metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.180D14, C14.412- 1+4, C14.862+ 1+4, C4⋊Q8⋊18D7, C4⋊C4.127D14, (C2×Q8).90D14, D14⋊3Q8⋊39C2, D14⋊Q8⋊49C2, C42⋊2D7⋊20C2, Dic7.Q8⋊43C2, Dic7⋊Q8⋊28C2, (C2×C28).641C23, (C4×C28).274C22, (C2×C14).279C24, D14⋊C4.76C22, D14.5D4.5C2, C28.23D4.9C2, C2.90(D4⋊6D14), (C2×D28).174C22, Dic7⋊C4.88C22, C4⋊Dic7.256C22, (Q8×C14).146C22, C22.300(C23×D7), C7⋊6(C22.57C24), (C4×Dic7).168C22, (C2×Dic7).147C23, (C22×D7).124C23, C2.42(Q8.10D14), (C2×Dic14).193C22, (C7×C4⋊Q8)⋊21C2, C4⋊C4⋊D7⋊48C2, (C2×C4×D7).152C22, (C7×C4⋊C4).222C22, (C2×C4).222(C22×D7), SmallGroup(448,1188)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.180D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 876 in 196 conjugacy classes, 91 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, D14, C2×C14, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.57C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C42⋊2D7, Dic7.Q8, D14.5D4, D14⋊Q8, C4⋊C4⋊D7, Dic7⋊Q8, D14⋊3Q8, C28.23D4, C7×C4⋊Q8, C42.180D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.57C24, C23×D7, D4⋊6D14, Q8.10D14, C42.180D14
►On 224 points
Generators in S224
(1 126 15 140)(2 113 16 127)(3 128 17 114)(4 115 18 129)(5 130 19 116)(6 117 20 131)(7 132 21 118)(8 119 22 133)(9 134 23 120)(10 121 24 135)(11 136 25 122)(12 123 26 137)(13 138 27 124)(14 125 28 139)(29 216 43 202)(30 203 44 217)(31 218 45 204)(32 205 46 219)(33 220 47 206)(34 207 48 221)(35 222 49 208)(36 209 50 223)(37 224 51 210)(38 211 52 197)(39 198 53 212)(40 213 54 199)(41 200 55 214)(42 215 56 201)(57 179 71 193)(58 194 72 180)(59 181 73 195)(60 196 74 182)(61 183 75 169)(62 170 76 184)(63 185 77 171)(64 172 78 186)(65 187 79 173)(66 174 80 188)(67 189 81 175)(68 176 82 190)(69 191 83 177)(70 178 84 192)(85 166 99 152)(86 153 100 167)(87 168 101 154)(88 155 102 141)(89 142 103 156)(90 157 104 143)(91 144 105 158)(92 159 106 145)(93 146 107 160)(94 161 108 147)(95 148 109 162)(96 163 110 149)(97 150 111 164)(98 165 112 151)
(1 76 41 87)(2 88 42 77)(3 78 43 89)(4 90 44 79)(5 80 45 91)(6 92 46 81)(7 82 47 93)(8 94 48 83)(9 84 49 95)(10 96 50 57)(11 58 51 97)(12 98 52 59)(13 60 53 99)(14 100 54 61)(15 62 55 101)(16 102 56 63)(17 64 29 103)(18 104 30 65)(19 66 31 105)(20 106 32 67)(21 68 33 107)(22 108 34 69)(23 70 35 109)(24 110 36 71)(25 72 37 111)(26 112 38 73)(27 74 39 85)(28 86 40 75)(113 155 215 171)(114 172 216 156)(115 157 217 173)(116 174 218 158)(117 159 219 175)(118 176 220 160)(119 161 221 177)(120 178 222 162)(121 163 223 179)(122 180 224 164)(123 165 197 181)(124 182 198 166)(125 167 199 183)(126 184 200 168)(127 141 201 185)(128 186 202 142)(129 143 203 187)(130 188 204 144)(131 145 205 189)(132 190 206 146)(133 147 207 191)(134 192 208 148)(135 149 209 193)(136 194 210 150)(137 151 211 195)(138 196 212 152)(139 153 213 169)(140 170 214 154)
(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 15 160)(2 159 16 145)(3 144 17 158)(4 157 18 143)(5 142 19 156)(6 155 20 141)(7 168 21 154)(8 153 22 167)(9 166 23 152)(10 151 24 165)(11 164 25 150)(12 149 26 163)(13 162 27 148)(14 147 28 161)(29 174 43 188)(30 187 44 173)(31 172 45 186)(32 185 46 171)(33 170 47 184)(34 183 48 169)(35 196 49 182)(36 181 50 195)(37 194 51 180)(38 179 52 193)(39 192 53 178)(40 177 54 191)(41 190 55 176)(42 175 56 189)(57 123 71 137)(58 136 72 122)(59 121 73 135)(60 134 74 120)(61 119 75 133)(62 132 76 118)(63 117 77 131)(64 130 78 116)(65 115 79 129)(66 128 80 114)(67 113 81 127)(68 126 82 140)(69 139 83 125)(70 124 84 138)(85 222 99 208)(86 207 100 221)(87 220 101 206)(88 205 102 219)(89 218 103 204)(90 203 104 217)(91 216 105 202)(92 201 106 215)(93 214 107 200)(94 199 108 213)(95 212 109 198)(96 197 110 211)(97 210 111 224)(98 223 112 209)
G:=sub<Sym(224)| (1,126,15,140)(2,113,16,127)(3,128,17,114)(4,115,18,129)(5,130,19,116)(6,117,20,131)(7,132,21,118)(8,119,22,133)(9,134,23,120)(10,121,24,135)(11,136,25,122)(12,123,26,137)(13,138,27,124)(14,125,28,139)(29,216,43,202)(30,203,44,217)(31,218,45,204)(32,205,46,219)(33,220,47,206)(34,207,48,221)(35,222,49,208)(36,209,50,223)(37,224,51,210)(38,211,52,197)(39,198,53,212)(40,213,54,199)(41,200,55,214)(42,215,56,201)(57,179,71,193)(58,194,72,180)(59,181,73,195)(60,196,74,182)(61,183,75,169)(62,170,76,184)(63,185,77,171)(64,172,78,186)(65,187,79,173)(66,174,80,188)(67,189,81,175)(68,176,82,190)(69,191,83,177)(70,178,84,192)(85,166,99,152)(86,153,100,167)(87,168,101,154)(88,155,102,141)(89,142,103,156)(90,157,104,143)(91,144,105,158)(92,159,106,145)(93,146,107,160)(94,161,108,147)(95,148,109,162)(96,163,110,149)(97,150,111,164)(98,165,112,151), (1,76,41,87)(2,88,42,77)(3,78,43,89)(4,90,44,79)(5,80,45,91)(6,92,46,81)(7,82,47,93)(8,94,48,83)(9,84,49,95)(10,96,50,57)(11,58,51,97)(12,98,52,59)(13,60,53,99)(14,100,54,61)(15,62,55,101)(16,102,56,63)(17,64,29,103)(18,104,30,65)(19,66,31,105)(20,106,32,67)(21,68,33,107)(22,108,34,69)(23,70,35,109)(24,110,36,71)(25,72,37,111)(26,112,38,73)(27,74,39,85)(28,86,40,75)(113,155,215,171)(114,172,216,156)(115,157,217,173)(116,174,218,158)(117,159,219,175)(118,176,220,160)(119,161,221,177)(120,178,222,162)(121,163,223,179)(122,180,224,164)(123,165,197,181)(124,182,198,166)(125,167,199,183)(126,184,200,168)(127,141,201,185)(128,186,202,142)(129,143,203,187)(130,188,204,144)(131,145,205,189)(132,190,206,146)(133,147,207,191)(134,192,208,148)(135,149,209,193)(136,194,210,150)(137,151,211,195)(138,196,212,152)(139,153,213,169)(140,170,214,154), (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), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,174,43,188)(30,187,44,173)(31,172,45,186)(32,185,46,171)(33,170,47,184)(34,183,48,169)(35,196,49,182)(36,181,50,195)(37,194,51,180)(38,179,52,193)(39,192,53,178)(40,177,54,191)(41,190,55,176)(42,175,56,189)(57,123,71,137)(58,136,72,122)(59,121,73,135)(60,134,74,120)(61,119,75,133)(62,132,76,118)(63,117,77,131)(64,130,78,116)(65,115,79,129)(66,128,80,114)(67,113,81,127)(68,126,82,140)(69,139,83,125)(70,124,84,138)(85,222,99,208)(86,207,100,221)(87,220,101,206)(88,205,102,219)(89,218,103,204)(90,203,104,217)(91,216,105,202)(92,201,106,215)(93,214,107,200)(94,199,108,213)(95,212,109,198)(96,197,110,211)(97,210,111,224)(98,223,112,209)>;
G:=Group( (1,126,15,140)(2,113,16,127)(3,128,17,114)(4,115,18,129)(5,130,19,116)(6,117,20,131)(7,132,21,118)(8,119,22,133)(9,134,23,120)(10,121,24,135)(11,136,25,122)(12,123,26,137)(13,138,27,124)(14,125,28,139)(29,216,43,202)(30,203,44,217)(31,218,45,204)(32,205,46,219)(33,220,47,206)(34,207,48,221)(35,222,49,208)(36,209,50,223)(37,224,51,210)(38,211,52,197)(39,198,53,212)(40,213,54,199)(41,200,55,214)(42,215,56,201)(57,179,71,193)(58,194,72,180)(59,181,73,195)(60,196,74,182)(61,183,75,169)(62,170,76,184)(63,185,77,171)(64,172,78,186)(65,187,79,173)(66,174,80,188)(67,189,81,175)(68,176,82,190)(69,191,83,177)(70,178,84,192)(85,166,99,152)(86,153,100,167)(87,168,101,154)(88,155,102,141)(89,142,103,156)(90,157,104,143)(91,144,105,158)(92,159,106,145)(93,146,107,160)(94,161,108,147)(95,148,109,162)(96,163,110,149)(97,150,111,164)(98,165,112,151), (1,76,41,87)(2,88,42,77)(3,78,43,89)(4,90,44,79)(5,80,45,91)(6,92,46,81)(7,82,47,93)(8,94,48,83)(9,84,49,95)(10,96,50,57)(11,58,51,97)(12,98,52,59)(13,60,53,99)(14,100,54,61)(15,62,55,101)(16,102,56,63)(17,64,29,103)(18,104,30,65)(19,66,31,105)(20,106,32,67)(21,68,33,107)(22,108,34,69)(23,70,35,109)(24,110,36,71)(25,72,37,111)(26,112,38,73)(27,74,39,85)(28,86,40,75)(113,155,215,171)(114,172,216,156)(115,157,217,173)(116,174,218,158)(117,159,219,175)(118,176,220,160)(119,161,221,177)(120,178,222,162)(121,163,223,179)(122,180,224,164)(123,165,197,181)(124,182,198,166)(125,167,199,183)(126,184,200,168)(127,141,201,185)(128,186,202,142)(129,143,203,187)(130,188,204,144)(131,145,205,189)(132,190,206,146)(133,147,207,191)(134,192,208,148)(135,149,209,193)(136,194,210,150)(137,151,211,195)(138,196,212,152)(139,153,213,169)(140,170,214,154), (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), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,174,43,188)(30,187,44,173)(31,172,45,186)(32,185,46,171)(33,170,47,184)(34,183,48,169)(35,196,49,182)(36,181,50,195)(37,194,51,180)(38,179,52,193)(39,192,53,178)(40,177,54,191)(41,190,55,176)(42,175,56,189)(57,123,71,137)(58,136,72,122)(59,121,73,135)(60,134,74,120)(61,119,75,133)(62,132,76,118)(63,117,77,131)(64,130,78,116)(65,115,79,129)(66,128,80,114)(67,113,81,127)(68,126,82,140)(69,139,83,125)(70,124,84,138)(85,222,99,208)(86,207,100,221)(87,220,101,206)(88,205,102,219)(89,218,103,204)(90,203,104,217)(91,216,105,202)(92,201,106,215)(93,214,107,200)(94,199,108,213)(95,212,109,198)(96,197,110,211)(97,210,111,224)(98,223,112,209) );
G=PermutationGroup([[(1,126,15,140),(2,113,16,127),(3,128,17,114),(4,115,18,129),(5,130,19,116),(6,117,20,131),(7,132,21,118),(8,119,22,133),(9,134,23,120),(10,121,24,135),(11,136,25,122),(12,123,26,137),(13,138,27,124),(14,125,28,139),(29,216,43,202),(30,203,44,217),(31,218,45,204),(32,205,46,219),(33,220,47,206),(34,207,48,221),(35,222,49,208),(36,209,50,223),(37,224,51,210),(38,211,52,197),(39,198,53,212),(40,213,54,199),(41,200,55,214),(42,215,56,201),(57,179,71,193),(58,194,72,180),(59,181,73,195),(60,196,74,182),(61,183,75,169),(62,170,76,184),(63,185,77,171),(64,172,78,186),(65,187,79,173),(66,174,80,188),(67,189,81,175),(68,176,82,190),(69,191,83,177),(70,178,84,192),(85,166,99,152),(86,153,100,167),(87,168,101,154),(88,155,102,141),(89,142,103,156),(90,157,104,143),(91,144,105,158),(92,159,106,145),(93,146,107,160),(94,161,108,147),(95,148,109,162),(96,163,110,149),(97,150,111,164),(98,165,112,151)], [(1,76,41,87),(2,88,42,77),(3,78,43,89),(4,90,44,79),(5,80,45,91),(6,92,46,81),(7,82,47,93),(8,94,48,83),(9,84,49,95),(10,96,50,57),(11,58,51,97),(12,98,52,59),(13,60,53,99),(14,100,54,61),(15,62,55,101),(16,102,56,63),(17,64,29,103),(18,104,30,65),(19,66,31,105),(20,106,32,67),(21,68,33,107),(22,108,34,69),(23,70,35,109),(24,110,36,71),(25,72,37,111),(26,112,38,73),(27,74,39,85),(28,86,40,75),(113,155,215,171),(114,172,216,156),(115,157,217,173),(116,174,218,158),(117,159,219,175),(118,176,220,160),(119,161,221,177),(120,178,222,162),(121,163,223,179),(122,180,224,164),(123,165,197,181),(124,182,198,166),(125,167,199,183),(126,184,200,168),(127,141,201,185),(128,186,202,142),(129,143,203,187),(130,188,204,144),(131,145,205,189),(132,190,206,146),(133,147,207,191),(134,192,208,148),(135,149,209,193),(136,194,210,150),(137,151,211,195),(138,196,212,152),(139,153,213,169),(140,170,214,154)], [(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)], [(1,146,15,160),(2,159,16,145),(3,144,17,158),(4,157,18,143),(5,142,19,156),(6,155,20,141),(7,168,21,154),(8,153,22,167),(9,166,23,152),(10,151,24,165),(11,164,25,150),(12,149,26,163),(13,162,27,148),(14,147,28,161),(29,174,43,188),(30,187,44,173),(31,172,45,186),(32,185,46,171),(33,170,47,184),(34,183,48,169),(35,196,49,182),(36,181,50,195),(37,194,51,180),(38,179,52,193),(39,192,53,178),(40,177,54,191),(41,190,55,176),(42,175,56,189),(57,123,71,137),(58,136,72,122),(59,121,73,135),(60,134,74,120),(61,119,75,133),(62,132,76,118),(63,117,77,131),(64,130,78,116),(65,115,79,129),(66,128,80,114),(67,113,81,127),(68,126,82,140),(69,139,83,125),(70,124,84,138),(85,222,99,208),(86,207,100,221),(87,220,101,206),(88,205,102,219),(89,218,103,204),(90,203,104,217),(91,216,105,202),(92,201,106,215),(93,214,107,200),(94,199,108,213),(95,212,109,198),(96,197,110,211),(97,210,111,224),(98,223,112,209)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4G | 4H | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | Q8.10D14 |
| kernel | C42.180D14 | C42⋊2D7 | Dic7.Q8 | D14.5D4 | D14⋊Q8 | C4⋊C4⋊D7 | Dic7⋊Q8 | D14⋊3Q8 | C28.23D4 | C7×C4⋊Q8 | C4⋊Q8 | C42 | C4⋊C4 | C2×Q8 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 1 | 3 | 3 | 12 | 6 | 1 | 2 | 6 | 12 |
Matrix representation of C42.180D14 ►in GL8(𝔽29)
| 11 | 2 | 11 | 27 | 0 | 0 | 0 | 0 |
| 27 | 18 | 0 | 2 | 0 | 0 | 0 | 0 |
| 13 | 13 | 20 | 27 | 0 | 0 | 0 | 0 |
| 0 | 28 | 11 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 0 | 25 | 15 |
| 0 | 0 | 0 | 0 | 22 | 8 | 28 | 4 |
| 28 | 0 | 24 | 18 | 0 | 0 | 0 | 0 |
| 0 | 28 | 22 | 18 | 0 | 0 | 0 | 0 |
| 28 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 27 | 18 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 16 | 11 | 4 |
| 0 | 0 | 0 | 0 | 13 | 5 | 25 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 | 9 | 13 |
| 0 | 0 | 0 | 0 | 14 | 24 | 5 | 20 |
| 4 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 4 | 25 | 0 | 0 | 0 | 0 |
| 4 | 22 | 25 | 0 | 0 | 0 | 0 | 0 |
| 11 | 16 | 0 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 26 | 25 | 5 |
| 0 | 0 | 0 | 0 | 26 | 10 | 7 | 4 |
| 0 | 0 | 0 | 0 | 19 | 10 | 20 | 3 |
| 0 | 0 | 0 | 0 | 0 | 6 | 17 | 3 |
| 7 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 0 | 10 | 22 | 0 | 0 | 0 | 0 |
| 18 | 25 | 2 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 5 | 16 | 27 |
| 0 | 0 | 0 | 0 | 5 | 16 | 10 | 7 |
| 0 | 0 | 0 | 0 | 17 | 11 | 21 | 24 |
| 0 | 0 | 0 | 0 | 15 | 23 | 2 | 5 |
G:=sub<GL(8,GF(29))| [11,27,13,0,0,0,0,0,2,18,13,28,0,0,0,0,11,0,20,11,0,0,0,0,27,2,27,9,0,0,0,0,0,0,0,0,9,14,21,22,0,0,0,0,15,20,0,8,0,0,0,0,0,0,25,28,0,0,0,0,0,0,15,4],[28,0,28,27,0,0,0,0,0,28,1,18,0,0,0,0,24,22,1,0,0,0,0,0,18,18,0,1,0,0,0,0,0,0,0,0,24,13,0,14,0,0,0,0,16,5,15,24,0,0,0,0,11,25,9,5,0,0,0,0,4,0,13,20],[4,0,4,11,0,0,0,0,0,4,22,16,0,0,0,0,25,4,25,0,0,0,0,0,0,25,0,25,0,0,0,0,0,0,0,0,25,26,19,0,0,0,0,0,26,10,10,6,0,0,0,0,25,7,20,17,0,0,0,0,5,4,3,3],[7,3,4,18,0,0,0,0,22,22,0,25,0,0,0,0,0,0,10,2,0,0,0,0,0,0,22,19,0,0,0,0,0,0,0,0,16,5,17,15,0,0,0,0,5,16,11,23,0,0,0,0,16,10,21,2,0,0,0,0,27,7,24,5] >;
C42.180D14 in GAP, Magma, Sage, TeX
C_4^2._{180}D_{14} % in TeX
G:=Group("C4^2.180D14"); // GroupNames label
G:=SmallGroup(448,1188);
// by ID
G=gap.SmallGroup(448,1188);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,100,1571,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=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=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations