metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.140D14, C14.722+ 1+4, C14.892- 1+4, (C2×Q8).83D14, C4.4D4.9D7, (C2×D4).109D14, (C2×C28).78C23, C22⋊C4.34D14, C28.6Q8⋊28C2, Dic7⋊Q8⋊23C2, (C2×C14).216C24, (C4×C28).221C22, C4⋊Dic7.50C22, C2.74(D4⋊6D14), C23.38(C22×D7), C22⋊Dic14⋊39C2, (D4×C14).209C22, C23.D14⋊38C2, Dic7⋊C4.83C22, (C22×C14).46C23, (Q8×C14).125C22, C22.237(C23×D7), C23.D7.53C22, C7⋊3(C22.57C24), (C2×Dic7).111C23, (C4×Dic7).132C22, C23.18D14.6C2, C2.50(D4.10D14), (C2×Dic14).176C22, (C22×Dic7).141C22, (C7×C4.4D4).7C2, (C2×C4).192(C22×D7), (C7×C22⋊C4).63C22, SmallGroup(448,1125)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.140D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c-1 >
Subgroups: 780 in 196 conjugacy classes, 91 normal (17 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C2×C14, C2×C14, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C22.57C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C22×Dic7, D4×C14, Q8×C14, C28.6Q8, C22⋊Dic14, C23.D14, C23.18D14, Dic7⋊Q8, C7×C4.4D4, C42.140D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.57C24, C23×D7, D4⋊6D14, D4.10D14, C42.140D14
►On 224 points
Generators in S224
(1 60 42 157)(2 68 36 165)(3 62 37 159)(4 70 38 167)(5 64 39 161)(6 58 40 155)(7 66 41 163)(8 160 17 63)(9 168 18 57)(10 162 19 65)(11 156 20 59)(12 164 21 67)(13 158 15 61)(14 166 16 69)(22 114 30 189)(23 122 31 183)(24 116 32 191)(25 124 33 185)(26 118 34 193)(27 126 35 187)(28 120 29 195)(43 188 54 113)(44 196 55 121)(45 190 56 115)(46 184 50 123)(47 192 51 117)(48 186 52 125)(49 194 53 119)(71 202 101 209)(72 131 102 138)(73 204 103 197)(74 133 104 140)(75 206 105 199)(76 135 106 128)(77 208 107 201)(78 137 108 130)(79 210 109 203)(80 139 110 132)(81 198 111 205)(82 127 112 134)(83 200 99 207)(84 129 100 136)(85 219 179 212)(86 145 180 152)(87 221 181 214)(88 147 182 154)(89 223 169 216)(90 149 170 142)(91 211 171 218)(92 151 172 144)(93 213 173 220)(94 153 174 146)(95 215 175 222)(96 141 176 148)(97 217 177 224)(98 143 178 150)
(1 171 12 178)(2 179 13 172)(3 173 14 180)(4 181 8 174)(5 175 9 182)(6 169 10 176)(7 177 11 170)(15 92 36 85)(16 86 37 93)(17 94 38 87)(18 88 39 95)(19 96 40 89)(20 90 41 97)(21 98 42 91)(22 105 44 112)(23 99 45 106)(24 107 46 100)(25 101 47 108)(26 109 48 102)(27 103 49 110)(28 111 43 104)(29 81 54 74)(30 75 55 82)(31 83 56 76)(32 77 50 84)(33 71 51 78)(34 79 52 72)(35 73 53 80)(57 147 161 215)(58 216 162 148)(59 149 163 217)(60 218 164 150)(61 151 165 219)(62 220 166 152)(63 153 167 221)(64 222 168 154)(65 141 155 223)(66 224 156 142)(67 143 157 211)(68 212 158 144)(69 145 159 213)(70 214 160 146)(113 133 195 198)(114 199 196 134)(115 135 183 200)(116 201 184 136)(117 137 185 202)(118 203 186 138)(119 139 187 204)(120 205 188 140)(121 127 189 206)(122 207 190 128)(123 129 191 208)(124 209 192 130)(125 131 193 210)(126 197 194 132)
(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 45 12 23)(2 44 13 22)(3 43 14 28)(4 49 8 27)(5 48 9 26)(6 47 10 25)(7 46 11 24)(15 30 36 55)(16 29 37 54)(17 35 38 53)(18 34 39 52)(19 33 40 51)(20 32 41 50)(21 31 42 56)(57 118 161 186)(58 117 162 185)(59 116 163 184)(60 115 164 183)(61 114 165 196)(62 113 166 195)(63 126 167 194)(64 125 168 193)(65 124 155 192)(66 123 156 191)(67 122 157 190)(68 121 158 189)(69 120 159 188)(70 119 160 187)(71 176 78 169)(72 175 79 182)(73 174 80 181)(74 173 81 180)(75 172 82 179)(76 171 83 178)(77 170 84 177)(85 105 92 112)(86 104 93 111)(87 103 94 110)(88 102 95 109)(89 101 96 108)(90 100 97 107)(91 99 98 106)(127 219 206 151)(128 218 207 150)(129 217 208 149)(130 216 209 148)(131 215 210 147)(132 214 197 146)(133 213 198 145)(134 212 199 144)(135 211 200 143)(136 224 201 142)(137 223 202 141)(138 222 203 154)(139 221 204 153)(140 220 205 152)
G:=sub<Sym(224)| (1,60,42,157)(2,68,36,165)(3,62,37,159)(4,70,38,167)(5,64,39,161)(6,58,40,155)(7,66,41,163)(8,160,17,63)(9,168,18,57)(10,162,19,65)(11,156,20,59)(12,164,21,67)(13,158,15,61)(14,166,16,69)(22,114,30,189)(23,122,31,183)(24,116,32,191)(25,124,33,185)(26,118,34,193)(27,126,35,187)(28,120,29,195)(43,188,54,113)(44,196,55,121)(45,190,56,115)(46,184,50,123)(47,192,51,117)(48,186,52,125)(49,194,53,119)(71,202,101,209)(72,131,102,138)(73,204,103,197)(74,133,104,140)(75,206,105,199)(76,135,106,128)(77,208,107,201)(78,137,108,130)(79,210,109,203)(80,139,110,132)(81,198,111,205)(82,127,112,134)(83,200,99,207)(84,129,100,136)(85,219,179,212)(86,145,180,152)(87,221,181,214)(88,147,182,154)(89,223,169,216)(90,149,170,142)(91,211,171,218)(92,151,172,144)(93,213,173,220)(94,153,174,146)(95,215,175,222)(96,141,176,148)(97,217,177,224)(98,143,178,150), (1,171,12,178)(2,179,13,172)(3,173,14,180)(4,181,8,174)(5,175,9,182)(6,169,10,176)(7,177,11,170)(15,92,36,85)(16,86,37,93)(17,94,38,87)(18,88,39,95)(19,96,40,89)(20,90,41,97)(21,98,42,91)(22,105,44,112)(23,99,45,106)(24,107,46,100)(25,101,47,108)(26,109,48,102)(27,103,49,110)(28,111,43,104)(29,81,54,74)(30,75,55,82)(31,83,56,76)(32,77,50,84)(33,71,51,78)(34,79,52,72)(35,73,53,80)(57,147,161,215)(58,216,162,148)(59,149,163,217)(60,218,164,150)(61,151,165,219)(62,220,166,152)(63,153,167,221)(64,222,168,154)(65,141,155,223)(66,224,156,142)(67,143,157,211)(68,212,158,144)(69,145,159,213)(70,214,160,146)(113,133,195,198)(114,199,196,134)(115,135,183,200)(116,201,184,136)(117,137,185,202)(118,203,186,138)(119,139,187,204)(120,205,188,140)(121,127,189,206)(122,207,190,128)(123,129,191,208)(124,209,192,130)(125,131,193,210)(126,197,194,132), (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), (1,45,12,23)(2,44,13,22)(3,43,14,28)(4,49,8,27)(5,48,9,26)(6,47,10,25)(7,46,11,24)(15,30,36,55)(16,29,37,54)(17,35,38,53)(18,34,39,52)(19,33,40,51)(20,32,41,50)(21,31,42,56)(57,118,161,186)(58,117,162,185)(59,116,163,184)(60,115,164,183)(61,114,165,196)(62,113,166,195)(63,126,167,194)(64,125,168,193)(65,124,155,192)(66,123,156,191)(67,122,157,190)(68,121,158,189)(69,120,159,188)(70,119,160,187)(71,176,78,169)(72,175,79,182)(73,174,80,181)(74,173,81,180)(75,172,82,179)(76,171,83,178)(77,170,84,177)(85,105,92,112)(86,104,93,111)(87,103,94,110)(88,102,95,109)(89,101,96,108)(90,100,97,107)(91,99,98,106)(127,219,206,151)(128,218,207,150)(129,217,208,149)(130,216,209,148)(131,215,210,147)(132,214,197,146)(133,213,198,145)(134,212,199,144)(135,211,200,143)(136,224,201,142)(137,223,202,141)(138,222,203,154)(139,221,204,153)(140,220,205,152)>;
G:=Group( (1,60,42,157)(2,68,36,165)(3,62,37,159)(4,70,38,167)(5,64,39,161)(6,58,40,155)(7,66,41,163)(8,160,17,63)(9,168,18,57)(10,162,19,65)(11,156,20,59)(12,164,21,67)(13,158,15,61)(14,166,16,69)(22,114,30,189)(23,122,31,183)(24,116,32,191)(25,124,33,185)(26,118,34,193)(27,126,35,187)(28,120,29,195)(43,188,54,113)(44,196,55,121)(45,190,56,115)(46,184,50,123)(47,192,51,117)(48,186,52,125)(49,194,53,119)(71,202,101,209)(72,131,102,138)(73,204,103,197)(74,133,104,140)(75,206,105,199)(76,135,106,128)(77,208,107,201)(78,137,108,130)(79,210,109,203)(80,139,110,132)(81,198,111,205)(82,127,112,134)(83,200,99,207)(84,129,100,136)(85,219,179,212)(86,145,180,152)(87,221,181,214)(88,147,182,154)(89,223,169,216)(90,149,170,142)(91,211,171,218)(92,151,172,144)(93,213,173,220)(94,153,174,146)(95,215,175,222)(96,141,176,148)(97,217,177,224)(98,143,178,150), (1,171,12,178)(2,179,13,172)(3,173,14,180)(4,181,8,174)(5,175,9,182)(6,169,10,176)(7,177,11,170)(15,92,36,85)(16,86,37,93)(17,94,38,87)(18,88,39,95)(19,96,40,89)(20,90,41,97)(21,98,42,91)(22,105,44,112)(23,99,45,106)(24,107,46,100)(25,101,47,108)(26,109,48,102)(27,103,49,110)(28,111,43,104)(29,81,54,74)(30,75,55,82)(31,83,56,76)(32,77,50,84)(33,71,51,78)(34,79,52,72)(35,73,53,80)(57,147,161,215)(58,216,162,148)(59,149,163,217)(60,218,164,150)(61,151,165,219)(62,220,166,152)(63,153,167,221)(64,222,168,154)(65,141,155,223)(66,224,156,142)(67,143,157,211)(68,212,158,144)(69,145,159,213)(70,214,160,146)(113,133,195,198)(114,199,196,134)(115,135,183,200)(116,201,184,136)(117,137,185,202)(118,203,186,138)(119,139,187,204)(120,205,188,140)(121,127,189,206)(122,207,190,128)(123,129,191,208)(124,209,192,130)(125,131,193,210)(126,197,194,132), (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), (1,45,12,23)(2,44,13,22)(3,43,14,28)(4,49,8,27)(5,48,9,26)(6,47,10,25)(7,46,11,24)(15,30,36,55)(16,29,37,54)(17,35,38,53)(18,34,39,52)(19,33,40,51)(20,32,41,50)(21,31,42,56)(57,118,161,186)(58,117,162,185)(59,116,163,184)(60,115,164,183)(61,114,165,196)(62,113,166,195)(63,126,167,194)(64,125,168,193)(65,124,155,192)(66,123,156,191)(67,122,157,190)(68,121,158,189)(69,120,159,188)(70,119,160,187)(71,176,78,169)(72,175,79,182)(73,174,80,181)(74,173,81,180)(75,172,82,179)(76,171,83,178)(77,170,84,177)(85,105,92,112)(86,104,93,111)(87,103,94,110)(88,102,95,109)(89,101,96,108)(90,100,97,107)(91,99,98,106)(127,219,206,151)(128,218,207,150)(129,217,208,149)(130,216,209,148)(131,215,210,147)(132,214,197,146)(133,213,198,145)(134,212,199,144)(135,211,200,143)(136,224,201,142)(137,223,202,141)(138,222,203,154)(139,221,204,153)(140,220,205,152) );
G=PermutationGroup([[(1,60,42,157),(2,68,36,165),(3,62,37,159),(4,70,38,167),(5,64,39,161),(6,58,40,155),(7,66,41,163),(8,160,17,63),(9,168,18,57),(10,162,19,65),(11,156,20,59),(12,164,21,67),(13,158,15,61),(14,166,16,69),(22,114,30,189),(23,122,31,183),(24,116,32,191),(25,124,33,185),(26,118,34,193),(27,126,35,187),(28,120,29,195),(43,188,54,113),(44,196,55,121),(45,190,56,115),(46,184,50,123),(47,192,51,117),(48,186,52,125),(49,194,53,119),(71,202,101,209),(72,131,102,138),(73,204,103,197),(74,133,104,140),(75,206,105,199),(76,135,106,128),(77,208,107,201),(78,137,108,130),(79,210,109,203),(80,139,110,132),(81,198,111,205),(82,127,112,134),(83,200,99,207),(84,129,100,136),(85,219,179,212),(86,145,180,152),(87,221,181,214),(88,147,182,154),(89,223,169,216),(90,149,170,142),(91,211,171,218),(92,151,172,144),(93,213,173,220),(94,153,174,146),(95,215,175,222),(96,141,176,148),(97,217,177,224),(98,143,178,150)], [(1,171,12,178),(2,179,13,172),(3,173,14,180),(4,181,8,174),(5,175,9,182),(6,169,10,176),(7,177,11,170),(15,92,36,85),(16,86,37,93),(17,94,38,87),(18,88,39,95),(19,96,40,89),(20,90,41,97),(21,98,42,91),(22,105,44,112),(23,99,45,106),(24,107,46,100),(25,101,47,108),(26,109,48,102),(27,103,49,110),(28,111,43,104),(29,81,54,74),(30,75,55,82),(31,83,56,76),(32,77,50,84),(33,71,51,78),(34,79,52,72),(35,73,53,80),(57,147,161,215),(58,216,162,148),(59,149,163,217),(60,218,164,150),(61,151,165,219),(62,220,166,152),(63,153,167,221),(64,222,168,154),(65,141,155,223),(66,224,156,142),(67,143,157,211),(68,212,158,144),(69,145,159,213),(70,214,160,146),(113,133,195,198),(114,199,196,134),(115,135,183,200),(116,201,184,136),(117,137,185,202),(118,203,186,138),(119,139,187,204),(120,205,188,140),(121,127,189,206),(122,207,190,128),(123,129,191,208),(124,209,192,130),(125,131,193,210),(126,197,194,132)], [(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)], [(1,45,12,23),(2,44,13,22),(3,43,14,28),(4,49,8,27),(5,48,9,26),(6,47,10,25),(7,46,11,24),(15,30,36,55),(16,29,37,54),(17,35,38,53),(18,34,39,52),(19,33,40,51),(20,32,41,50),(21,31,42,56),(57,118,161,186),(58,117,162,185),(59,116,163,184),(60,115,164,183),(61,114,165,196),(62,113,166,195),(63,126,167,194),(64,125,168,193),(65,124,155,192),(66,123,156,191),(67,122,157,190),(68,121,158,189),(69,120,159,188),(70,119,160,187),(71,176,78,169),(72,175,79,182),(73,174,80,181),(74,173,81,180),(75,172,82,179),(76,171,83,178),(77,170,84,177),(85,105,92,112),(86,104,93,111),(87,103,94,110),(88,102,95,109),(89,101,96,108),(90,100,97,107),(91,99,98,106),(127,219,206,151),(128,218,207,150),(129,217,208,149),(130,216,209,148),(131,215,210,147),(132,214,197,146),(133,213,198,145),(134,212,199,144),(135,211,200,143),(136,224,201,142),(137,223,202,141),(138,222,203,154),(139,221,204,153),(140,220,205,152)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4E | 4F | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D4.10D14 |
| kernel | C42.140D14 | C28.6Q8 | C22⋊Dic14 | C23.D14 | C23.18D14 | Dic7⋊Q8 | C7×C4.4D4 | C4.4D4 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 4 | 4 | 2 | 2 | 1 | 3 | 3 | 12 | 3 | 3 | 1 | 2 | 6 | 12 |
Matrix representation of C42.140D14 ►in GL10(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 24 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 28 | 22 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 17 | 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 8 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 17 | 8 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 9 | 22 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 11 | 28 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 27 | 15 | 12 | 1 |
| 19 | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 23 | 6 | 17 | 28 |
| 23 | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 6 | 11 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 0 | 22 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 20 | 8 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 21 | 23 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 6 | 21 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 14 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 19 | 19 | 15 | 2 |
G:=sub<GL(10,GF(29))| [28,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,1,13,12,11,0,0,0,0,0,0,0,28,0,17,0,0,0,0,0,0,24,22,28,16,0,0,0,0,0,0,0,5,0,1,0,0,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,12,1,0,0,0,0,0,0,0,0,2,17],[28,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,21,7,20,26,0,0,0,0,0,0,28,8,17,9,0,0,0,0,0,0,0,0,8,22,0,0,0,0,0,0,0,0,1,21,0,0,0,0,0,0,0,0,0,0,0,28,28,27,0,0,0,0,0,0,1,0,11,15,0,0,0,0,0,0,0,0,28,12,0,0,0,0,0,0,0,0,24,1],[19,10,0,0,0,0,0,0,0,0,19,7,0,0,0,0,0,0,0,0,0,0,1,13,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,1,13,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,1,0,0,23,0,0,0,0,0,0,0,28,28,6,0,0,0,0,0,0,0,0,1,17,0,0,0,0,0,0,0,0,0,28],[23,8,0,0,0,0,0,0,0,0,21,6,0,0,0,0,0,0,0,0,0,0,7,21,20,0,0,0,0,0,0,0,0,6,0,20,0,0,0,0,0,0,12,11,22,8,0,0,0,0,0,0,0,17,0,23,0,0,0,0,0,0,0,0,0,0,21,6,0,19,0,0,0,0,0,0,23,21,21,19,0,0,0,0,0,0,12,12,14,15,0,0,0,0,0,0,0,2,1,2] >;
C42.140D14 in GAP, Magma, Sage, TeX
C_4^2._{140}D_{14} % in TeX
G:=Group("C4^2.140D14"); // GroupNames label
G:=SmallGroup(448,1125);
// by ID
G=gap.SmallGroup(448,1125);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,219,184,1571,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^-1>;
// generators/relations