metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.72D14, C4⋊1D4.4D7, (C2×D4).54D14, (C2×C28).291D4, C28.75(C4○D4), D4⋊Dic7⋊21C2, C28.6Q8⋊13C2, C4.23(D4⋊2D7), C14.93(C8⋊C22), (C2×C28).389C23, (C4×C28).119C22, (D4×C14).70C22, C42.D7⋊12C2, C14.44(C4.4D4), C4⋊Dic7.155C22, C2.14(D4.D14), C2.11(C28.17D4), C7⋊4(C42.29C22), (C7×C4⋊1D4).3C2, (C2×C14).520(C2×D4), (C2×C4).69(C7⋊D4), (C2×C7⋊C8).129C22, (C2×C4).487(C22×D7), C22.193(C2×C7⋊D4), SmallGroup(448,605)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.72D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=dbd-1=b-1, dcd-1=a2bc-1 >
Subgroups: 428 in 110 conjugacy classes, 39 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, C23, C14, C14, C14, C42, C4⋊C4, C2×C8, C2×D4, C2×D4, Dic7, C28, C28, C2×C14, C2×C14, C8⋊C4, D4⋊C4, C42.C2, C4⋊1D4, C7⋊C8, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C42.29C22, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4×C28, D4×C14, D4×C14, C42.D7, D4⋊Dic7, C28.6Q8, C7×C4⋊1D4, C42.72D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C7⋊D4, C22×D7, C42.29C22, D4⋊2D7, C2×C7⋊D4, D4.D14, C28.17D4, C42.72D14
►On 224 points
Generators in S224
(1 8 42 35)(2 36 29 9)(3 10 30 37)(4 38 31 11)(5 12 32 39)(6 40 33 13)(7 14 34 41)(15 124 139 96)(16 97 140 125)(17 126 127 98)(18 85 128 113)(19 114 129 86)(20 87 130 115)(21 116 131 88)(22 89 132 117)(23 118 133 90)(24 91 134 119)(25 120 135 92)(26 93 136 121)(27 122 137 94)(28 95 138 123)(43 66 59 50)(44 51 60 67)(45 68 61 52)(46 53 62 69)(47 70 63 54)(48 55 64 57)(49 58 65 56)(71 211 99 145)(72 146 100 212)(73 213 101 147)(74 148 102 214)(75 215 103 149)(76 150 104 216)(77 217 105 151)(78 152 106 218)(79 219 107 153)(80 154 108 220)(81 221 109 141)(82 142 110 222)(83 223 111 143)(84 144 112 224)(155 200 181 184)(156 185 182 201)(157 202 169 186)(158 187 170 203)(159 204 171 188)(160 189 172 205)(161 206 173 190)(162 191 174 207)(163 208 175 192)(164 193 176 209)(165 210 177 194)(166 195 178 197)(167 198 179 196)(168 183 180 199)
(1 90 46 16)(2 17 47 91)(3 92 48 18)(4 19 49 93)(5 94 50 20)(6 21 51 95)(7 96 52 22)(8 23 53 97)(9 98 54 24)(10 25 55 85)(11 86 56 26)(12 27 43 87)(13 88 44 28)(14 15 45 89)(29 127 63 119)(30 120 64 128)(31 129 65 121)(32 122 66 130)(33 131 67 123)(34 124 68 132)(35 133 69 125)(36 126 70 134)(37 135 57 113)(38 114 58 136)(39 137 59 115)(40 116 60 138)(41 139 61 117)(42 118 62 140)(71 218 201 163)(72 164 202 219)(73 220 203 165)(74 166 204 221)(75 222 205 167)(76 168 206 223)(77 224 207 155)(78 156 208 211)(79 212 209 157)(80 158 210 213)(81 214 197 159)(82 160 198 215)(83 216 199 161)(84 162 200 217)(99 152 185 175)(100 176 186 153)(101 154 187 177)(102 178 188 141)(103 142 189 179)(104 180 190 143)(105 144 191 181)(106 182 192 145)(107 146 193 169)(108 170 194 147)(109 148 195 171)(110 172 196 149)(111 150 183 173)(112 174 184 151)
(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)
(1 146 42 212)(2 208 29 192)(3 144 30 224)(4 206 31 190)(5 142 32 222)(6 204 33 188)(7 154 34 220)(8 202 35 186)(9 152 36 218)(10 200 37 184)(11 150 38 216)(12 198 39 196)(13 148 40 214)(14 210 41 194)(15 158 139 170)(16 193 140 209)(17 156 127 182)(18 191 128 207)(19 168 129 180)(20 189 130 205)(21 166 131 178)(22 187 132 203)(23 164 133 176)(24 185 134 201)(25 162 135 174)(26 183 136 199)(27 160 137 172)(28 195 138 197)(43 82 59 110)(44 171 60 159)(45 80 61 108)(46 169 62 157)(47 78 63 106)(48 181 64 155)(49 76 65 104)(50 179 66 167)(51 74 67 102)(52 177 68 165)(53 72 69 100)(54 175 70 163)(55 84 57 112)(56 173 58 161)(71 98 99 126)(73 96 101 124)(75 94 103 122)(77 92 105 120)(79 90 107 118)(81 88 109 116)(83 86 111 114)(85 217 113 151)(87 215 115 149)(89 213 117 147)(91 211 119 145)(93 223 121 143)(95 221 123 141)(97 219 125 153)
G:=sub<Sym(224)| (1,8,42,35)(2,36,29,9)(3,10,30,37)(4,38,31,11)(5,12,32,39)(6,40,33,13)(7,14,34,41)(15,124,139,96)(16,97,140,125)(17,126,127,98)(18,85,128,113)(19,114,129,86)(20,87,130,115)(21,116,131,88)(22,89,132,117)(23,118,133,90)(24,91,134,119)(25,120,135,92)(26,93,136,121)(27,122,137,94)(28,95,138,123)(43,66,59,50)(44,51,60,67)(45,68,61,52)(46,53,62,69)(47,70,63,54)(48,55,64,57)(49,58,65,56)(71,211,99,145)(72,146,100,212)(73,213,101,147)(74,148,102,214)(75,215,103,149)(76,150,104,216)(77,217,105,151)(78,152,106,218)(79,219,107,153)(80,154,108,220)(81,221,109,141)(82,142,110,222)(83,223,111,143)(84,144,112,224)(155,200,181,184)(156,185,182,201)(157,202,169,186)(158,187,170,203)(159,204,171,188)(160,189,172,205)(161,206,173,190)(162,191,174,207)(163,208,175,192)(164,193,176,209)(165,210,177,194)(166,195,178,197)(167,198,179,196)(168,183,180,199), (1,90,46,16)(2,17,47,91)(3,92,48,18)(4,19,49,93)(5,94,50,20)(6,21,51,95)(7,96,52,22)(8,23,53,97)(9,98,54,24)(10,25,55,85)(11,86,56,26)(12,27,43,87)(13,88,44,28)(14,15,45,89)(29,127,63,119)(30,120,64,128)(31,129,65,121)(32,122,66,130)(33,131,67,123)(34,124,68,132)(35,133,69,125)(36,126,70,134)(37,135,57,113)(38,114,58,136)(39,137,59,115)(40,116,60,138)(41,139,61,117)(42,118,62,140)(71,218,201,163)(72,164,202,219)(73,220,203,165)(74,166,204,221)(75,222,205,167)(76,168,206,223)(77,224,207,155)(78,156,208,211)(79,212,209,157)(80,158,210,213)(81,214,197,159)(82,160,198,215)(83,216,199,161)(84,162,200,217)(99,152,185,175)(100,176,186,153)(101,154,187,177)(102,178,188,141)(103,142,189,179)(104,180,190,143)(105,144,191,181)(106,182,192,145)(107,146,193,169)(108,170,194,147)(109,148,195,171)(110,172,196,149)(111,150,183,173)(112,174,184,151), (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), (1,146,42,212)(2,208,29,192)(3,144,30,224)(4,206,31,190)(5,142,32,222)(6,204,33,188)(7,154,34,220)(8,202,35,186)(9,152,36,218)(10,200,37,184)(11,150,38,216)(12,198,39,196)(13,148,40,214)(14,210,41,194)(15,158,139,170)(16,193,140,209)(17,156,127,182)(18,191,128,207)(19,168,129,180)(20,189,130,205)(21,166,131,178)(22,187,132,203)(23,164,133,176)(24,185,134,201)(25,162,135,174)(26,183,136,199)(27,160,137,172)(28,195,138,197)(43,82,59,110)(44,171,60,159)(45,80,61,108)(46,169,62,157)(47,78,63,106)(48,181,64,155)(49,76,65,104)(50,179,66,167)(51,74,67,102)(52,177,68,165)(53,72,69,100)(54,175,70,163)(55,84,57,112)(56,173,58,161)(71,98,99,126)(73,96,101,124)(75,94,103,122)(77,92,105,120)(79,90,107,118)(81,88,109,116)(83,86,111,114)(85,217,113,151)(87,215,115,149)(89,213,117,147)(91,211,119,145)(93,223,121,143)(95,221,123,141)(97,219,125,153)>;
G:=Group( (1,8,42,35)(2,36,29,9)(3,10,30,37)(4,38,31,11)(5,12,32,39)(6,40,33,13)(7,14,34,41)(15,124,139,96)(16,97,140,125)(17,126,127,98)(18,85,128,113)(19,114,129,86)(20,87,130,115)(21,116,131,88)(22,89,132,117)(23,118,133,90)(24,91,134,119)(25,120,135,92)(26,93,136,121)(27,122,137,94)(28,95,138,123)(43,66,59,50)(44,51,60,67)(45,68,61,52)(46,53,62,69)(47,70,63,54)(48,55,64,57)(49,58,65,56)(71,211,99,145)(72,146,100,212)(73,213,101,147)(74,148,102,214)(75,215,103,149)(76,150,104,216)(77,217,105,151)(78,152,106,218)(79,219,107,153)(80,154,108,220)(81,221,109,141)(82,142,110,222)(83,223,111,143)(84,144,112,224)(155,200,181,184)(156,185,182,201)(157,202,169,186)(158,187,170,203)(159,204,171,188)(160,189,172,205)(161,206,173,190)(162,191,174,207)(163,208,175,192)(164,193,176,209)(165,210,177,194)(166,195,178,197)(167,198,179,196)(168,183,180,199), (1,90,46,16)(2,17,47,91)(3,92,48,18)(4,19,49,93)(5,94,50,20)(6,21,51,95)(7,96,52,22)(8,23,53,97)(9,98,54,24)(10,25,55,85)(11,86,56,26)(12,27,43,87)(13,88,44,28)(14,15,45,89)(29,127,63,119)(30,120,64,128)(31,129,65,121)(32,122,66,130)(33,131,67,123)(34,124,68,132)(35,133,69,125)(36,126,70,134)(37,135,57,113)(38,114,58,136)(39,137,59,115)(40,116,60,138)(41,139,61,117)(42,118,62,140)(71,218,201,163)(72,164,202,219)(73,220,203,165)(74,166,204,221)(75,222,205,167)(76,168,206,223)(77,224,207,155)(78,156,208,211)(79,212,209,157)(80,158,210,213)(81,214,197,159)(82,160,198,215)(83,216,199,161)(84,162,200,217)(99,152,185,175)(100,176,186,153)(101,154,187,177)(102,178,188,141)(103,142,189,179)(104,180,190,143)(105,144,191,181)(106,182,192,145)(107,146,193,169)(108,170,194,147)(109,148,195,171)(110,172,196,149)(111,150,183,173)(112,174,184,151), (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), (1,146,42,212)(2,208,29,192)(3,144,30,224)(4,206,31,190)(5,142,32,222)(6,204,33,188)(7,154,34,220)(8,202,35,186)(9,152,36,218)(10,200,37,184)(11,150,38,216)(12,198,39,196)(13,148,40,214)(14,210,41,194)(15,158,139,170)(16,193,140,209)(17,156,127,182)(18,191,128,207)(19,168,129,180)(20,189,130,205)(21,166,131,178)(22,187,132,203)(23,164,133,176)(24,185,134,201)(25,162,135,174)(26,183,136,199)(27,160,137,172)(28,195,138,197)(43,82,59,110)(44,171,60,159)(45,80,61,108)(46,169,62,157)(47,78,63,106)(48,181,64,155)(49,76,65,104)(50,179,66,167)(51,74,67,102)(52,177,68,165)(53,72,69,100)(54,175,70,163)(55,84,57,112)(56,173,58,161)(71,98,99,126)(73,96,101,124)(75,94,103,122)(77,92,105,120)(79,90,107,118)(81,88,109,116)(83,86,111,114)(85,217,113,151)(87,215,115,149)(89,213,117,147)(91,211,119,145)(93,223,121,143)(95,221,123,141)(97,219,125,153) );
G=PermutationGroup([[(1,8,42,35),(2,36,29,9),(3,10,30,37),(4,38,31,11),(5,12,32,39),(6,40,33,13),(7,14,34,41),(15,124,139,96),(16,97,140,125),(17,126,127,98),(18,85,128,113),(19,114,129,86),(20,87,130,115),(21,116,131,88),(22,89,132,117),(23,118,133,90),(24,91,134,119),(25,120,135,92),(26,93,136,121),(27,122,137,94),(28,95,138,123),(43,66,59,50),(44,51,60,67),(45,68,61,52),(46,53,62,69),(47,70,63,54),(48,55,64,57),(49,58,65,56),(71,211,99,145),(72,146,100,212),(73,213,101,147),(74,148,102,214),(75,215,103,149),(76,150,104,216),(77,217,105,151),(78,152,106,218),(79,219,107,153),(80,154,108,220),(81,221,109,141),(82,142,110,222),(83,223,111,143),(84,144,112,224),(155,200,181,184),(156,185,182,201),(157,202,169,186),(158,187,170,203),(159,204,171,188),(160,189,172,205),(161,206,173,190),(162,191,174,207),(163,208,175,192),(164,193,176,209),(165,210,177,194),(166,195,178,197),(167,198,179,196),(168,183,180,199)], [(1,90,46,16),(2,17,47,91),(3,92,48,18),(4,19,49,93),(5,94,50,20),(6,21,51,95),(7,96,52,22),(8,23,53,97),(9,98,54,24),(10,25,55,85),(11,86,56,26),(12,27,43,87),(13,88,44,28),(14,15,45,89),(29,127,63,119),(30,120,64,128),(31,129,65,121),(32,122,66,130),(33,131,67,123),(34,124,68,132),(35,133,69,125),(36,126,70,134),(37,135,57,113),(38,114,58,136),(39,137,59,115),(40,116,60,138),(41,139,61,117),(42,118,62,140),(71,218,201,163),(72,164,202,219),(73,220,203,165),(74,166,204,221),(75,222,205,167),(76,168,206,223),(77,224,207,155),(78,156,208,211),(79,212,209,157),(80,158,210,213),(81,214,197,159),(82,160,198,215),(83,216,199,161),(84,162,200,217),(99,152,185,175),(100,176,186,153),(101,154,187,177),(102,178,188,141),(103,142,189,179),(104,180,190,143),(105,144,191,181),(106,182,192,145),(107,146,193,169),(108,170,194,147),(109,148,195,171),(110,172,196,149),(111,150,183,173),(112,174,184,151)], [(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)], [(1,146,42,212),(2,208,29,192),(3,144,30,224),(4,206,31,190),(5,142,32,222),(6,204,33,188),(7,154,34,220),(8,202,35,186),(9,152,36,218),(10,200,37,184),(11,150,38,216),(12,198,39,196),(13,148,40,214),(14,210,41,194),(15,158,139,170),(16,193,140,209),(17,156,127,182),(18,191,128,207),(19,168,129,180),(20,189,130,205),(21,166,131,178),(22,187,132,203),(23,164,133,176),(24,185,134,201),(25,162,135,174),(26,183,136,199),(27,160,137,172),(28,195,138,197),(43,82,59,110),(44,171,60,159),(45,80,61,108),(46,169,62,157),(47,78,63,106),(48,181,64,155),(49,76,65,104),(50,179,66,167),(51,74,67,102),(52,177,68,165),(53,72,69,100),(54,175,70,163),(55,84,57,112),(56,173,58,161),(71,98,99,126),(73,96,101,124),(75,94,103,122),(77,92,105,120),(79,90,107,118),(81,88,109,116),(83,86,111,114),(85,217,113,151),(87,215,115,149),(89,213,117,147),(91,211,119,145),(93,223,121,143),(95,221,123,141),(97,219,125,153)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 2 | 2 | 4 | 4 | 56 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | C8⋊C22 | D4⋊2D7 | D4.D14 |
| kernel | C42.72D14 | C42.D7 | D4⋊Dic7 | C28.6Q8 | C7×C4⋊1D4 | C2×C28 | C4⋊1D4 | C28 | C42 | C2×D4 | C2×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 12 | 2 | 6 | 12 |
Matrix representation of C42.72D14 ►in GL6(𝔽113)
| 81 | 1 | 0 | 0 | 0 | 0 |
| 105 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 58 | 7 | 36 | 36 |
| 0 | 0 | 76 | 91 | 0 | 32 |
| 0 | 0 | 62 | 106 | 84 | 106 |
| 0 | 0 | 84 | 0 | 84 | 106 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 1 |
| 0 | 0 | 24 | 112 | 111 | 24 |
| 0 | 0 | 33 | 41 | 1 | 0 |
| 0 | 0 | 32 | 41 | 1 | 0 |
| 32 | 112 | 0 | 0 | 0 | 0 |
| 6 | 81 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 6 | 0 | 94 |
| 0 | 0 | 47 | 31 | 19 | 90 |
| 0 | 0 | 107 | 0 | 6 | 107 |
| 0 | 0 | 6 | 107 | 6 | 107 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 56 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 86 | 31 | 37 | 74 |
| 0 | 0 | 25 | 101 | 95 | 37 |
| 0 | 0 | 44 | 17 | 82 | 109 |
| 0 | 0 | 5 | 17 | 6 | 70 |
G:=sub<GL(6,GF(113))| [81,105,0,0,0,0,1,32,0,0,0,0,0,0,58,76,62,84,0,0,7,91,106,0,0,0,36,0,84,84,0,0,36,32,106,106],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,24,33,32,0,0,0,112,41,41,0,0,112,111,1,1,0,0,1,24,0,0],[32,6,0,0,0,0,112,81,0,0,0,0,0,0,82,47,107,6,0,0,6,31,0,107,0,0,0,19,6,6,0,0,94,90,107,107],[15,56,0,0,0,0,0,98,0,0,0,0,0,0,86,25,44,5,0,0,31,101,17,17,0,0,37,95,82,6,0,0,74,37,109,70] >;
C42.72D14 in GAP, Magma, Sage, TeX
C_4^2._{72}D_{14} % in TeX
G:=Group("C4^2.72D14"); // GroupNames label
G:=SmallGroup(448,605);
// by ID
G=gap.SmallGroup(448,605);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,477,64,590,135,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=a^2*b*c^-1>;
// generators/relations