metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.90D14, C14.482- 1+4, C14.922+ 1+4, (C2×C28)⋊5Q8, C28⋊Q8⋊11C2, C28⋊2Q8⋊6C2, (C2×C4)⋊4Dic14, C28.78(C2×Q8), C4⋊C4.268D14, (C4×C28).7C22, C28.6Q8⋊4C2, (C2×C14).63C24, C22⋊C4.91D14, C28.3Q8⋊11C2, C4.34(C2×Dic14), C2.6(D4⋊8D14), C14.11(C22×Q8), (C2×C28).142C23, C42⋊C2.13D7, (C22×C4).187D14, Dic7⋊C4.2C22, C4⋊Dic7.32C22, C22.7(C2×Dic14), C22.96(C23×D7), C22⋊Dic14.1C2, (C4×Dic7).68C22, (C2×Dic7).22C23, C2.13(C22×Dic14), C23.151(C22×D7), C2.7(D4.10D14), C23.D7.92C22, (C22×C28).223C22, (C22×C14).133C23, C7⋊2(C23.41C23), (C2×Dic14).23C22, C23.21D14.23C2, (C22×Dic7).85C22, (C2×C14).13(C2×Q8), (C2×C4⋊Dic7).44C2, (C7×C4⋊C4).304C22, (C2×C4).148(C22×D7), (C7×C42⋊C2).14C2, (C7×C22⋊C4).99C22, SmallGroup(448,972)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.90D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, cac-1=ab2, dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 820 in 206 conjugacy classes, 111 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C42⋊C2, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.41C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×C28, C28⋊2Q8, C28.6Q8, C22⋊Dic14, C28⋊Q8, C28.3Q8, C2×C4⋊Dic7, C23.21D14, C7×C42⋊C2, C42.90D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C24, D14, C22×Q8, 2+ 1+4, 2- 1+4, Dic14, C22×D7, C23.41C23, C2×Dic14, C23×D7, C22×Dic14, D4⋊8D14, D4.10D14, C42.90D14
►On 224 points
Generators in S224
(1 172 22 163)(2 180 23 157)(3 174 24 165)(4 182 25 159)(5 176 26 167)(6 170 27 161)(7 178 28 155)(8 175 35 166)(9 169 29 160)(10 177 30 168)(11 171 31 162)(12 179 32 156)(13 173 33 164)(14 181 34 158)(15 196 106 210)(16 190 107 204)(17 184 108 198)(18 192 109 206)(19 186 110 200)(20 194 111 208)(21 188 112 202)(36 141 101 216)(37 149 102 224)(38 143 103 218)(39 151 104 212)(40 145 105 220)(41 153 99 214)(42 147 100 222)(43 154 53 215)(44 148 54 223)(45 142 55 217)(46 150 56 211)(47 144 50 219)(48 152 51 213)(49 146 52 221)(57 132 80 118)(58 140 81 126)(59 134 82 120)(60 128 83 114)(61 136 84 122)(62 130 78 116)(63 138 79 124)(64 139 71 125)(65 133 72 119)(66 127 73 113)(67 135 74 121)(68 129 75 115)(69 137 76 123)(70 131 77 117)(85 189 96 203)(86 183 97 197)(87 191 98 205)(88 185 92 199)(89 193 93 207)(90 187 94 201)(91 195 95 209)
(1 64 12 57)(2 65 13 58)(3 66 14 59)(4 67 8 60)(5 68 9 61)(6 69 10 62)(7 70 11 63)(15 103 85 56)(16 104 86 50)(17 105 87 51)(18 99 88 52)(19 100 89 53)(20 101 90 54)(21 102 91 55)(22 71 32 80)(23 72 33 81)(24 73 34 82)(25 74 35 83)(26 75 29 84)(27 76 30 78)(28 77 31 79)(36 94 44 111)(37 95 45 112)(38 96 46 106)(39 97 47 107)(40 98 48 108)(41 92 49 109)(42 93 43 110)(113 158 120 165)(114 159 121 166)(115 160 122 167)(116 161 123 168)(117 162 124 155)(118 163 125 156)(119 164 126 157)(127 181 134 174)(128 182 135 175)(129 169 136 176)(130 170 137 177)(131 171 138 178)(132 172 139 179)(133 173 140 180)(141 201 148 208)(142 202 149 209)(143 203 150 210)(144 204 151 197)(145 205 152 198)(146 206 153 199)(147 207 154 200)(183 219 190 212)(184 220 191 213)(185 221 192 214)(186 222 193 215)(187 223 194 216)(188 224 195 217)(189 211 196 218)
(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 96 32 15)(2 95 33 21)(3 94 34 20)(4 93 35 19)(5 92 29 18)(6 98 30 17)(7 97 31 16)(8 110 25 89)(9 109 26 88)(10 108 27 87)(11 107 28 86)(12 106 22 85)(13 112 23 91)(14 111 24 90)(36 82 54 66)(37 81 55 65)(38 80 56 64)(39 79 50 70)(40 78 51 69)(41 84 52 68)(42 83 53 67)(43 74 100 60)(44 73 101 59)(45 72 102 58)(46 71 103 57)(47 77 104 63)(48 76 105 62)(49 75 99 61)(113 141 134 223)(114 154 135 222)(115 153 136 221)(116 152 137 220)(117 151 138 219)(118 150 139 218)(119 149 140 217)(120 148 127 216)(121 147 128 215)(122 146 129 214)(123 145 130 213)(124 144 131 212)(125 143 132 211)(126 142 133 224)(155 197 171 190)(156 210 172 189)(157 209 173 188)(158 208 174 187)(159 207 175 186)(160 206 176 185)(161 205 177 184)(162 204 178 183)(163 203 179 196)(164 202 180 195)(165 201 181 194)(166 200 182 193)(167 199 169 192)(168 198 170 191)
G:=sub<Sym(224)| (1,172,22,163)(2,180,23,157)(3,174,24,165)(4,182,25,159)(5,176,26,167)(6,170,27,161)(7,178,28,155)(8,175,35,166)(9,169,29,160)(10,177,30,168)(11,171,31,162)(12,179,32,156)(13,173,33,164)(14,181,34,158)(15,196,106,210)(16,190,107,204)(17,184,108,198)(18,192,109,206)(19,186,110,200)(20,194,111,208)(21,188,112,202)(36,141,101,216)(37,149,102,224)(38,143,103,218)(39,151,104,212)(40,145,105,220)(41,153,99,214)(42,147,100,222)(43,154,53,215)(44,148,54,223)(45,142,55,217)(46,150,56,211)(47,144,50,219)(48,152,51,213)(49,146,52,221)(57,132,80,118)(58,140,81,126)(59,134,82,120)(60,128,83,114)(61,136,84,122)(62,130,78,116)(63,138,79,124)(64,139,71,125)(65,133,72,119)(66,127,73,113)(67,135,74,121)(68,129,75,115)(69,137,76,123)(70,131,77,117)(85,189,96,203)(86,183,97,197)(87,191,98,205)(88,185,92,199)(89,193,93,207)(90,187,94,201)(91,195,95,209), (1,64,12,57)(2,65,13,58)(3,66,14,59)(4,67,8,60)(5,68,9,61)(6,69,10,62)(7,70,11,63)(15,103,85,56)(16,104,86,50)(17,105,87,51)(18,99,88,52)(19,100,89,53)(20,101,90,54)(21,102,91,55)(22,71,32,80)(23,72,33,81)(24,73,34,82)(25,74,35,83)(26,75,29,84)(27,76,30,78)(28,77,31,79)(36,94,44,111)(37,95,45,112)(38,96,46,106)(39,97,47,107)(40,98,48,108)(41,92,49,109)(42,93,43,110)(113,158,120,165)(114,159,121,166)(115,160,122,167)(116,161,123,168)(117,162,124,155)(118,163,125,156)(119,164,126,157)(127,181,134,174)(128,182,135,175)(129,169,136,176)(130,170,137,177)(131,171,138,178)(132,172,139,179)(133,173,140,180)(141,201,148,208)(142,202,149,209)(143,203,150,210)(144,204,151,197)(145,205,152,198)(146,206,153,199)(147,207,154,200)(183,219,190,212)(184,220,191,213)(185,221,192,214)(186,222,193,215)(187,223,194,216)(188,224,195,217)(189,211,196,218), (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), (1,96,32,15)(2,95,33,21)(3,94,34,20)(4,93,35,19)(5,92,29,18)(6,98,30,17)(7,97,31,16)(8,110,25,89)(9,109,26,88)(10,108,27,87)(11,107,28,86)(12,106,22,85)(13,112,23,91)(14,111,24,90)(36,82,54,66)(37,81,55,65)(38,80,56,64)(39,79,50,70)(40,78,51,69)(41,84,52,68)(42,83,53,67)(43,74,100,60)(44,73,101,59)(45,72,102,58)(46,71,103,57)(47,77,104,63)(48,76,105,62)(49,75,99,61)(113,141,134,223)(114,154,135,222)(115,153,136,221)(116,152,137,220)(117,151,138,219)(118,150,139,218)(119,149,140,217)(120,148,127,216)(121,147,128,215)(122,146,129,214)(123,145,130,213)(124,144,131,212)(125,143,132,211)(126,142,133,224)(155,197,171,190)(156,210,172,189)(157,209,173,188)(158,208,174,187)(159,207,175,186)(160,206,176,185)(161,205,177,184)(162,204,178,183)(163,203,179,196)(164,202,180,195)(165,201,181,194)(166,200,182,193)(167,199,169,192)(168,198,170,191)>;
G:=Group( (1,172,22,163)(2,180,23,157)(3,174,24,165)(4,182,25,159)(5,176,26,167)(6,170,27,161)(7,178,28,155)(8,175,35,166)(9,169,29,160)(10,177,30,168)(11,171,31,162)(12,179,32,156)(13,173,33,164)(14,181,34,158)(15,196,106,210)(16,190,107,204)(17,184,108,198)(18,192,109,206)(19,186,110,200)(20,194,111,208)(21,188,112,202)(36,141,101,216)(37,149,102,224)(38,143,103,218)(39,151,104,212)(40,145,105,220)(41,153,99,214)(42,147,100,222)(43,154,53,215)(44,148,54,223)(45,142,55,217)(46,150,56,211)(47,144,50,219)(48,152,51,213)(49,146,52,221)(57,132,80,118)(58,140,81,126)(59,134,82,120)(60,128,83,114)(61,136,84,122)(62,130,78,116)(63,138,79,124)(64,139,71,125)(65,133,72,119)(66,127,73,113)(67,135,74,121)(68,129,75,115)(69,137,76,123)(70,131,77,117)(85,189,96,203)(86,183,97,197)(87,191,98,205)(88,185,92,199)(89,193,93,207)(90,187,94,201)(91,195,95,209), (1,64,12,57)(2,65,13,58)(3,66,14,59)(4,67,8,60)(5,68,9,61)(6,69,10,62)(7,70,11,63)(15,103,85,56)(16,104,86,50)(17,105,87,51)(18,99,88,52)(19,100,89,53)(20,101,90,54)(21,102,91,55)(22,71,32,80)(23,72,33,81)(24,73,34,82)(25,74,35,83)(26,75,29,84)(27,76,30,78)(28,77,31,79)(36,94,44,111)(37,95,45,112)(38,96,46,106)(39,97,47,107)(40,98,48,108)(41,92,49,109)(42,93,43,110)(113,158,120,165)(114,159,121,166)(115,160,122,167)(116,161,123,168)(117,162,124,155)(118,163,125,156)(119,164,126,157)(127,181,134,174)(128,182,135,175)(129,169,136,176)(130,170,137,177)(131,171,138,178)(132,172,139,179)(133,173,140,180)(141,201,148,208)(142,202,149,209)(143,203,150,210)(144,204,151,197)(145,205,152,198)(146,206,153,199)(147,207,154,200)(183,219,190,212)(184,220,191,213)(185,221,192,214)(186,222,193,215)(187,223,194,216)(188,224,195,217)(189,211,196,218), (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), (1,96,32,15)(2,95,33,21)(3,94,34,20)(4,93,35,19)(5,92,29,18)(6,98,30,17)(7,97,31,16)(8,110,25,89)(9,109,26,88)(10,108,27,87)(11,107,28,86)(12,106,22,85)(13,112,23,91)(14,111,24,90)(36,82,54,66)(37,81,55,65)(38,80,56,64)(39,79,50,70)(40,78,51,69)(41,84,52,68)(42,83,53,67)(43,74,100,60)(44,73,101,59)(45,72,102,58)(46,71,103,57)(47,77,104,63)(48,76,105,62)(49,75,99,61)(113,141,134,223)(114,154,135,222)(115,153,136,221)(116,152,137,220)(117,151,138,219)(118,150,139,218)(119,149,140,217)(120,148,127,216)(121,147,128,215)(122,146,129,214)(123,145,130,213)(124,144,131,212)(125,143,132,211)(126,142,133,224)(155,197,171,190)(156,210,172,189)(157,209,173,188)(158,208,174,187)(159,207,175,186)(160,206,176,185)(161,205,177,184)(162,204,178,183)(163,203,179,196)(164,202,180,195)(165,201,181,194)(166,200,182,193)(167,199,169,192)(168,198,170,191) );
G=PermutationGroup([[(1,172,22,163),(2,180,23,157),(3,174,24,165),(4,182,25,159),(5,176,26,167),(6,170,27,161),(7,178,28,155),(8,175,35,166),(9,169,29,160),(10,177,30,168),(11,171,31,162),(12,179,32,156),(13,173,33,164),(14,181,34,158),(15,196,106,210),(16,190,107,204),(17,184,108,198),(18,192,109,206),(19,186,110,200),(20,194,111,208),(21,188,112,202),(36,141,101,216),(37,149,102,224),(38,143,103,218),(39,151,104,212),(40,145,105,220),(41,153,99,214),(42,147,100,222),(43,154,53,215),(44,148,54,223),(45,142,55,217),(46,150,56,211),(47,144,50,219),(48,152,51,213),(49,146,52,221),(57,132,80,118),(58,140,81,126),(59,134,82,120),(60,128,83,114),(61,136,84,122),(62,130,78,116),(63,138,79,124),(64,139,71,125),(65,133,72,119),(66,127,73,113),(67,135,74,121),(68,129,75,115),(69,137,76,123),(70,131,77,117),(85,189,96,203),(86,183,97,197),(87,191,98,205),(88,185,92,199),(89,193,93,207),(90,187,94,201),(91,195,95,209)], [(1,64,12,57),(2,65,13,58),(3,66,14,59),(4,67,8,60),(5,68,9,61),(6,69,10,62),(7,70,11,63),(15,103,85,56),(16,104,86,50),(17,105,87,51),(18,99,88,52),(19,100,89,53),(20,101,90,54),(21,102,91,55),(22,71,32,80),(23,72,33,81),(24,73,34,82),(25,74,35,83),(26,75,29,84),(27,76,30,78),(28,77,31,79),(36,94,44,111),(37,95,45,112),(38,96,46,106),(39,97,47,107),(40,98,48,108),(41,92,49,109),(42,93,43,110),(113,158,120,165),(114,159,121,166),(115,160,122,167),(116,161,123,168),(117,162,124,155),(118,163,125,156),(119,164,126,157),(127,181,134,174),(128,182,135,175),(129,169,136,176),(130,170,137,177),(131,171,138,178),(132,172,139,179),(133,173,140,180),(141,201,148,208),(142,202,149,209),(143,203,150,210),(144,204,151,197),(145,205,152,198),(146,206,153,199),(147,207,154,200),(183,219,190,212),(184,220,191,213),(185,221,192,214),(186,222,193,215),(187,223,194,216),(188,224,195,217),(189,211,196,218)], [(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)], [(1,96,32,15),(2,95,33,21),(3,94,34,20),(4,93,35,19),(5,92,29,18),(6,98,30,17),(7,97,31,16),(8,110,25,89),(9,109,26,88),(10,108,27,87),(11,107,28,86),(12,106,22,85),(13,112,23,91),(14,111,24,90),(36,82,54,66),(37,81,55,65),(38,80,56,64),(39,79,50,70),(40,78,51,69),(41,84,52,68),(42,83,53,67),(43,74,100,60),(44,73,101,59),(45,72,102,58),(46,71,103,57),(47,77,104,63),(48,76,105,62),(49,75,99,61),(113,141,134,223),(114,154,135,222),(115,153,136,221),(116,152,137,220),(117,151,138,219),(118,150,139,218),(119,149,140,217),(120,148,127,216),(121,147,128,215),(122,146,129,214),(123,145,130,213),(124,144,131,212),(125,143,132,211),(126,142,133,224),(155,197,171,190),(156,210,172,189),(157,209,173,188),(158,208,174,187),(159,207,175,186),(160,206,176,185),(161,205,177,184),(162,204,178,183),(163,203,179,196),(164,202,180,195),(165,201,181,194),(166,200,182,193),(167,199,169,192),(168,198,170,191)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | D14 | D14 | D14 | D14 | Dic14 | 2+ 1+4 | 2- 1+4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.90D14 | C28⋊2Q8 | C28.6Q8 | C22⋊Dic14 | C28⋊Q8 | C28.3Q8 | C2×C4⋊Dic7 | C23.21D14 | C7×C42⋊C2 | C2×C28 | C42⋊C2 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 4 | 2 | 2 | 1 | 1 | 1 | 4 | 3 | 6 | 6 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.90D14 ►in GL6(𝔽29)
| 27 | 22 | 0 | 0 | 0 | 0 |
| 9 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 18 | 0 | 0 |
| 0 | 0 | 9 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 11 |
| 0 | 0 | 0 | 0 | 20 | 10 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 | 0 |
| 0 | 0 | 26 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 28 | 2 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 3 | 23 | 0 | 0 |
G:=sub<GL(6,GF(29))| [27,9,0,0,0,0,22,2,0,0,0,0,0,0,10,9,0,0,0,0,18,19,0,0,0,0,0,0,19,20,0,0,0,0,11,10],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,23,26,0,0,0,0,0,6,0,0,0,0,0,0,24,12,0,0,0,0,0,5],[28,28,0,0,0,0,2,1,0,0,0,0,0,0,0,0,6,3,0,0,0,0,0,23,0,0,24,12,0,0,0,0,0,5,0,0] >;
C42.90D14 in GAP, Magma, Sage, TeX
C_4^2._{90}D_{14} % in TeX
G:=Group("C4^2.90D14"); // GroupNames label
G:=SmallGroup(448,972);
// by ID
G=gap.SmallGroup(448,972);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,758,184,675,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations