metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.148D14, C14.952- 1+4, C14.1302+ 1+4, (C4×D7)⋊1Q8, C28⋊Q8⋊35C2, C4.39(Q8×D7), D14.4(C2×Q8), C28.50(C2×Q8), C42.C2⋊4D7, C4⋊C4.111D14, C28⋊2Q8⋊32C2, Dic7.6(C2×Q8), Dic7.Q8⋊32C2, (C2×C28).87C23, D14⋊Q8.2C2, C28.3Q8⋊33C2, C42⋊D7.6C2, C14.42(C22×Q8), (C4×C28).193C22, (C2×C14).233C24, D14⋊C4.39C22, D14⋊2Q8.11C2, C2.55(D4⋊8D14), C4⋊Dic7.240C22, C22.254(C23×D7), Dic7⋊C4.122C22, C7⋊4(C23.41C23), (C2×Dic7).121C23, (C4×Dic7).140C22, (C2×Dic14).40C22, (C22×D7).220C23, C2.57(D4.10D14), C2.25(C2×Q8×D7), (D7×C4⋊C4).11C2, (C7×C42.C2)⋊6C2, C4⋊C4⋊7D7.12C2, (C2×C4×D7).124C22, (C7×C4⋊C4).188C22, (C2×C4).203(C22×D7), SmallGroup(448,1142)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.148D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=c13 >
Subgroups: 892 in 206 conjugacy classes, 103 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C22⋊Q8, C42.C2, C42.C2, C4⋊Q8, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C23.41C23, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C28⋊2Q8, C42⋊D7, C28⋊Q8, C28⋊Q8, Dic7.Q8, C28.3Q8, D7×C4⋊C4, C4⋊C4⋊7D7, D14⋊Q8, D14⋊2Q8, C7×C42.C2, C42.148D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C24, D14, C22×Q8, 2+ 1+4, 2- 1+4, C22×D7, C23.41C23, Q8×D7, C23×D7, C2×Q8×D7, D4⋊8D14, D4.10D14, C42.148D14
►On 224 points
Generators in S224
(1 180 69 112)(2 85 70 181)(3 182 71 86)(4 87 72 183)(5 184 73 88)(6 89 74 185)(7 186 75 90)(8 91 76 187)(9 188 77 92)(10 93 78 189)(11 190 79 94)(12 95 80 191)(13 192 81 96)(14 97 82 193)(15 194 83 98)(16 99 84 195)(17 196 57 100)(18 101 58 169)(19 170 59 102)(20 103 60 171)(21 172 61 104)(22 105 62 173)(23 174 63 106)(24 107 64 175)(25 176 65 108)(26 109 66 177)(27 178 67 110)(28 111 68 179)(29 213 115 154)(30 155 116 214)(31 215 117 156)(32 157 118 216)(33 217 119 158)(34 159 120 218)(35 219 121 160)(36 161 122 220)(37 221 123 162)(38 163 124 222)(39 223 125 164)(40 165 126 224)(41 197 127 166)(42 167 128 198)(43 199 129 168)(44 141 130 200)(45 201 131 142)(46 143 132 202)(47 203 133 144)(48 145 134 204)(49 205 135 146)(50 147 136 206)(51 207 137 148)(52 149 138 208)(53 209 139 150)(54 151 140 210)(55 211 113 152)(56 153 114 212)
(1 134 15 120)(2 35 16 49)(3 136 17 122)(4 37 18 51)(5 138 19 124)(6 39 20 53)(7 140 21 126)(8 41 22 55)(9 114 23 128)(10 43 24 29)(11 116 25 130)(12 45 26 31)(13 118 27 132)(14 47 28 33)(30 65 44 79)(32 67 46 81)(34 69 48 83)(36 71 50 57)(38 73 52 59)(40 75 54 61)(42 77 56 63)(58 137 72 123)(60 139 74 125)(62 113 76 127)(64 115 78 129)(66 117 80 131)(68 119 82 133)(70 121 84 135)(85 219 99 205)(86 147 100 161)(87 221 101 207)(88 149 102 163)(89 223 103 209)(90 151 104 165)(91 197 105 211)(92 153 106 167)(93 199 107 213)(94 155 108 141)(95 201 109 215)(96 157 110 143)(97 203 111 217)(98 159 112 145)(142 177 156 191)(144 179 158 193)(146 181 160 195)(148 183 162 169)(150 185 164 171)(152 187 166 173)(154 189 168 175)(170 222 184 208)(172 224 186 210)(174 198 188 212)(176 200 190 214)(178 202 192 216)(180 204 194 218)(182 206 196 220)
(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 124 43 138)(30 137 44 123)(31 122 45 136)(32 135 46 121)(33 120 47 134)(34 133 48 119)(35 118 49 132)(36 131 50 117)(37 116 51 130)(38 129 52 115)(39 114 53 128)(40 127 54 113)(41 140 55 126)(42 125 56 139)(57 66 71 80)(58 79 72 65)(59 64 73 78)(60 77 74 63)(61 62 75 76)(67 84 81 70)(68 69 82 83)(85 110 99 96)(86 95 100 109)(87 108 101 94)(88 93 102 107)(89 106 103 92)(90 91 104 105)(97 98 111 112)(141 221 155 207)(142 206 156 220)(143 219 157 205)(144 204 158 218)(145 217 159 203)(146 202 160 216)(147 215 161 201)(148 200 162 214)(149 213 163 199)(150 198 164 212)(151 211 165 197)(152 224 166 210)(153 209 167 223)(154 222 168 208)(169 190 183 176)(170 175 184 189)(171 188 185 174)(172 173 186 187)(177 182 191 196)(178 195 192 181)(179 180 193 194)
G:=sub<Sym(224)| (1,180,69,112)(2,85,70,181)(3,182,71,86)(4,87,72,183)(5,184,73,88)(6,89,74,185)(7,186,75,90)(8,91,76,187)(9,188,77,92)(10,93,78,189)(11,190,79,94)(12,95,80,191)(13,192,81,96)(14,97,82,193)(15,194,83,98)(16,99,84,195)(17,196,57,100)(18,101,58,169)(19,170,59,102)(20,103,60,171)(21,172,61,104)(22,105,62,173)(23,174,63,106)(24,107,64,175)(25,176,65,108)(26,109,66,177)(27,178,67,110)(28,111,68,179)(29,213,115,154)(30,155,116,214)(31,215,117,156)(32,157,118,216)(33,217,119,158)(34,159,120,218)(35,219,121,160)(36,161,122,220)(37,221,123,162)(38,163,124,222)(39,223,125,164)(40,165,126,224)(41,197,127,166)(42,167,128,198)(43,199,129,168)(44,141,130,200)(45,201,131,142)(46,143,132,202)(47,203,133,144)(48,145,134,204)(49,205,135,146)(50,147,136,206)(51,207,137,148)(52,149,138,208)(53,209,139,150)(54,151,140,210)(55,211,113,152)(56,153,114,212), (1,134,15,120)(2,35,16,49)(3,136,17,122)(4,37,18,51)(5,138,19,124)(6,39,20,53)(7,140,21,126)(8,41,22,55)(9,114,23,128)(10,43,24,29)(11,116,25,130)(12,45,26,31)(13,118,27,132)(14,47,28,33)(30,65,44,79)(32,67,46,81)(34,69,48,83)(36,71,50,57)(38,73,52,59)(40,75,54,61)(42,77,56,63)(58,137,72,123)(60,139,74,125)(62,113,76,127)(64,115,78,129)(66,117,80,131)(68,119,82,133)(70,121,84,135)(85,219,99,205)(86,147,100,161)(87,221,101,207)(88,149,102,163)(89,223,103,209)(90,151,104,165)(91,197,105,211)(92,153,106,167)(93,199,107,213)(94,155,108,141)(95,201,109,215)(96,157,110,143)(97,203,111,217)(98,159,112,145)(142,177,156,191)(144,179,158,193)(146,181,160,195)(148,183,162,169)(150,185,164,171)(152,187,166,173)(154,189,168,175)(170,222,184,208)(172,224,186,210)(174,198,188,212)(176,200,190,214)(178,202,192,216)(180,204,194,218)(182,206,196,220), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,124,43,138)(30,137,44,123)(31,122,45,136)(32,135,46,121)(33,120,47,134)(34,133,48,119)(35,118,49,132)(36,131,50,117)(37,116,51,130)(38,129,52,115)(39,114,53,128)(40,127,54,113)(41,140,55,126)(42,125,56,139)(57,66,71,80)(58,79,72,65)(59,64,73,78)(60,77,74,63)(61,62,75,76)(67,84,81,70)(68,69,82,83)(85,110,99,96)(86,95,100,109)(87,108,101,94)(88,93,102,107)(89,106,103,92)(90,91,104,105)(97,98,111,112)(141,221,155,207)(142,206,156,220)(143,219,157,205)(144,204,158,218)(145,217,159,203)(146,202,160,216)(147,215,161,201)(148,200,162,214)(149,213,163,199)(150,198,164,212)(151,211,165,197)(152,224,166,210)(153,209,167,223)(154,222,168,208)(169,190,183,176)(170,175,184,189)(171,188,185,174)(172,173,186,187)(177,182,191,196)(178,195,192,181)(179,180,193,194)>;
G:=Group( (1,180,69,112)(2,85,70,181)(3,182,71,86)(4,87,72,183)(5,184,73,88)(6,89,74,185)(7,186,75,90)(8,91,76,187)(9,188,77,92)(10,93,78,189)(11,190,79,94)(12,95,80,191)(13,192,81,96)(14,97,82,193)(15,194,83,98)(16,99,84,195)(17,196,57,100)(18,101,58,169)(19,170,59,102)(20,103,60,171)(21,172,61,104)(22,105,62,173)(23,174,63,106)(24,107,64,175)(25,176,65,108)(26,109,66,177)(27,178,67,110)(28,111,68,179)(29,213,115,154)(30,155,116,214)(31,215,117,156)(32,157,118,216)(33,217,119,158)(34,159,120,218)(35,219,121,160)(36,161,122,220)(37,221,123,162)(38,163,124,222)(39,223,125,164)(40,165,126,224)(41,197,127,166)(42,167,128,198)(43,199,129,168)(44,141,130,200)(45,201,131,142)(46,143,132,202)(47,203,133,144)(48,145,134,204)(49,205,135,146)(50,147,136,206)(51,207,137,148)(52,149,138,208)(53,209,139,150)(54,151,140,210)(55,211,113,152)(56,153,114,212), (1,134,15,120)(2,35,16,49)(3,136,17,122)(4,37,18,51)(5,138,19,124)(6,39,20,53)(7,140,21,126)(8,41,22,55)(9,114,23,128)(10,43,24,29)(11,116,25,130)(12,45,26,31)(13,118,27,132)(14,47,28,33)(30,65,44,79)(32,67,46,81)(34,69,48,83)(36,71,50,57)(38,73,52,59)(40,75,54,61)(42,77,56,63)(58,137,72,123)(60,139,74,125)(62,113,76,127)(64,115,78,129)(66,117,80,131)(68,119,82,133)(70,121,84,135)(85,219,99,205)(86,147,100,161)(87,221,101,207)(88,149,102,163)(89,223,103,209)(90,151,104,165)(91,197,105,211)(92,153,106,167)(93,199,107,213)(94,155,108,141)(95,201,109,215)(96,157,110,143)(97,203,111,217)(98,159,112,145)(142,177,156,191)(144,179,158,193)(146,181,160,195)(148,183,162,169)(150,185,164,171)(152,187,166,173)(154,189,168,175)(170,222,184,208)(172,224,186,210)(174,198,188,212)(176,200,190,214)(178,202,192,216)(180,204,194,218)(182,206,196,220), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,124,43,138)(30,137,44,123)(31,122,45,136)(32,135,46,121)(33,120,47,134)(34,133,48,119)(35,118,49,132)(36,131,50,117)(37,116,51,130)(38,129,52,115)(39,114,53,128)(40,127,54,113)(41,140,55,126)(42,125,56,139)(57,66,71,80)(58,79,72,65)(59,64,73,78)(60,77,74,63)(61,62,75,76)(67,84,81,70)(68,69,82,83)(85,110,99,96)(86,95,100,109)(87,108,101,94)(88,93,102,107)(89,106,103,92)(90,91,104,105)(97,98,111,112)(141,221,155,207)(142,206,156,220)(143,219,157,205)(144,204,158,218)(145,217,159,203)(146,202,160,216)(147,215,161,201)(148,200,162,214)(149,213,163,199)(150,198,164,212)(151,211,165,197)(152,224,166,210)(153,209,167,223)(154,222,168,208)(169,190,183,176)(170,175,184,189)(171,188,185,174)(172,173,186,187)(177,182,191,196)(178,195,192,181)(179,180,193,194) );
G=PermutationGroup([[(1,180,69,112),(2,85,70,181),(3,182,71,86),(4,87,72,183),(5,184,73,88),(6,89,74,185),(7,186,75,90),(8,91,76,187),(9,188,77,92),(10,93,78,189),(11,190,79,94),(12,95,80,191),(13,192,81,96),(14,97,82,193),(15,194,83,98),(16,99,84,195),(17,196,57,100),(18,101,58,169),(19,170,59,102),(20,103,60,171),(21,172,61,104),(22,105,62,173),(23,174,63,106),(24,107,64,175),(25,176,65,108),(26,109,66,177),(27,178,67,110),(28,111,68,179),(29,213,115,154),(30,155,116,214),(31,215,117,156),(32,157,118,216),(33,217,119,158),(34,159,120,218),(35,219,121,160),(36,161,122,220),(37,221,123,162),(38,163,124,222),(39,223,125,164),(40,165,126,224),(41,197,127,166),(42,167,128,198),(43,199,129,168),(44,141,130,200),(45,201,131,142),(46,143,132,202),(47,203,133,144),(48,145,134,204),(49,205,135,146),(50,147,136,206),(51,207,137,148),(52,149,138,208),(53,209,139,150),(54,151,140,210),(55,211,113,152),(56,153,114,212)], [(1,134,15,120),(2,35,16,49),(3,136,17,122),(4,37,18,51),(5,138,19,124),(6,39,20,53),(7,140,21,126),(8,41,22,55),(9,114,23,128),(10,43,24,29),(11,116,25,130),(12,45,26,31),(13,118,27,132),(14,47,28,33),(30,65,44,79),(32,67,46,81),(34,69,48,83),(36,71,50,57),(38,73,52,59),(40,75,54,61),(42,77,56,63),(58,137,72,123),(60,139,74,125),(62,113,76,127),(64,115,78,129),(66,117,80,131),(68,119,82,133),(70,121,84,135),(85,219,99,205),(86,147,100,161),(87,221,101,207),(88,149,102,163),(89,223,103,209),(90,151,104,165),(91,197,105,211),(92,153,106,167),(93,199,107,213),(94,155,108,141),(95,201,109,215),(96,157,110,143),(97,203,111,217),(98,159,112,145),(142,177,156,191),(144,179,158,193),(146,181,160,195),(148,183,162,169),(150,185,164,171),(152,187,166,173),(154,189,168,175),(170,222,184,208),(172,224,186,210),(174,198,188,212),(176,200,190,214),(178,202,192,216),(180,204,194,218),(182,206,196,220)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,124,43,138),(30,137,44,123),(31,122,45,136),(32,135,46,121),(33,120,47,134),(34,133,48,119),(35,118,49,132),(36,131,50,117),(37,116,51,130),(38,129,52,115),(39,114,53,128),(40,127,54,113),(41,140,55,126),(42,125,56,139),(57,66,71,80),(58,79,72,65),(59,64,73,78),(60,77,74,63),(61,62,75,76),(67,84,81,70),(68,69,82,83),(85,110,99,96),(86,95,100,109),(87,108,101,94),(88,93,102,107),(89,106,103,92),(90,91,104,105),(97,98,111,112),(141,221,155,207),(142,206,156,220),(143,219,157,205),(144,204,158,218),(145,217,159,203),(146,202,160,216),(147,215,161,201),(148,200,162,214),(149,213,163,199),(150,198,164,212),(151,211,165,197),(152,224,166,210),(153,209,167,223),(154,222,168,208),(169,190,183,176),(170,175,184,189),(171,188,185,174),(172,173,186,187),(177,182,191,196),(178,195,192,181),(179,180,193,194)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8×D7 | D4⋊8D14 | D4.10D14 |
| kernel | C42.148D14 | C28⋊2Q8 | C42⋊D7 | C28⋊Q8 | Dic7.Q8 | C28.3Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14⋊Q8 | D14⋊2Q8 | C7×C42.C2 | C4×D7 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 3 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 3 | 3 | 18 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.148D14 ►in GL8(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 19 | 21 | 19 |
| 0 | 0 | 0 | 0 | 23 | 21 | 7 | 27 |
| 0 | 0 | 0 | 0 | 15 | 24 | 25 | 2 |
| 0 | 0 | 0 | 0 | 16 | 16 | 11 | 16 |
| 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 | 16 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 1 | 21 | 23 |
| 0 | 0 | 0 | 0 | 9 | 23 | 6 | 8 |
| 13 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 16 | 10 | 24 |
| 0 | 0 | 0 | 0 | 14 | 4 | 16 | 13 |
| 0 | 0 | 0 | 0 | 10 | 24 | 6 | 9 |
| 0 | 0 | 0 | 0 | 10 | 27 | 26 | 26 |
| 0 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 5 | 24 | 10 |
| 0 | 0 | 0 | 0 | 15 | 25 | 13 | 16 |
| 0 | 0 | 0 | 0 | 9 | 3 | 9 | 6 |
| 0 | 0 | 0 | 0 | 11 | 19 | 26 | 26 |
G:=sub<GL(8,GF(29))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,25,23,15,16,0,0,0,0,19,21,24,16,0,0,0,0,21,7,25,11,0,0,0,0,19,27,2,16],[0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,9,2,9,0,0,0,0,23,13,1,23,0,0,0,0,0,0,21,6,0,0,0,0,0,0,23,8],[13,10,0,0,0,0,0,0,19,19,0,0,0,0,0,0,0,0,16,19,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,22,14,10,10,0,0,0,0,16,4,24,27,0,0,0,0,10,16,6,26,0,0,0,0,24,13,9,26],[0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,27,15,9,11,0,0,0,0,5,25,3,19,0,0,0,0,24,13,9,26,0,0,0,0,10,16,6,26] >;
C42.148D14 in GAP, Magma, Sage, TeX
C_4^2._{148}D_{14} % in TeX
G:=Group("C4^2.148D14"); // GroupNames label
G:=SmallGroup(448,1142);
// by ID
G=gap.SmallGroup(448,1142);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,297,192,18822]);
// 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=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations