(3,72,100,93)(4,73,101,94)(5,74,102,95)(6,75,103,96)(7,76,104,97)(8,77,105,98)(9,78,106,85)(10,79,107,86)(11,80,108,87)(12,81,109,88)(13,82,110,89)(14,83,111,90)(15,133,113,218)(16,134,114,219)(17,135,115,220)(18,136,116,221)(19,137,117,222)(20,138,118,223)(21,139,119,224)(22,140,120,211)(23,127,121,212)(24,128,122,213)(25,129,123,214)(26,130,124,215)(27,131,125,216)(28,132,126,217)(29,142,203,190)(30,143,204,191)(31,144,205,192)(32,145,206,193)(33,146,207,194)(34,147,208,195)(35,148,209,196)(36,149,210,183)(37,150,197,184)(38,151,198,185)(39,152,199,186)(40,153,200,187)(41,154,201,188)(42,141,202,189)(43,155,59,179)(44,156,60,180)(45,157,61,181)(46,158,62,182)(47,159,63,169)(48,160,64,170)(49,161,65,171)(50,162,66,172)(51,163,67,173)(52,164,68,174)(53,165,69,175)(54,166,70,176)(55,167,57,177)(56,168,58,178), (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), (1,147,105,154)(2,194,106,187)(3,145,107,152)(4,192,108,185)(5,143,109,150)(6,190,110,183)(7,141,111,148)(8,188,112,195)(9,153,99,146)(10,186,100,193)(11,151,101,144)(12,184,102,191)(13,149,103,142)(14,196,104,189)(15,72,22,86)(16,92,23,78)(17,84,24,98)(18,90,25,76)(19,82,26,96)(20,88,27,74)(21,80,28,94)(29,175,36,158)(30,164,37,181)(31,173,38,156)(32,162,39,179)(33,171,40,168)(34,160,41,177)(35,169,42,166)(43,133,66,140)(44,217,67,224)(45,131,68,138)(46,215,69,222)(47,129,70,136)(48,213,57,220)(49,127,58,134)(50,211,59,218)(51,139,60,132)(52,223,61,216)(53,137,62,130)(54,221,63,214)(55,135,64,128)(56,219,65,212)(71,121,85,114)(73,119,87,126)(75,117,89,124)(77,115,91,122)(79,113,93,120)(81,125,95,118)(83,123,97,116)(155,206,172,199)(157,204,174,197)(159,202,176,209)(161,200,178,207)(163,198,180,205)(165,210,182,203)(167,208,170,201)>;
G:=Group( (1,48,8,55)(2,49,9,56)(3,50,10,43)(4,51,11,44)(5,52,12,45)(6,53,13,46)(7,54,14,47)(15,32,120,199)(16,33,121,200)(17,34,122,201)(18,35,123,202)(19,36,124,203)(20,37,125,204)(21,38,126,205)(22,39,113,206)(23,40,114,207)(24,41,115,208)(25,42,116,209)(26,29,117,210)(27,30,118,197)(28,31,119,198)(57,112,64,105)(58,99,65,106)(59,100,66,107)(60,101,67,108)(61,102,68,109)(62,103,69,110)(63,104,70,111)(71,168,78,161)(72,155,79,162)(73,156,80,163)(74,157,81,164)(75,158,82,165)(76,159,83,166)(77,160,84,167)(85,171,92,178)(86,172,93,179)(87,173,94,180)(88,174,95,181)(89,175,96,182)(90,176,97,169)(91,177,98,170)(127,194,219,153)(128,195,220,154)(129,196,221,141)(130,183,222,142)(131,184,223,143)(132,185,224,144)(133,186,211,145)(134,187,212,146)(135,188,213,147)(136,189,214,148)(137,190,215,149)(138,191,216,150)(139,192,217,151)(140,193,218,152), (1,84,112,91)(2,71,99,92)(3,72,100,93)(4,73,101,94)(5,74,102,95)(6,75,103,96)(7,76,104,97)(8,77,105,98)(9,78,106,85)(10,79,107,86)(11,80,108,87)(12,81,109,88)(13,82,110,89)(14,83,111,90)(15,133,113,218)(16,134,114,219)(17,135,115,220)(18,136,116,221)(19,137,117,222)(20,138,118,223)(21,139,119,224)(22,140,120,211)(23,127,121,212)(24,128,122,213)(25,129,123,214)(26,130,124,215)(27,131,125,216)(28,132,126,217)(29,142,203,190)(30,143,204,191)(31,144,205,192)(32,145,206,193)(33,146,207,194)(34,147,208,195)(35,148,209,196)(36,149,210,183)(37,150,197,184)(38,151,198,185)(39,152,199,186)(40,153,200,187)(41,154,201,188)(42,141,202,189)(43,155,59,179)(44,156,60,180)(45,157,61,181)(46,158,62,182)(47,159,63,169)(48,160,64,170)(49,161,65,171)(50,162,66,172)(51,163,67,173)(52,164,68,174)(53,165,69,175)(54,166,70,176)(55,167,57,177)(56,168,58,178), (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), (1,147,105,154)(2,194,106,187)(3,145,107,152)(4,192,108,185)(5,143,109,150)(6,190,110,183)(7,141,111,148)(8,188,112,195)(9,153,99,146)(10,186,100,193)(11,151,101,144)(12,184,102,191)(13,149,103,142)(14,196,104,189)(15,72,22,86)(16,92,23,78)(17,84,24,98)(18,90,25,76)(19,82,26,96)(20,88,27,74)(21,80,28,94)(29,175,36,158)(30,164,37,181)(31,173,38,156)(32,162,39,179)(33,171,40,168)(34,160,41,177)(35,169,42,166)(43,133,66,140)(44,217,67,224)(45,131,68,138)(46,215,69,222)(47,129,70,136)(48,213,57,220)(49,127,58,134)(50,211,59,218)(51,139,60,132)(52,223,61,216)(53,137,62,130)(54,221,63,214)(55,135,64,128)(56,219,65,212)(71,121,85,114)(73,119,87,126)(75,117,89,124)(77,115,91,122)(79,113,93,120)(81,125,95,118)(83,123,97,116)(155,206,172,199)(157,204,174,197)(159,202,176,209)(161,200,178,207)(163,198,180,205)(165,210,182,203)(167,208,170,201) );
G=PermutationGroup([[(1,48,8,55),(2,49,9,56),(3,50,10,43),(4,51,11,44),(5,52,12,45),(6,53,13,46),(7,54,14,47),(15,32,120,199),(16,33,121,200),(17,34,122,201),(18,35,123,202),(19,36,124,203),(20,37,125,204),(21,38,126,205),(22,39,113,206),(23,40,114,207),(24,41,115,208),(25,42,116,209),(26,29,117,210),(27,30,118,197),(28,31,119,198),(57,112,64,105),(58,99,65,106),(59,100,66,107),(60,101,67,108),(61,102,68,109),(62,103,69,110),(63,104,70,111),(71,168,78,161),(72,155,79,162),(73,156,80,163),(74,157,81,164),(75,158,82,165),(76,159,83,166),(77,160,84,167),(85,171,92,178),(86,172,93,179),(87,173,94,180),(88,174,95,181),(89,175,96,182),(90,176,97,169),(91,177,98,170),(127,194,219,153),(128,195,220,154),(129,196,221,141),(130,183,222,142),(131,184,223,143),(132,185,224,144),(133,186,211,145),(134,187,212,146),(135,188,213,147),(136,189,214,148),(137,190,215,149),(138,191,216,150),(139,192,217,151),(140,193,218,152)], [(1,84,112,91),(2,71,99,92),(3,72,100,93),(4,73,101,94),(5,74,102,95),(6,75,103,96),(7,76,104,97),(8,77,105,98),(9,78,106,85),(10,79,107,86),(11,80,108,87),(12,81,109,88),(13,82,110,89),(14,83,111,90),(15,133,113,218),(16,134,114,219),(17,135,115,220),(18,136,116,221),(19,137,117,222),(20,138,118,223),(21,139,119,224),(22,140,120,211),(23,127,121,212),(24,128,122,213),(25,129,123,214),(26,130,124,215),(27,131,125,216),(28,132,126,217),(29,142,203,190),(30,143,204,191),(31,144,205,192),(32,145,206,193),(33,146,207,194),(34,147,208,195),(35,148,209,196),(36,149,210,183),(37,150,197,184),(38,151,198,185),(39,152,199,186),(40,153,200,187),(41,154,201,188),(42,141,202,189),(43,155,59,179),(44,156,60,180),(45,157,61,181),(46,158,62,182),(47,159,63,169),(48,160,64,170),(49,161,65,171),(50,162,66,172),(51,163,67,173),(52,164,68,174),(53,165,69,175),(54,166,70,176),(55,167,57,177),(56,168,58,178)], [(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)], [(1,147,105,154),(2,194,106,187),(3,145,107,152),(4,192,108,185),(5,143,109,150),(6,190,110,183),(7,141,111,148),(8,188,112,195),(9,153,99,146),(10,186,100,193),(11,151,101,144),(12,184,102,191),(13,149,103,142),(14,196,104,189),(15,72,22,86),(16,92,23,78),(17,84,24,98),(18,90,25,76),(19,82,26,96),(20,88,27,74),(21,80,28,94),(29,175,36,158),(30,164,37,181),(31,173,38,156),(32,162,39,179),(33,171,40,168),(34,160,41,177),(35,169,42,166),(43,133,66,140),(44,217,67,224),(45,131,68,138),(46,215,69,222),(47,129,70,136),(48,213,57,220),(49,127,58,134),(50,211,59,218),(51,139,60,132),(52,223,61,216),(53,137,62,130),(54,221,63,214),(55,135,64,128),(56,219,65,212),(71,121,85,114),(73,119,87,126),(75,117,89,124),(77,115,91,122),(79,113,93,120),(81,125,95,118),(83,123,97,116),(155,206,172,199),(157,204,174,197),(159,202,176,209),(161,200,178,207),(163,198,180,205),(165,210,182,203),(167,208,170,201)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 56 | 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 | D4.D7 | C28.C23 |
| kernel | C4⋊C4.231D14 | C4.Dic14 | C14.Q16 | C28.55D4 | C28.48D4 | 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⋊C4.231D14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 105 |
| 0 | 0 | 85 | 1 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 112 | 105 |
| 0 | 0 | 0 | 1 |
| 30 | 0 | 0 | 0 |
| 0 | 64 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 49 | 0 | 0 |
| 83 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 |
| 0 | 0 | 25 | 0 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,112,85,0,0,105,1],[98,0,0,0,0,98,0,0,0,0,112,0,0,0,105,1],[30,0,0,0,0,64,0,0,0,0,112,0,0,0,0,112],[0,83,0,0,49,0,0,0,0,0,0,25,0,0,9,0] >;
C4⋊C4.231D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{231}D_{14} % in TeX
G:=Group("C4:C4.231D14"); // GroupNames label
G:=SmallGroup(448,505);
// by ID
G=gap.SmallGroup(448,505);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,100,1123,297,136,18822]);
// 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^-1*b,d*c*d^-1=b^2*c^-1>;
// generators/relations