metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.157D14, C14.312- 1+4, C14.1352+ 1+4, C28⋊Q8⋊38C2, C4⋊C4.114D14, C42.C2⋊13D7, D14⋊2Q8⋊39C2, D14⋊Q8⋊37C2, C28.6Q8⋊30C2, (C2×C28).190C23, (C2×C14).243C24, (C4×C28).224C22, D14⋊C4.43C22, D14.5D4.4C2, C4.D28.12C2, (C2×D28).36C22, C2.60(D4⋊8D14), Dic7⋊C4.86C22, C4⋊Dic7.245C22, C22.264(C23×D7), C7⋊4(C22.57C24), (C2×Dic7).125C23, (C4×Dic7).148C22, (C2×Dic14).41C22, (C22×D7).108C23, C2.61(D4.10D14), C2.32(Q8.10D14), C4⋊C4⋊D7⋊38C2, (C7×C42.C2)⋊16C2, (C2×C4×D7).133C22, (C7×C4⋊C4).198C22, (C2×C4).207(C22×D7), SmallGroup(448,1152)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.157D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 924 in 196 conjugacy classes, 91 normal (31 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22.57C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×D28, C28.6Q8, C4.D28, C28⋊Q8, D14.5D4, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42.C2, C42.157D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.57C24, C23×D7, Q8.10D14, D4⋊8D14, D4.10D14, C42.157D14
►On 224 points
Generators in S224
(1 175 78 198)(2 190 79 213)(3 177 80 200)(4 192 81 215)(5 179 82 202)(6 194 83 217)(7 181 84 204)(8 196 57 219)(9 183 58 206)(10 170 59 221)(11 185 60 208)(12 172 61 223)(13 187 62 210)(14 174 63 197)(15 189 64 212)(16 176 65 199)(17 191 66 214)(18 178 67 201)(19 193 68 216)(20 180 69 203)(21 195 70 218)(22 182 71 205)(23 169 72 220)(24 184 73 207)(25 171 74 222)(26 186 75 209)(27 173 76 224)(28 188 77 211)(29 128 168 88)(30 115 141 103)(31 130 142 90)(32 117 143 105)(33 132 144 92)(34 119 145 107)(35 134 146 94)(36 121 147 109)(37 136 148 96)(38 123 149 111)(39 138 150 98)(40 125 151 85)(41 140 152 100)(42 127 153 87)(43 114 154 102)(44 129 155 89)(45 116 156 104)(46 131 157 91)(47 118 158 106)(48 133 159 93)(49 120 160 108)(50 135 161 95)(51 122 162 110)(52 137 163 97)(53 124 164 112)(54 139 165 99)(55 126 166 86)(56 113 167 101)
(1 121 64 95)(2 96 65 122)(3 123 66 97)(4 98 67 124)(5 125 68 99)(6 100 69 126)(7 127 70 101)(8 102 71 128)(9 129 72 103)(10 104 73 130)(11 131 74 105)(12 106 75 132)(13 133 76 107)(14 108 77 134)(15 135 78 109)(16 110 79 136)(17 137 80 111)(18 112 81 138)(19 139 82 85)(20 86 83 140)(21 113 84 87)(22 88 57 114)(23 115 58 89)(24 90 59 116)(25 117 60 91)(26 92 61 118)(27 119 62 93)(28 94 63 120)(29 219 154 182)(30 183 155 220)(31 221 156 184)(32 185 157 222)(33 223 158 186)(34 187 159 224)(35 197 160 188)(36 189 161 198)(37 199 162 190)(38 191 163 200)(39 201 164 192)(40 193 165 202)(41 203 166 194)(42 195 167 204)(43 205 168 196)(44 169 141 206)(45 207 142 170)(46 171 143 208)(47 209 144 172)(48 173 145 210)(49 211 146 174)(50 175 147 212)(51 213 148 176)(52 177 149 214)(53 215 150 178)(54 179 151 216)(55 217 152 180)(56 181 153 218)
(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)
(1 146 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 70 43 84)(30 83 44 69)(31 68 45 82)(32 81 46 67)(33 66 47 80)(34 79 48 65)(35 64 49 78)(36 77 50 63)(37 62 51 76)(38 75 52 61)(39 60 53 74)(40 73 54 59)(41 58 55 72)(42 71 56 57)(85 207 99 221)(86 220 100 206)(87 205 101 219)(88 218 102 204)(89 203 103 217)(90 216 104 202)(91 201 105 215)(92 214 106 200)(93 199 107 213)(94 212 108 198)(95 197 109 211)(96 210 110 224)(97 223 111 209)(98 208 112 222)(113 196 127 182)(114 181 128 195)(115 194 129 180)(116 179 130 193)(117 192 131 178)(118 177 132 191)(119 190 133 176)(120 175 134 189)(121 188 135 174)(122 173 136 187)(123 186 137 172)(124 171 138 185)(125 184 139 170)(126 169 140 183)
G:=sub<Sym(224)| (1,175,78,198)(2,190,79,213)(3,177,80,200)(4,192,81,215)(5,179,82,202)(6,194,83,217)(7,181,84,204)(8,196,57,219)(9,183,58,206)(10,170,59,221)(11,185,60,208)(12,172,61,223)(13,187,62,210)(14,174,63,197)(15,189,64,212)(16,176,65,199)(17,191,66,214)(18,178,67,201)(19,193,68,216)(20,180,69,203)(21,195,70,218)(22,182,71,205)(23,169,72,220)(24,184,73,207)(25,171,74,222)(26,186,75,209)(27,173,76,224)(28,188,77,211)(29,128,168,88)(30,115,141,103)(31,130,142,90)(32,117,143,105)(33,132,144,92)(34,119,145,107)(35,134,146,94)(36,121,147,109)(37,136,148,96)(38,123,149,111)(39,138,150,98)(40,125,151,85)(41,140,152,100)(42,127,153,87)(43,114,154,102)(44,129,155,89)(45,116,156,104)(46,131,157,91)(47,118,158,106)(48,133,159,93)(49,120,160,108)(50,135,161,95)(51,122,162,110)(52,137,163,97)(53,124,164,112)(54,139,165,99)(55,126,166,86)(56,113,167,101), (1,121,64,95)(2,96,65,122)(3,123,66,97)(4,98,67,124)(5,125,68,99)(6,100,69,126)(7,127,70,101)(8,102,71,128)(9,129,72,103)(10,104,73,130)(11,131,74,105)(12,106,75,132)(13,133,76,107)(14,108,77,134)(15,135,78,109)(16,110,79,136)(17,137,80,111)(18,112,81,138)(19,139,82,85)(20,86,83,140)(21,113,84,87)(22,88,57,114)(23,115,58,89)(24,90,59,116)(25,117,60,91)(26,92,61,118)(27,119,62,93)(28,94,63,120)(29,219,154,182)(30,183,155,220)(31,221,156,184)(32,185,157,222)(33,223,158,186)(34,187,159,224)(35,197,160,188)(36,189,161,198)(37,199,162,190)(38,191,163,200)(39,201,164,192)(40,193,165,202)(41,203,166,194)(42,195,167,204)(43,205,168,196)(44,169,141,206)(45,207,142,170)(46,171,143,208)(47,209,144,172)(48,173,145,210)(49,211,146,174)(50,175,147,212)(51,213,148,176)(52,177,149,214)(53,215,150,178)(54,179,151,216)(55,217,152,180)(56,181,153,218), (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), (1,146,15,160)(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)(29,70,43,84)(30,83,44,69)(31,68,45,82)(32,81,46,67)(33,66,47,80)(34,79,48,65)(35,64,49,78)(36,77,50,63)(37,62,51,76)(38,75,52,61)(39,60,53,74)(40,73,54,59)(41,58,55,72)(42,71,56,57)(85,207,99,221)(86,220,100,206)(87,205,101,219)(88,218,102,204)(89,203,103,217)(90,216,104,202)(91,201,105,215)(92,214,106,200)(93,199,107,213)(94,212,108,198)(95,197,109,211)(96,210,110,224)(97,223,111,209)(98,208,112,222)(113,196,127,182)(114,181,128,195)(115,194,129,180)(116,179,130,193)(117,192,131,178)(118,177,132,191)(119,190,133,176)(120,175,134,189)(121,188,135,174)(122,173,136,187)(123,186,137,172)(124,171,138,185)(125,184,139,170)(126,169,140,183)>;
G:=Group( (1,175,78,198)(2,190,79,213)(3,177,80,200)(4,192,81,215)(5,179,82,202)(6,194,83,217)(7,181,84,204)(8,196,57,219)(9,183,58,206)(10,170,59,221)(11,185,60,208)(12,172,61,223)(13,187,62,210)(14,174,63,197)(15,189,64,212)(16,176,65,199)(17,191,66,214)(18,178,67,201)(19,193,68,216)(20,180,69,203)(21,195,70,218)(22,182,71,205)(23,169,72,220)(24,184,73,207)(25,171,74,222)(26,186,75,209)(27,173,76,224)(28,188,77,211)(29,128,168,88)(30,115,141,103)(31,130,142,90)(32,117,143,105)(33,132,144,92)(34,119,145,107)(35,134,146,94)(36,121,147,109)(37,136,148,96)(38,123,149,111)(39,138,150,98)(40,125,151,85)(41,140,152,100)(42,127,153,87)(43,114,154,102)(44,129,155,89)(45,116,156,104)(46,131,157,91)(47,118,158,106)(48,133,159,93)(49,120,160,108)(50,135,161,95)(51,122,162,110)(52,137,163,97)(53,124,164,112)(54,139,165,99)(55,126,166,86)(56,113,167,101), (1,121,64,95)(2,96,65,122)(3,123,66,97)(4,98,67,124)(5,125,68,99)(6,100,69,126)(7,127,70,101)(8,102,71,128)(9,129,72,103)(10,104,73,130)(11,131,74,105)(12,106,75,132)(13,133,76,107)(14,108,77,134)(15,135,78,109)(16,110,79,136)(17,137,80,111)(18,112,81,138)(19,139,82,85)(20,86,83,140)(21,113,84,87)(22,88,57,114)(23,115,58,89)(24,90,59,116)(25,117,60,91)(26,92,61,118)(27,119,62,93)(28,94,63,120)(29,219,154,182)(30,183,155,220)(31,221,156,184)(32,185,157,222)(33,223,158,186)(34,187,159,224)(35,197,160,188)(36,189,161,198)(37,199,162,190)(38,191,163,200)(39,201,164,192)(40,193,165,202)(41,203,166,194)(42,195,167,204)(43,205,168,196)(44,169,141,206)(45,207,142,170)(46,171,143,208)(47,209,144,172)(48,173,145,210)(49,211,146,174)(50,175,147,212)(51,213,148,176)(52,177,149,214)(53,215,150,178)(54,179,151,216)(55,217,152,180)(56,181,153,218), (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), (1,146,15,160)(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)(29,70,43,84)(30,83,44,69)(31,68,45,82)(32,81,46,67)(33,66,47,80)(34,79,48,65)(35,64,49,78)(36,77,50,63)(37,62,51,76)(38,75,52,61)(39,60,53,74)(40,73,54,59)(41,58,55,72)(42,71,56,57)(85,207,99,221)(86,220,100,206)(87,205,101,219)(88,218,102,204)(89,203,103,217)(90,216,104,202)(91,201,105,215)(92,214,106,200)(93,199,107,213)(94,212,108,198)(95,197,109,211)(96,210,110,224)(97,223,111,209)(98,208,112,222)(113,196,127,182)(114,181,128,195)(115,194,129,180)(116,179,130,193)(117,192,131,178)(118,177,132,191)(119,190,133,176)(120,175,134,189)(121,188,135,174)(122,173,136,187)(123,186,137,172)(124,171,138,185)(125,184,139,170)(126,169,140,183) );
G=PermutationGroup([[(1,175,78,198),(2,190,79,213),(3,177,80,200),(4,192,81,215),(5,179,82,202),(6,194,83,217),(7,181,84,204),(8,196,57,219),(9,183,58,206),(10,170,59,221),(11,185,60,208),(12,172,61,223),(13,187,62,210),(14,174,63,197),(15,189,64,212),(16,176,65,199),(17,191,66,214),(18,178,67,201),(19,193,68,216),(20,180,69,203),(21,195,70,218),(22,182,71,205),(23,169,72,220),(24,184,73,207),(25,171,74,222),(26,186,75,209),(27,173,76,224),(28,188,77,211),(29,128,168,88),(30,115,141,103),(31,130,142,90),(32,117,143,105),(33,132,144,92),(34,119,145,107),(35,134,146,94),(36,121,147,109),(37,136,148,96),(38,123,149,111),(39,138,150,98),(40,125,151,85),(41,140,152,100),(42,127,153,87),(43,114,154,102),(44,129,155,89),(45,116,156,104),(46,131,157,91),(47,118,158,106),(48,133,159,93),(49,120,160,108),(50,135,161,95),(51,122,162,110),(52,137,163,97),(53,124,164,112),(54,139,165,99),(55,126,166,86),(56,113,167,101)], [(1,121,64,95),(2,96,65,122),(3,123,66,97),(4,98,67,124),(5,125,68,99),(6,100,69,126),(7,127,70,101),(8,102,71,128),(9,129,72,103),(10,104,73,130),(11,131,74,105),(12,106,75,132),(13,133,76,107),(14,108,77,134),(15,135,78,109),(16,110,79,136),(17,137,80,111),(18,112,81,138),(19,139,82,85),(20,86,83,140),(21,113,84,87),(22,88,57,114),(23,115,58,89),(24,90,59,116),(25,117,60,91),(26,92,61,118),(27,119,62,93),(28,94,63,120),(29,219,154,182),(30,183,155,220),(31,221,156,184),(32,185,157,222),(33,223,158,186),(34,187,159,224),(35,197,160,188),(36,189,161,198),(37,199,162,190),(38,191,163,200),(39,201,164,192),(40,193,165,202),(41,203,166,194),(42,195,167,204),(43,205,168,196),(44,169,141,206),(45,207,142,170),(46,171,143,208),(47,209,144,172),(48,173,145,210),(49,211,146,174),(50,175,147,212),(51,213,148,176),(52,177,149,214),(53,215,150,178),(54,179,151,216),(55,217,152,180),(56,181,153,218)], [(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)], [(1,146,15,160),(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),(29,70,43,84),(30,83,44,69),(31,68,45,82),(32,81,46,67),(33,66,47,80),(34,79,48,65),(35,64,49,78),(36,77,50,63),(37,62,51,76),(38,75,52,61),(39,60,53,74),(40,73,54,59),(41,58,55,72),(42,71,56,57),(85,207,99,221),(86,220,100,206),(87,205,101,219),(88,218,102,204),(89,203,103,217),(90,216,104,202),(91,201,105,215),(92,214,106,200),(93,199,107,213),(94,212,108,198),(95,197,109,211),(96,210,110,224),(97,223,111,209),(98,208,112,222),(113,196,127,182),(114,181,128,195),(115,194,129,180),(116,179,130,193),(117,192,131,178),(118,177,132,191),(119,190,133,176),(120,175,134,189),(121,188,135,174),(122,173,136,187),(123,186,137,172),(124,171,138,185),(125,184,139,170),(126,169,140,183)]])
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 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8.10D14 | D4⋊8D14 | D4.10D14 |
| kernel | C42.157D14 | C28.6Q8 | C4.D28 | C28⋊Q8 | D14.5D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 1 | 3 | 3 | 18 | 1 | 2 | 6 | 6 | 6 |
Matrix representation of C42.157D14 ►in GL8(𝔽29)
| 0 | 0 | 21 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 8 | 0 | 0 | 0 | 0 |
| 8 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 21 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 8 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 21 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 20 | 16 | 15 | 12 | 0 | 0 | 0 | 0 |
| 24 | 2 | 18 | 16 | 0 | 0 | 0 | 0 |
| 15 | 12 | 9 | 13 | 0 | 0 | 0 | 0 |
| 18 | 16 | 5 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 23 | 19 | 14 |
| 0 | 0 | 0 | 0 | 4 | 12 | 10 | 0 |
| 0 | 0 | 0 | 0 | 19 | 14 | 21 | 6 |
| 0 | 0 | 0 | 0 | 10 | 0 | 25 | 17 |
| 21 | 10 | 23 | 22 | 0 | 0 | 0 | 0 |
| 23 | 8 | 10 | 6 | 0 | 0 | 0 | 0 |
| 23 | 22 | 8 | 19 | 0 | 0 | 0 | 0 |
| 10 | 6 | 6 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 3 | 2 | 0 |
| 0 | 0 | 0 | 0 | 11 | 28 | 18 | 27 |
| 0 | 0 | 0 | 0 | 27 | 0 | 1 | 3 |
| 0 | 0 | 0 | 0 | 11 | 2 | 11 | 28 |
G:=sub<GL(8,GF(29))| [0,0,8,2,0,0,0,0,0,0,11,21,0,0,0,0,21,27,0,0,0,0,0,0,18,8,0,0,0,0,0,0,0,0,0,0,8,13,0,0,0,0,0,0,24,21,0,0,0,0,0,0,0,0,8,13,0,0,0,0,0,0,24,21],[0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[20,24,15,18,0,0,0,0,16,2,12,16,0,0,0,0,15,18,9,5,0,0,0,0,12,16,13,27,0,0,0,0,0,0,0,0,8,4,19,10,0,0,0,0,23,12,14,0,0,0,0,0,19,10,21,25,0,0,0,0,14,0,6,17],[21,23,23,10,0,0,0,0,10,8,22,6,0,0,0,0,23,10,8,6,0,0,0,0,22,6,19,21,0,0,0,0,0,0,0,0,1,11,27,11,0,0,0,0,3,28,0,2,0,0,0,0,2,18,1,11,0,0,0,0,0,27,3,28] >;
C42.157D14 in GAP, Magma, Sage, TeX
C_4^2._{157}D_{14} % in TeX
G:=Group("C4^2.157D14"); // GroupNames label
G:=SmallGroup(448,1152);
// by ID
G=gap.SmallGroup(448,1152);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,1571,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^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^13>;
// generators/relations