metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.65D14, C7⋊C8.7D4, C4.13(D4×D7), C28.27(C2×D4), (C2×C28).83D4, C7⋊2(C8.2D4), C28⋊2Q8⋊18C2, (C2×D4).50D14, (C2×Q8).40D14, C4.4D4.7D7, C14.19(C4⋊1D4), C2.10(C28⋊D4), (C4×C28).109C22, (C2×C28).378C23, (D4×C14).66C22, C42.D7⋊10C2, (Q8×C14).58C22, C2.19(D4.9D14), C14.120(C8.C22), (C2×Dic14).108C22, (C2×C7⋊Q16)⋊14C2, (C2×D4.D7).7C2, (C2×C14).509(C2×D4), (C2×C4).63(C7⋊D4), (C2×C7⋊C8).123C22, (C7×C4.4D4).5C2, (C2×C4).478(C22×D7), C22.184(C2×C7⋊D4), SmallGroup(448,594)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.65D14
G = < a,b,c,d | a4=b4=c14=1, d2=b, ab=ba, cac-1=a-1b2, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c-1 >
Subgroups: 556 in 124 conjugacy classes, 43 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, SD16, Q16, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C8⋊C4, C4.4D4, C4⋊Q8, C2×SD16, C2×Q16, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C8.2D4, C2×C7⋊C8, C4⋊Dic7, D4.D7, C7⋊Q16, C4×C28, C7×C22⋊C4, C2×Dic14, D4×C14, Q8×C14, C42.D7, C28⋊2Q8, C2×D4.D7, C2×C7⋊Q16, C7×C4.4D4, C42.65D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C4⋊1D4, C8.C22, C7⋊D4, C22×D7, C8.2D4, D4×D7, C2×C7⋊D4, C28⋊D4, D4.9D14, C42.65D14
►On 224 points
Generators in S224
(1 37 19 177)(2 31 20 171)(3 39 21 179)(4 33 15 173)(5 41 16 181)(6 35 17 175)(7 29 18 169)(8 178 27 38)(9 172 28 32)(10 180 22 40)(11 174 23 34)(12 182 24 42)(13 176 25 36)(14 170 26 30)(43 98 50 67)(44 61 51 92)(45 86 52 69)(46 63 53 94)(47 88 54 57)(48 65 55 96)(49 90 56 59)(58 142 89 149)(60 144 91 151)(62 146 93 153)(64 148 95 141)(66 150 97 143)(68 152 85 145)(70 154 87 147)(71 211 192 200)(72 121 193 128)(73 213 194 202)(74 123 195 130)(75 215 196 204)(76 125 183 132)(77 217 184 206)(78 113 185 134)(79 219 186 208)(80 115 187 136)(81 221 188 210)(82 117 189 138)(83 223 190 198)(84 119 191 140)(99 224 165 199)(100 120 166 127)(101 212 167 201)(102 122 168 129)(103 214 155 203)(104 124 156 131)(105 216 157 205)(106 126 158 133)(107 218 159 207)(108 114 160 135)(109 220 161 209)(110 116 162 137)(111 222 163 197)(112 118 164 139)
(1 69 14 62)(2 63 8 70)(3 57 9 64)(4 65 10 58)(5 59 11 66)(6 67 12 60)(7 61 13 68)(15 96 22 89)(16 90 23 97)(17 98 24 91)(18 92 25 85)(19 86 26 93)(20 94 27 87)(21 88 28 95)(29 51 176 152)(30 153 177 52)(31 53 178 154)(32 141 179 54)(33 55 180 142)(34 143 181 56)(35 43 182 144)(36 145 169 44)(37 45 170 146)(38 147 171 46)(39 47 172 148)(40 149 173 48)(41 49 174 150)(42 151 175 50)(71 107 166 185)(72 186 167 108)(73 109 168 187)(74 188 155 110)(75 111 156 189)(76 190 157 112)(77 99 158 191)(78 192 159 100)(79 101 160 193)(80 194 161 102)(81 103 162 195)(82 196 163 104)(83 105 164 183)(84 184 165 106)(113 200 207 120)(114 121 208 201)(115 202 209 122)(116 123 210 203)(117 204 197 124)(118 125 198 205)(119 206 199 126)(127 134 211 218)(128 219 212 135)(129 136 213 220)(130 221 214 137)(131 138 215 222)(132 223 216 139)(133 140 217 224)
(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)
(1 120 69 113 14 200 62 207)(2 126 63 119 8 206 70 199)(3 118 57 125 9 198 64 205)(4 124 65 117 10 204 58 197)(5 116 59 123 11 210 66 203)(6 122 67 115 12 202 60 209)(7 114 61 121 13 208 68 201)(15 131 96 138 22 215 89 222)(16 137 90 130 23 221 97 214)(17 129 98 136 24 213 91 220)(18 135 92 128 25 219 85 212)(19 127 86 134 26 211 93 218)(20 133 94 140 27 217 87 224)(21 139 88 132 28 223 95 216)(29 79 51 101 176 160 152 193)(30 100 153 78 177 192 52 159)(31 77 53 99 178 158 154 191)(32 112 141 76 179 190 54 157)(33 75 55 111 180 156 142 189)(34 110 143 74 181 188 56 155)(35 73 43 109 182 168 144 187)(36 108 145 72 169 186 44 167)(37 71 45 107 170 166 146 185)(38 106 147 84 171 184 46 165)(39 83 47 105 172 164 148 183)(40 104 149 82 173 196 48 163)(41 81 49 103 174 162 150 195)(42 102 151 80 175 194 50 161)
G:=sub<Sym(224)| (1,37,19,177)(2,31,20,171)(3,39,21,179)(4,33,15,173)(5,41,16,181)(6,35,17,175)(7,29,18,169)(8,178,27,38)(9,172,28,32)(10,180,22,40)(11,174,23,34)(12,182,24,42)(13,176,25,36)(14,170,26,30)(43,98,50,67)(44,61,51,92)(45,86,52,69)(46,63,53,94)(47,88,54,57)(48,65,55,96)(49,90,56,59)(58,142,89,149)(60,144,91,151)(62,146,93,153)(64,148,95,141)(66,150,97,143)(68,152,85,145)(70,154,87,147)(71,211,192,200)(72,121,193,128)(73,213,194,202)(74,123,195,130)(75,215,196,204)(76,125,183,132)(77,217,184,206)(78,113,185,134)(79,219,186,208)(80,115,187,136)(81,221,188,210)(82,117,189,138)(83,223,190,198)(84,119,191,140)(99,224,165,199)(100,120,166,127)(101,212,167,201)(102,122,168,129)(103,214,155,203)(104,124,156,131)(105,216,157,205)(106,126,158,133)(107,218,159,207)(108,114,160,135)(109,220,161,209)(110,116,162,137)(111,222,163,197)(112,118,164,139), (1,69,14,62)(2,63,8,70)(3,57,9,64)(4,65,10,58)(5,59,11,66)(6,67,12,60)(7,61,13,68)(15,96,22,89)(16,90,23,97)(17,98,24,91)(18,92,25,85)(19,86,26,93)(20,94,27,87)(21,88,28,95)(29,51,176,152)(30,153,177,52)(31,53,178,154)(32,141,179,54)(33,55,180,142)(34,143,181,56)(35,43,182,144)(36,145,169,44)(37,45,170,146)(38,147,171,46)(39,47,172,148)(40,149,173,48)(41,49,174,150)(42,151,175,50)(71,107,166,185)(72,186,167,108)(73,109,168,187)(74,188,155,110)(75,111,156,189)(76,190,157,112)(77,99,158,191)(78,192,159,100)(79,101,160,193)(80,194,161,102)(81,103,162,195)(82,196,163,104)(83,105,164,183)(84,184,165,106)(113,200,207,120)(114,121,208,201)(115,202,209,122)(116,123,210,203)(117,204,197,124)(118,125,198,205)(119,206,199,126)(127,134,211,218)(128,219,212,135)(129,136,213,220)(130,221,214,137)(131,138,215,222)(132,223,216,139)(133,140,217,224), (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), (1,120,69,113,14,200,62,207)(2,126,63,119,8,206,70,199)(3,118,57,125,9,198,64,205)(4,124,65,117,10,204,58,197)(5,116,59,123,11,210,66,203)(6,122,67,115,12,202,60,209)(7,114,61,121,13,208,68,201)(15,131,96,138,22,215,89,222)(16,137,90,130,23,221,97,214)(17,129,98,136,24,213,91,220)(18,135,92,128,25,219,85,212)(19,127,86,134,26,211,93,218)(20,133,94,140,27,217,87,224)(21,139,88,132,28,223,95,216)(29,79,51,101,176,160,152,193)(30,100,153,78,177,192,52,159)(31,77,53,99,178,158,154,191)(32,112,141,76,179,190,54,157)(33,75,55,111,180,156,142,189)(34,110,143,74,181,188,56,155)(35,73,43,109,182,168,144,187)(36,108,145,72,169,186,44,167)(37,71,45,107,170,166,146,185)(38,106,147,84,171,184,46,165)(39,83,47,105,172,164,148,183)(40,104,149,82,173,196,48,163)(41,81,49,103,174,162,150,195)(42,102,151,80,175,194,50,161)>;
G:=Group( (1,37,19,177)(2,31,20,171)(3,39,21,179)(4,33,15,173)(5,41,16,181)(6,35,17,175)(7,29,18,169)(8,178,27,38)(9,172,28,32)(10,180,22,40)(11,174,23,34)(12,182,24,42)(13,176,25,36)(14,170,26,30)(43,98,50,67)(44,61,51,92)(45,86,52,69)(46,63,53,94)(47,88,54,57)(48,65,55,96)(49,90,56,59)(58,142,89,149)(60,144,91,151)(62,146,93,153)(64,148,95,141)(66,150,97,143)(68,152,85,145)(70,154,87,147)(71,211,192,200)(72,121,193,128)(73,213,194,202)(74,123,195,130)(75,215,196,204)(76,125,183,132)(77,217,184,206)(78,113,185,134)(79,219,186,208)(80,115,187,136)(81,221,188,210)(82,117,189,138)(83,223,190,198)(84,119,191,140)(99,224,165,199)(100,120,166,127)(101,212,167,201)(102,122,168,129)(103,214,155,203)(104,124,156,131)(105,216,157,205)(106,126,158,133)(107,218,159,207)(108,114,160,135)(109,220,161,209)(110,116,162,137)(111,222,163,197)(112,118,164,139), (1,69,14,62)(2,63,8,70)(3,57,9,64)(4,65,10,58)(5,59,11,66)(6,67,12,60)(7,61,13,68)(15,96,22,89)(16,90,23,97)(17,98,24,91)(18,92,25,85)(19,86,26,93)(20,94,27,87)(21,88,28,95)(29,51,176,152)(30,153,177,52)(31,53,178,154)(32,141,179,54)(33,55,180,142)(34,143,181,56)(35,43,182,144)(36,145,169,44)(37,45,170,146)(38,147,171,46)(39,47,172,148)(40,149,173,48)(41,49,174,150)(42,151,175,50)(71,107,166,185)(72,186,167,108)(73,109,168,187)(74,188,155,110)(75,111,156,189)(76,190,157,112)(77,99,158,191)(78,192,159,100)(79,101,160,193)(80,194,161,102)(81,103,162,195)(82,196,163,104)(83,105,164,183)(84,184,165,106)(113,200,207,120)(114,121,208,201)(115,202,209,122)(116,123,210,203)(117,204,197,124)(118,125,198,205)(119,206,199,126)(127,134,211,218)(128,219,212,135)(129,136,213,220)(130,221,214,137)(131,138,215,222)(132,223,216,139)(133,140,217,224), (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), (1,120,69,113,14,200,62,207)(2,126,63,119,8,206,70,199)(3,118,57,125,9,198,64,205)(4,124,65,117,10,204,58,197)(5,116,59,123,11,210,66,203)(6,122,67,115,12,202,60,209)(7,114,61,121,13,208,68,201)(15,131,96,138,22,215,89,222)(16,137,90,130,23,221,97,214)(17,129,98,136,24,213,91,220)(18,135,92,128,25,219,85,212)(19,127,86,134,26,211,93,218)(20,133,94,140,27,217,87,224)(21,139,88,132,28,223,95,216)(29,79,51,101,176,160,152,193)(30,100,153,78,177,192,52,159)(31,77,53,99,178,158,154,191)(32,112,141,76,179,190,54,157)(33,75,55,111,180,156,142,189)(34,110,143,74,181,188,56,155)(35,73,43,109,182,168,144,187)(36,108,145,72,169,186,44,167)(37,71,45,107,170,166,146,185)(38,106,147,84,171,184,46,165)(39,83,47,105,172,164,148,183)(40,104,149,82,173,196,48,163)(41,81,49,103,174,162,150,195)(42,102,151,80,175,194,50,161) );
G=PermutationGroup([[(1,37,19,177),(2,31,20,171),(3,39,21,179),(4,33,15,173),(5,41,16,181),(6,35,17,175),(7,29,18,169),(8,178,27,38),(9,172,28,32),(10,180,22,40),(11,174,23,34),(12,182,24,42),(13,176,25,36),(14,170,26,30),(43,98,50,67),(44,61,51,92),(45,86,52,69),(46,63,53,94),(47,88,54,57),(48,65,55,96),(49,90,56,59),(58,142,89,149),(60,144,91,151),(62,146,93,153),(64,148,95,141),(66,150,97,143),(68,152,85,145),(70,154,87,147),(71,211,192,200),(72,121,193,128),(73,213,194,202),(74,123,195,130),(75,215,196,204),(76,125,183,132),(77,217,184,206),(78,113,185,134),(79,219,186,208),(80,115,187,136),(81,221,188,210),(82,117,189,138),(83,223,190,198),(84,119,191,140),(99,224,165,199),(100,120,166,127),(101,212,167,201),(102,122,168,129),(103,214,155,203),(104,124,156,131),(105,216,157,205),(106,126,158,133),(107,218,159,207),(108,114,160,135),(109,220,161,209),(110,116,162,137),(111,222,163,197),(112,118,164,139)], [(1,69,14,62),(2,63,8,70),(3,57,9,64),(4,65,10,58),(5,59,11,66),(6,67,12,60),(7,61,13,68),(15,96,22,89),(16,90,23,97),(17,98,24,91),(18,92,25,85),(19,86,26,93),(20,94,27,87),(21,88,28,95),(29,51,176,152),(30,153,177,52),(31,53,178,154),(32,141,179,54),(33,55,180,142),(34,143,181,56),(35,43,182,144),(36,145,169,44),(37,45,170,146),(38,147,171,46),(39,47,172,148),(40,149,173,48),(41,49,174,150),(42,151,175,50),(71,107,166,185),(72,186,167,108),(73,109,168,187),(74,188,155,110),(75,111,156,189),(76,190,157,112),(77,99,158,191),(78,192,159,100),(79,101,160,193),(80,194,161,102),(81,103,162,195),(82,196,163,104),(83,105,164,183),(84,184,165,106),(113,200,207,120),(114,121,208,201),(115,202,209,122),(116,123,210,203),(117,204,197,124),(118,125,198,205),(119,206,199,126),(127,134,211,218),(128,219,212,135),(129,136,213,220),(130,221,214,137),(131,138,215,222),(132,223,216,139),(133,140,217,224)], [(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)], [(1,120,69,113,14,200,62,207),(2,126,63,119,8,206,70,199),(3,118,57,125,9,198,64,205),(4,124,65,117,10,204,58,197),(5,116,59,123,11,210,66,203),(6,122,67,115,12,202,60,209),(7,114,61,121,13,208,68,201),(15,131,96,138,22,215,89,222),(16,137,90,130,23,221,97,214),(17,129,98,136,24,213,91,220),(18,135,92,128,25,219,85,212),(19,127,86,134,26,211,93,218),(20,133,94,140,27,217,87,224),(21,139,88,132,28,223,95,216),(29,79,51,101,176,160,152,193),(30,100,153,78,177,192,52,159),(31,77,53,99,178,158,154,191),(32,112,141,76,179,190,54,157),(33,75,55,111,180,156,142,189),(34,110,143,74,181,188,56,155),(35,73,43,109,182,168,144,187),(36,108,145,72,169,186,44,167),(37,71,45,107,170,166,146,185),(38,106,147,84,171,184,46,165),(39,83,47,105,172,164,148,183),(40,104,149,82,173,196,48,163),(41,81,49,103,174,162,150,195),(42,102,151,80,175,194,50,161)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 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 | 8 | 2 | 2 | 4 | 4 | 8 | 56 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D14 | D14 | D14 | C7⋊D4 | C8.C22 | D4×D7 | D4.9D14 |
| kernel | C42.65D14 | C42.D7 | C28⋊2Q8 | C2×D4.D7 | C2×C7⋊Q16 | C7×C4.4D4 | C7⋊C8 | C2×C28 | C4.4D4 | C42 | C2×D4 | C2×Q8 | C2×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 2 | 3 | 3 | 3 | 3 | 12 | 2 | 6 | 12 |
Matrix representation of C42.65D14 ►in GL6(𝔽113)
| 75 | 36 | 0 | 0 | 0 | 0 |
| 76 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 79 | 105 | 2 | 74 |
| 0 | 0 | 56 | 73 | 25 | 17 |
| 0 | 0 | 16 | 75 | 17 | 8 |
| 0 | 0 | 74 | 48 | 107 | 57 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 1 |
| 0 | 0 | 89 | 1 | 63 | 24 |
| 0 | 0 | 6 | 28 | 112 | 0 |
| 0 | 0 | 70 | 30 | 7 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 23 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 33 | 103 | 0 | 0 |
| 0 | 0 | 63 | 46 | 0 | 0 |
| 0 | 0 | 31 | 98 | 10 | 10 |
| 0 | 0 | 108 | 2 | 103 | 24 |
| 38 | 77 | 0 | 0 | 0 | 0 |
| 37 | 75 | 0 | 0 | 0 | 0 |
| 0 | 0 | 41 | 0 | 34 | 72 |
| 0 | 0 | 86 | 0 | 85 | 27 |
| 0 | 0 | 20 | 18 | 98 | 58 |
| 0 | 0 | 19 | 48 | 71 | 87 |
G:=sub<GL(6,GF(113))| [75,76,0,0,0,0,36,38,0,0,0,0,0,0,79,56,16,74,0,0,105,73,75,48,0,0,2,25,17,107,0,0,74,17,8,57],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,89,6,70,0,0,0,1,28,30,0,0,7,63,112,7,0,0,1,24,0,0],[112,23,0,0,0,0,0,1,0,0,0,0,0,0,33,63,31,108,0,0,103,46,98,2,0,0,0,0,10,103,0,0,0,0,10,24],[38,37,0,0,0,0,77,75,0,0,0,0,0,0,41,86,20,19,0,0,0,0,18,48,0,0,34,85,98,71,0,0,72,27,58,87] >;
C42.65D14 in GAP, Magma, Sage, TeX
C_4^2._{65}D_{14} % in TeX
G:=Group("C4^2.65D14"); // GroupNames label
G:=SmallGroup(448,594);
// by ID
G=gap.SmallGroup(448,594);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,120,254,555,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations