metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.145D14, C14.932- 1+4, C14.742+ 1+4, C4.4D4⋊17D7, (C2×Q8).84D14, D14⋊D4⋊43C2, D14⋊3Q8⋊34C2, (C2×D4).113D14, C4.D28⋊31C2, C22⋊C4.38D14, C28.6Q8⋊29C2, Dic7⋊D4⋊35C2, D14.D4⋊47C2, (C2×C14).228C24, (C2×C28).633C23, (C4×C28).222C22, D14⋊C4.73C22, (C2×D28).35C22, C4⋊Dic7.52C22, C2.78(D4⋊6D14), C2.54(D4⋊8D14), C23.50(C22×D7), C22⋊Dic14⋊43C2, (D4×C14).213C22, C22.D28⋊28C2, Dic7⋊C4.84C22, (C22×C14).58C23, (Q8×C14).131C22, C22.249(C23×D7), C23.D7.60C22, C7⋊4(C22.56C24), (C2×Dic7).118C23, (C2×Dic14).39C22, (C22×D7).100C23, C2.54(D4.10D14), (C22×Dic7).147C22, (C7×C4.4D4)⋊20C2, (C2×C4×D7).123C22, (C2×C4).201(C22×D7), (C2×C7⋊D4).66C22, (C7×C22⋊C4).69C22, SmallGroup(448,1137)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.145D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1100 in 220 conjugacy classes, 91 normal (31 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C4.4D4, C42.C2, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C22.56C24, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C28.6Q8, C4.D28, C22⋊Dic14, D14.D4, D14⋊D4, C22.D28, Dic7⋊D4, D14⋊3Q8, C7×C4.4D4, C42.145D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.56C24, C23×D7, D4⋊6D14, D4⋊8D14, D4.10D14, C42.145D14
►On 224 points
Generators in S224
(1 152 212 62)(2 77 213 167)(3 154 214 64)(4 79 215 141)(5 156 216 66)(6 81 217 143)(7 158 218 68)(8 83 219 145)(9 160 220 70)(10 57 221 147)(11 162 222 72)(12 59 223 149)(13 164 224 74)(14 61 197 151)(15 166 198 76)(16 63 199 153)(17 168 200 78)(18 65 201 155)(19 142 202 80)(20 67 203 157)(21 144 204 82)(22 69 205 159)(23 146 206 84)(24 71 207 161)(25 148 208 58)(26 73 209 163)(27 150 210 60)(28 75 211 165)(29 129 183 98)(30 85 184 116)(31 131 185 100)(32 87 186 118)(33 133 187 102)(34 89 188 120)(35 135 189 104)(36 91 190 122)(37 137 191 106)(38 93 192 124)(39 139 193 108)(40 95 194 126)(41 113 195 110)(42 97 196 128)(43 115 169 112)(44 99 170 130)(45 117 171 86)(46 101 172 132)(47 119 173 88)(48 103 174 134)(49 121 175 90)(50 105 176 136)(51 123 177 92)(52 107 178 138)(53 125 179 94)(54 109 180 140)(55 127 181 96)(56 111 182 114)
(1 69 15 83)(2 84 16 70)(3 71 17 57)(4 58 18 72)(5 73 19 59)(6 60 20 74)(7 75 21 61)(8 62 22 76)(9 77 23 63)(10 64 24 78)(11 79 25 65)(12 66 26 80)(13 81 27 67)(14 68 28 82)(29 122 43 136)(30 137 44 123)(31 124 45 138)(32 139 46 125)(33 126 47 140)(34 113 48 127)(35 128 49 114)(36 115 50 129)(37 130 51 116)(38 117 52 131)(39 132 53 118)(40 119 54 133)(41 134 55 120)(42 121 56 135)(85 191 99 177)(86 178 100 192)(87 193 101 179)(88 180 102 194)(89 195 103 181)(90 182 104 196)(91 169 105 183)(92 184 106 170)(93 171 107 185)(94 186 108 172)(95 173 109 187)(96 188 110 174)(97 175 111 189)(98 190 112 176)(141 208 155 222)(142 223 156 209)(143 210 157 224)(144 197 158 211)(145 212 159 198)(146 199 160 213)(147 214 161 200)(148 201 162 215)(149 216 163 202)(150 203 164 217)(151 218 165 204)(152 205 166 219)(153 220 167 206)(154 207 168 221)
(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 52 15 38)(2 37 16 51)(3 50 17 36)(4 35 18 49)(5 48 19 34)(6 33 20 47)(7 46 21 32)(8 31 22 45)(9 44 23 30)(10 29 24 43)(11 42 25 56)(12 55 26 41)(13 40 27 54)(14 53 28 39)(57 98 71 112)(58 111 72 97)(59 96 73 110)(60 109 74 95)(61 94 75 108)(62 107 76 93)(63 92 77 106)(64 105 78 91)(65 90 79 104)(66 103 80 89)(67 88 81 102)(68 101 82 87)(69 86 83 100)(70 99 84 85)(113 149 127 163)(114 162 128 148)(115 147 129 161)(116 160 130 146)(117 145 131 159)(118 158 132 144)(119 143 133 157)(120 156 134 142)(121 141 135 155)(122 154 136 168)(123 167 137 153)(124 152 138 166)(125 165 139 151)(126 150 140 164)(169 221 183 207)(170 206 184 220)(171 219 185 205)(172 204 186 218)(173 217 187 203)(174 202 188 216)(175 215 189 201)(176 200 190 214)(177 213 191 199)(178 198 192 212)(179 211 193 197)(180 224 194 210)(181 209 195 223)(182 222 196 208)
G:=sub<Sym(224)| (1,152,212,62)(2,77,213,167)(3,154,214,64)(4,79,215,141)(5,156,216,66)(6,81,217,143)(7,158,218,68)(8,83,219,145)(9,160,220,70)(10,57,221,147)(11,162,222,72)(12,59,223,149)(13,164,224,74)(14,61,197,151)(15,166,198,76)(16,63,199,153)(17,168,200,78)(18,65,201,155)(19,142,202,80)(20,67,203,157)(21,144,204,82)(22,69,205,159)(23,146,206,84)(24,71,207,161)(25,148,208,58)(26,73,209,163)(27,150,210,60)(28,75,211,165)(29,129,183,98)(30,85,184,116)(31,131,185,100)(32,87,186,118)(33,133,187,102)(34,89,188,120)(35,135,189,104)(36,91,190,122)(37,137,191,106)(38,93,192,124)(39,139,193,108)(40,95,194,126)(41,113,195,110)(42,97,196,128)(43,115,169,112)(44,99,170,130)(45,117,171,86)(46,101,172,132)(47,119,173,88)(48,103,174,134)(49,121,175,90)(50,105,176,136)(51,123,177,92)(52,107,178,138)(53,125,179,94)(54,109,180,140)(55,127,181,96)(56,111,182,114), (1,69,15,83)(2,84,16,70)(3,71,17,57)(4,58,18,72)(5,73,19,59)(6,60,20,74)(7,75,21,61)(8,62,22,76)(9,77,23,63)(10,64,24,78)(11,79,25,65)(12,66,26,80)(13,81,27,67)(14,68,28,82)(29,122,43,136)(30,137,44,123)(31,124,45,138)(32,139,46,125)(33,126,47,140)(34,113,48,127)(35,128,49,114)(36,115,50,129)(37,130,51,116)(38,117,52,131)(39,132,53,118)(40,119,54,133)(41,134,55,120)(42,121,56,135)(85,191,99,177)(86,178,100,192)(87,193,101,179)(88,180,102,194)(89,195,103,181)(90,182,104,196)(91,169,105,183)(92,184,106,170)(93,171,107,185)(94,186,108,172)(95,173,109,187)(96,188,110,174)(97,175,111,189)(98,190,112,176)(141,208,155,222)(142,223,156,209)(143,210,157,224)(144,197,158,211)(145,212,159,198)(146,199,160,213)(147,214,161,200)(148,201,162,215)(149,216,163,202)(150,203,164,217)(151,218,165,204)(152,205,166,219)(153,220,167,206)(154,207,168,221), (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), (1,52,15,38)(2,37,16,51)(3,50,17,36)(4,35,18,49)(5,48,19,34)(6,33,20,47)(7,46,21,32)(8,31,22,45)(9,44,23,30)(10,29,24,43)(11,42,25,56)(12,55,26,41)(13,40,27,54)(14,53,28,39)(57,98,71,112)(58,111,72,97)(59,96,73,110)(60,109,74,95)(61,94,75,108)(62,107,76,93)(63,92,77,106)(64,105,78,91)(65,90,79,104)(66,103,80,89)(67,88,81,102)(68,101,82,87)(69,86,83,100)(70,99,84,85)(113,149,127,163)(114,162,128,148)(115,147,129,161)(116,160,130,146)(117,145,131,159)(118,158,132,144)(119,143,133,157)(120,156,134,142)(121,141,135,155)(122,154,136,168)(123,167,137,153)(124,152,138,166)(125,165,139,151)(126,150,140,164)(169,221,183,207)(170,206,184,220)(171,219,185,205)(172,204,186,218)(173,217,187,203)(174,202,188,216)(175,215,189,201)(176,200,190,214)(177,213,191,199)(178,198,192,212)(179,211,193,197)(180,224,194,210)(181,209,195,223)(182,222,196,208)>;
G:=Group( (1,152,212,62)(2,77,213,167)(3,154,214,64)(4,79,215,141)(5,156,216,66)(6,81,217,143)(7,158,218,68)(8,83,219,145)(9,160,220,70)(10,57,221,147)(11,162,222,72)(12,59,223,149)(13,164,224,74)(14,61,197,151)(15,166,198,76)(16,63,199,153)(17,168,200,78)(18,65,201,155)(19,142,202,80)(20,67,203,157)(21,144,204,82)(22,69,205,159)(23,146,206,84)(24,71,207,161)(25,148,208,58)(26,73,209,163)(27,150,210,60)(28,75,211,165)(29,129,183,98)(30,85,184,116)(31,131,185,100)(32,87,186,118)(33,133,187,102)(34,89,188,120)(35,135,189,104)(36,91,190,122)(37,137,191,106)(38,93,192,124)(39,139,193,108)(40,95,194,126)(41,113,195,110)(42,97,196,128)(43,115,169,112)(44,99,170,130)(45,117,171,86)(46,101,172,132)(47,119,173,88)(48,103,174,134)(49,121,175,90)(50,105,176,136)(51,123,177,92)(52,107,178,138)(53,125,179,94)(54,109,180,140)(55,127,181,96)(56,111,182,114), (1,69,15,83)(2,84,16,70)(3,71,17,57)(4,58,18,72)(5,73,19,59)(6,60,20,74)(7,75,21,61)(8,62,22,76)(9,77,23,63)(10,64,24,78)(11,79,25,65)(12,66,26,80)(13,81,27,67)(14,68,28,82)(29,122,43,136)(30,137,44,123)(31,124,45,138)(32,139,46,125)(33,126,47,140)(34,113,48,127)(35,128,49,114)(36,115,50,129)(37,130,51,116)(38,117,52,131)(39,132,53,118)(40,119,54,133)(41,134,55,120)(42,121,56,135)(85,191,99,177)(86,178,100,192)(87,193,101,179)(88,180,102,194)(89,195,103,181)(90,182,104,196)(91,169,105,183)(92,184,106,170)(93,171,107,185)(94,186,108,172)(95,173,109,187)(96,188,110,174)(97,175,111,189)(98,190,112,176)(141,208,155,222)(142,223,156,209)(143,210,157,224)(144,197,158,211)(145,212,159,198)(146,199,160,213)(147,214,161,200)(148,201,162,215)(149,216,163,202)(150,203,164,217)(151,218,165,204)(152,205,166,219)(153,220,167,206)(154,207,168,221), (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), (1,52,15,38)(2,37,16,51)(3,50,17,36)(4,35,18,49)(5,48,19,34)(6,33,20,47)(7,46,21,32)(8,31,22,45)(9,44,23,30)(10,29,24,43)(11,42,25,56)(12,55,26,41)(13,40,27,54)(14,53,28,39)(57,98,71,112)(58,111,72,97)(59,96,73,110)(60,109,74,95)(61,94,75,108)(62,107,76,93)(63,92,77,106)(64,105,78,91)(65,90,79,104)(66,103,80,89)(67,88,81,102)(68,101,82,87)(69,86,83,100)(70,99,84,85)(113,149,127,163)(114,162,128,148)(115,147,129,161)(116,160,130,146)(117,145,131,159)(118,158,132,144)(119,143,133,157)(120,156,134,142)(121,141,135,155)(122,154,136,168)(123,167,137,153)(124,152,138,166)(125,165,139,151)(126,150,140,164)(169,221,183,207)(170,206,184,220)(171,219,185,205)(172,204,186,218)(173,217,187,203)(174,202,188,216)(175,215,189,201)(176,200,190,214)(177,213,191,199)(178,198,192,212)(179,211,193,197)(180,224,194,210)(181,209,195,223)(182,222,196,208) );
G=PermutationGroup([[(1,152,212,62),(2,77,213,167),(3,154,214,64),(4,79,215,141),(5,156,216,66),(6,81,217,143),(7,158,218,68),(8,83,219,145),(9,160,220,70),(10,57,221,147),(11,162,222,72),(12,59,223,149),(13,164,224,74),(14,61,197,151),(15,166,198,76),(16,63,199,153),(17,168,200,78),(18,65,201,155),(19,142,202,80),(20,67,203,157),(21,144,204,82),(22,69,205,159),(23,146,206,84),(24,71,207,161),(25,148,208,58),(26,73,209,163),(27,150,210,60),(28,75,211,165),(29,129,183,98),(30,85,184,116),(31,131,185,100),(32,87,186,118),(33,133,187,102),(34,89,188,120),(35,135,189,104),(36,91,190,122),(37,137,191,106),(38,93,192,124),(39,139,193,108),(40,95,194,126),(41,113,195,110),(42,97,196,128),(43,115,169,112),(44,99,170,130),(45,117,171,86),(46,101,172,132),(47,119,173,88),(48,103,174,134),(49,121,175,90),(50,105,176,136),(51,123,177,92),(52,107,178,138),(53,125,179,94),(54,109,180,140),(55,127,181,96),(56,111,182,114)], [(1,69,15,83),(2,84,16,70),(3,71,17,57),(4,58,18,72),(5,73,19,59),(6,60,20,74),(7,75,21,61),(8,62,22,76),(9,77,23,63),(10,64,24,78),(11,79,25,65),(12,66,26,80),(13,81,27,67),(14,68,28,82),(29,122,43,136),(30,137,44,123),(31,124,45,138),(32,139,46,125),(33,126,47,140),(34,113,48,127),(35,128,49,114),(36,115,50,129),(37,130,51,116),(38,117,52,131),(39,132,53,118),(40,119,54,133),(41,134,55,120),(42,121,56,135),(85,191,99,177),(86,178,100,192),(87,193,101,179),(88,180,102,194),(89,195,103,181),(90,182,104,196),(91,169,105,183),(92,184,106,170),(93,171,107,185),(94,186,108,172),(95,173,109,187),(96,188,110,174),(97,175,111,189),(98,190,112,176),(141,208,155,222),(142,223,156,209),(143,210,157,224),(144,197,158,211),(145,212,159,198),(146,199,160,213),(147,214,161,200),(148,201,162,215),(149,216,163,202),(150,203,164,217),(151,218,165,204),(152,205,166,219),(153,220,167,206),(154,207,168,221)], [(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)], [(1,52,15,38),(2,37,16,51),(3,50,17,36),(4,35,18,49),(5,48,19,34),(6,33,20,47),(7,46,21,32),(8,31,22,45),(9,44,23,30),(10,29,24,43),(11,42,25,56),(12,55,26,41),(13,40,27,54),(14,53,28,39),(57,98,71,112),(58,111,72,97),(59,96,73,110),(60,109,74,95),(61,94,75,108),(62,107,76,93),(63,92,77,106),(64,105,78,91),(65,90,79,104),(66,103,80,89),(67,88,81,102),(68,101,82,87),(69,86,83,100),(70,99,84,85),(113,149,127,163),(114,162,128,148),(115,147,129,161),(116,160,130,146),(117,145,131,159),(118,158,132,144),(119,143,133,157),(120,156,134,142),(121,141,135,155),(122,154,136,168),(123,167,137,153),(124,152,138,166),(125,165,139,151),(126,150,140,164),(169,221,183,207),(170,206,184,220),(171,219,185,205),(172,204,186,218),(173,217,187,203),(174,202,188,216),(175,215,189,201),(176,200,190,214),(177,213,191,199),(178,198,192,212),(179,211,193,197),(180,224,194,210),(181,209,195,223),(182,222,196,208)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4E | 4F | ··· | 4K | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 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 | 28 | 28 | 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 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D4⋊8D14 | D4.10D14 |
| kernel | C42.145D14 | C28.6Q8 | C4.D28 | C22⋊Dic14 | D14.D4 | D14⋊D4 | C22.D28 | Dic7⋊D4 | D14⋊3Q8 | C7×C4.4D4 | C4.4D4 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 3 | 3 | 12 | 3 | 3 | 2 | 1 | 6 | 6 | 6 |
Matrix representation of C42.145D14 ►in GL8(𝔽29)
| 16 | 24 | 10 | 6 | 0 | 0 | 0 | 0 |
| 5 | 13 | 21 | 20 | 0 | 0 | 0 | 0 |
| 17 | 21 | 27 | 5 | 0 | 0 | 0 | 0 |
| 1 | 23 | 28 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 | 23 | 10 |
| 0 | 0 | 0 | 0 | 14 | 9 | 27 | 7 |
| 0 | 0 | 0 | 0 | 27 | 7 | 25 | 14 |
| 0 | 0 | 0 | 0 | 16 | 10 | 1 | 4 |
| 1 | 0 | 3 | 4 | 0 | 0 | 0 | 0 |
| 0 | 1 | 25 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 28 | 0 | 0 | 0 | 0 | 0 |
| 14 | 25 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 15 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 25 |
| 26 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 26 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 11 | 12 | 26 | 0 | 0 | 0 | 0 |
| 28 | 12 | 18 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 10 | 3 | 5 |
| 0 | 0 | 0 | 0 | 19 | 22 | 10 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 19 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 6 |
| 0 | 12 | 10 | 0 | 0 | 0 | 0 | 0 |
| 12 | 0 | 7 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 9 |
G:=sub<GL(8,GF(29))| [16,5,17,1,0,0,0,0,24,13,21,23,0,0,0,0,10,21,27,28,0,0,0,0,6,20,5,2,0,0,0,0,0,0,0,0,20,14,27,16,0,0,0,0,15,9,7,10,0,0,0,0,23,27,25,1,0,0,0,0,10,7,14,4],[1,0,0,14,0,0,0,0,0,1,15,25,0,0,0,0,3,25,28,0,0,0,0,0,4,0,0,28,0,0,0,0,0,0,0,0,20,14,0,0,0,0,0,0,15,9,0,0,0,0,0,0,0,0,4,28,0,0,0,0,0,0,15,25],[26,26,13,28,0,0,0,0,3,22,11,12,0,0,0,0,0,0,12,18,0,0,0,0,0,0,26,27,0,0,0,0,0,0,0,0,10,19,0,0,0,0,0,0,10,22,0,0,0,0,0,0,3,10,20,20,0,0,0,0,5,24,19,6],[0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,10,7,9,27,0,0,0,0,0,19,12,20,0,0,0,0,0,0,0,0,20,4,0,0,0,0,0,0,9,9,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,25,9] >;
C42.145D14 in GAP, Magma, Sage, TeX
C_4^2._{145}D_{14} % in TeX
G:=Group("C4^2.145D14"); // GroupNames label
G:=SmallGroup(448,1137);
// by ID
G=gap.SmallGroup(448,1137);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=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^13>;
// generators/relations