metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.125D14, C14.92- 1+4, (Q8×D7)⋊5C4, (C4×Q8)⋊6D7, (Q8×C28)⋊7C2, (Q8×Dic7)⋊8C2, Q8.12(C4×D7), C4⋊C4.323D14, (C4×Dic14)⋊38C2, C14.25(C23×C4), C28.35(C22×C4), (C2×Q8).200D14, C42⋊D7.3C2, Dic7⋊3Q8⋊18C2, (C2×C14).116C24, (C4×C28).168C22, (C2×C28).495C23, Dic14.20(C2×C4), D14.19(C22×C4), C22.35(C23×D7), D14⋊C4.124C22, C4⋊Dic7.366C22, (Q8×C14).216C22, Dic7.11(C22×C4), (C4×Dic7).84C22, C2.4(D4.10D14), Dic7⋊C4.137C22, C2.2(Q8.10D14), C7⋊2(C23.32C23), (C2×Dic7).212C23, (C22×D7).175C23, (C2×Dic14).290C22, C4.35(C2×C4×D7), (C2×Q8×D7).6C2, (C4×D7).9(C2×C4), C2.27(D7×C22×C4), (C7×Q8).16(C2×C4), (C2×C4×D7).69C22, C4⋊C4⋊7D7.10C2, (C7×C4⋊C4).344C22, (C2×C4).288(C22×D7), SmallGroup(448,1025)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.125D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 932 in 266 conjugacy classes, 151 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C42⋊C2, C4×Q8, C4×Q8, C22×Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.32C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, Q8×D7, Q8×C14, C4×Dic14, C42⋊D7, Dic7⋊3Q8, C4⋊C4⋊7D7, Q8×Dic7, Q8×C28, C2×Q8×D7, C42.125D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2- 1+4, C4×D7, C22×D7, C23.32C23, C2×C4×D7, C23×D7, D7×C22×C4, Q8.10D14, D4.10D14, C42.125D14
►On 224 points
Generators in S224
(1 54 15 40)(2 41 16 55)(3 56 17 42)(4 43 18 29)(5 30 19 44)(6 45 20 31)(7 32 21 46)(8 47 22 33)(9 34 23 48)(10 49 24 35)(11 36 25 50)(12 51 26 37)(13 38 27 52)(14 53 28 39)(57 100 71 86)(58 87 72 101)(59 102 73 88)(60 89 74 103)(61 104 75 90)(62 91 76 105)(63 106 77 92)(64 93 78 107)(65 108 79 94)(66 95 80 109)(67 110 81 96)(68 97 82 111)(69 112 83 98)(70 99 84 85)(113 177 127 191)(114 192 128 178)(115 179 129 193)(116 194 130 180)(117 181 131 195)(118 196 132 182)(119 183 133 169)(120 170 134 184)(121 185 135 171)(122 172 136 186)(123 187 137 173)(124 174 138 188)(125 189 139 175)(126 176 140 190)(141 205 155 219)(142 220 156 206)(143 207 157 221)(144 222 158 208)(145 209 159 223)(146 224 160 210)(147 211 161 197)(148 198 162 212)(149 213 163 199)(150 200 164 214)(151 215 165 201)(152 202 166 216)(153 217 167 203)(154 204 168 218)
(1 212 85 134)(2 213 86 135)(3 214 87 136)(4 215 88 137)(5 216 89 138)(6 217 90 139)(7 218 91 140)(8 219 92 113)(9 220 93 114)(10 221 94 115)(11 222 95 116)(12 223 96 117)(13 224 97 118)(14 197 98 119)(15 198 99 120)(16 199 100 121)(17 200 101 122)(18 201 102 123)(19 202 103 124)(20 203 104 125)(21 204 105 126)(22 205 106 127)(23 206 107 128)(24 207 108 129)(25 208 109 130)(26 209 110 131)(27 210 111 132)(28 211 112 133)(29 151 73 187)(30 152 74 188)(31 153 75 189)(32 154 76 190)(33 155 77 191)(34 156 78 192)(35 157 79 193)(36 158 80 194)(37 159 81 195)(38 160 82 196)(39 161 83 169)(40 162 84 170)(41 163 57 171)(42 164 58 172)(43 165 59 173)(44 166 60 174)(45 167 61 175)(46 168 62 176)(47 141 63 177)(48 142 64 178)(49 143 65 179)(50 144 66 180)(51 145 67 181)(52 146 68 182)(53 147 69 183)(54 148 70 184)(55 149 71 185)(56 150 72 186)
(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 98 15 112)(2 111 16 97)(3 96 17 110)(4 109 18 95)(5 94 19 108)(6 107 20 93)(7 92 21 106)(8 105 22 91)(9 90 23 104)(10 103 24 89)(11 88 25 102)(12 101 26 87)(13 86 27 100)(14 99 28 85)(29 66 43 80)(30 79 44 65)(31 64 45 78)(32 77 46 63)(33 62 47 76)(34 75 48 61)(35 60 49 74)(36 73 50 59)(37 58 51 72)(38 71 52 57)(39 84 53 70)(40 69 54 83)(41 82 55 68)(42 67 56 81)(113 218 127 204)(114 203 128 217)(115 216 129 202)(116 201 130 215)(117 214 131 200)(118 199 132 213)(119 212 133 198)(120 197 134 211)(121 210 135 224)(122 223 136 209)(123 208 137 222)(124 221 138 207)(125 206 139 220)(126 219 140 205)(141 176 155 190)(142 189 156 175)(143 174 157 188)(144 187 158 173)(145 172 159 186)(146 185 160 171)(147 170 161 184)(148 183 162 169)(149 196 163 182)(150 181 164 195)(151 194 165 180)(152 179 166 193)(153 192 167 178)(154 177 168 191)
G:=sub<Sym(224)| (1,54,15,40)(2,41,16,55)(3,56,17,42)(4,43,18,29)(5,30,19,44)(6,45,20,31)(7,32,21,46)(8,47,22,33)(9,34,23,48)(10,49,24,35)(11,36,25,50)(12,51,26,37)(13,38,27,52)(14,53,28,39)(57,100,71,86)(58,87,72,101)(59,102,73,88)(60,89,74,103)(61,104,75,90)(62,91,76,105)(63,106,77,92)(64,93,78,107)(65,108,79,94)(66,95,80,109)(67,110,81,96)(68,97,82,111)(69,112,83,98)(70,99,84,85)(113,177,127,191)(114,192,128,178)(115,179,129,193)(116,194,130,180)(117,181,131,195)(118,196,132,182)(119,183,133,169)(120,170,134,184)(121,185,135,171)(122,172,136,186)(123,187,137,173)(124,174,138,188)(125,189,139,175)(126,176,140,190)(141,205,155,219)(142,220,156,206)(143,207,157,221)(144,222,158,208)(145,209,159,223)(146,224,160,210)(147,211,161,197)(148,198,162,212)(149,213,163,199)(150,200,164,214)(151,215,165,201)(152,202,166,216)(153,217,167,203)(154,204,168,218), (1,212,85,134)(2,213,86,135)(3,214,87,136)(4,215,88,137)(5,216,89,138)(6,217,90,139)(7,218,91,140)(8,219,92,113)(9,220,93,114)(10,221,94,115)(11,222,95,116)(12,223,96,117)(13,224,97,118)(14,197,98,119)(15,198,99,120)(16,199,100,121)(17,200,101,122)(18,201,102,123)(19,202,103,124)(20,203,104,125)(21,204,105,126)(22,205,106,127)(23,206,107,128)(24,207,108,129)(25,208,109,130)(26,209,110,131)(27,210,111,132)(28,211,112,133)(29,151,73,187)(30,152,74,188)(31,153,75,189)(32,154,76,190)(33,155,77,191)(34,156,78,192)(35,157,79,193)(36,158,80,194)(37,159,81,195)(38,160,82,196)(39,161,83,169)(40,162,84,170)(41,163,57,171)(42,164,58,172)(43,165,59,173)(44,166,60,174)(45,167,61,175)(46,168,62,176)(47,141,63,177)(48,142,64,178)(49,143,65,179)(50,144,66,180)(51,145,67,181)(52,146,68,182)(53,147,69,183)(54,148,70,184)(55,149,71,185)(56,150,72,186), (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), (1,98,15,112)(2,111,16,97)(3,96,17,110)(4,109,18,95)(5,94,19,108)(6,107,20,93)(7,92,21,106)(8,105,22,91)(9,90,23,104)(10,103,24,89)(11,88,25,102)(12,101,26,87)(13,86,27,100)(14,99,28,85)(29,66,43,80)(30,79,44,65)(31,64,45,78)(32,77,46,63)(33,62,47,76)(34,75,48,61)(35,60,49,74)(36,73,50,59)(37,58,51,72)(38,71,52,57)(39,84,53,70)(40,69,54,83)(41,82,55,68)(42,67,56,81)(113,218,127,204)(114,203,128,217)(115,216,129,202)(116,201,130,215)(117,214,131,200)(118,199,132,213)(119,212,133,198)(120,197,134,211)(121,210,135,224)(122,223,136,209)(123,208,137,222)(124,221,138,207)(125,206,139,220)(126,219,140,205)(141,176,155,190)(142,189,156,175)(143,174,157,188)(144,187,158,173)(145,172,159,186)(146,185,160,171)(147,170,161,184)(148,183,162,169)(149,196,163,182)(150,181,164,195)(151,194,165,180)(152,179,166,193)(153,192,167,178)(154,177,168,191)>;
G:=Group( (1,54,15,40)(2,41,16,55)(3,56,17,42)(4,43,18,29)(5,30,19,44)(6,45,20,31)(7,32,21,46)(8,47,22,33)(9,34,23,48)(10,49,24,35)(11,36,25,50)(12,51,26,37)(13,38,27,52)(14,53,28,39)(57,100,71,86)(58,87,72,101)(59,102,73,88)(60,89,74,103)(61,104,75,90)(62,91,76,105)(63,106,77,92)(64,93,78,107)(65,108,79,94)(66,95,80,109)(67,110,81,96)(68,97,82,111)(69,112,83,98)(70,99,84,85)(113,177,127,191)(114,192,128,178)(115,179,129,193)(116,194,130,180)(117,181,131,195)(118,196,132,182)(119,183,133,169)(120,170,134,184)(121,185,135,171)(122,172,136,186)(123,187,137,173)(124,174,138,188)(125,189,139,175)(126,176,140,190)(141,205,155,219)(142,220,156,206)(143,207,157,221)(144,222,158,208)(145,209,159,223)(146,224,160,210)(147,211,161,197)(148,198,162,212)(149,213,163,199)(150,200,164,214)(151,215,165,201)(152,202,166,216)(153,217,167,203)(154,204,168,218), (1,212,85,134)(2,213,86,135)(3,214,87,136)(4,215,88,137)(5,216,89,138)(6,217,90,139)(7,218,91,140)(8,219,92,113)(9,220,93,114)(10,221,94,115)(11,222,95,116)(12,223,96,117)(13,224,97,118)(14,197,98,119)(15,198,99,120)(16,199,100,121)(17,200,101,122)(18,201,102,123)(19,202,103,124)(20,203,104,125)(21,204,105,126)(22,205,106,127)(23,206,107,128)(24,207,108,129)(25,208,109,130)(26,209,110,131)(27,210,111,132)(28,211,112,133)(29,151,73,187)(30,152,74,188)(31,153,75,189)(32,154,76,190)(33,155,77,191)(34,156,78,192)(35,157,79,193)(36,158,80,194)(37,159,81,195)(38,160,82,196)(39,161,83,169)(40,162,84,170)(41,163,57,171)(42,164,58,172)(43,165,59,173)(44,166,60,174)(45,167,61,175)(46,168,62,176)(47,141,63,177)(48,142,64,178)(49,143,65,179)(50,144,66,180)(51,145,67,181)(52,146,68,182)(53,147,69,183)(54,148,70,184)(55,149,71,185)(56,150,72,186), (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), (1,98,15,112)(2,111,16,97)(3,96,17,110)(4,109,18,95)(5,94,19,108)(6,107,20,93)(7,92,21,106)(8,105,22,91)(9,90,23,104)(10,103,24,89)(11,88,25,102)(12,101,26,87)(13,86,27,100)(14,99,28,85)(29,66,43,80)(30,79,44,65)(31,64,45,78)(32,77,46,63)(33,62,47,76)(34,75,48,61)(35,60,49,74)(36,73,50,59)(37,58,51,72)(38,71,52,57)(39,84,53,70)(40,69,54,83)(41,82,55,68)(42,67,56,81)(113,218,127,204)(114,203,128,217)(115,216,129,202)(116,201,130,215)(117,214,131,200)(118,199,132,213)(119,212,133,198)(120,197,134,211)(121,210,135,224)(122,223,136,209)(123,208,137,222)(124,221,138,207)(125,206,139,220)(126,219,140,205)(141,176,155,190)(142,189,156,175)(143,174,157,188)(144,187,158,173)(145,172,159,186)(146,185,160,171)(147,170,161,184)(148,183,162,169)(149,196,163,182)(150,181,164,195)(151,194,165,180)(152,179,166,193)(153,192,167,178)(154,177,168,191) );
G=PermutationGroup([[(1,54,15,40),(2,41,16,55),(3,56,17,42),(4,43,18,29),(5,30,19,44),(6,45,20,31),(7,32,21,46),(8,47,22,33),(9,34,23,48),(10,49,24,35),(11,36,25,50),(12,51,26,37),(13,38,27,52),(14,53,28,39),(57,100,71,86),(58,87,72,101),(59,102,73,88),(60,89,74,103),(61,104,75,90),(62,91,76,105),(63,106,77,92),(64,93,78,107),(65,108,79,94),(66,95,80,109),(67,110,81,96),(68,97,82,111),(69,112,83,98),(70,99,84,85),(113,177,127,191),(114,192,128,178),(115,179,129,193),(116,194,130,180),(117,181,131,195),(118,196,132,182),(119,183,133,169),(120,170,134,184),(121,185,135,171),(122,172,136,186),(123,187,137,173),(124,174,138,188),(125,189,139,175),(126,176,140,190),(141,205,155,219),(142,220,156,206),(143,207,157,221),(144,222,158,208),(145,209,159,223),(146,224,160,210),(147,211,161,197),(148,198,162,212),(149,213,163,199),(150,200,164,214),(151,215,165,201),(152,202,166,216),(153,217,167,203),(154,204,168,218)], [(1,212,85,134),(2,213,86,135),(3,214,87,136),(4,215,88,137),(5,216,89,138),(6,217,90,139),(7,218,91,140),(8,219,92,113),(9,220,93,114),(10,221,94,115),(11,222,95,116),(12,223,96,117),(13,224,97,118),(14,197,98,119),(15,198,99,120),(16,199,100,121),(17,200,101,122),(18,201,102,123),(19,202,103,124),(20,203,104,125),(21,204,105,126),(22,205,106,127),(23,206,107,128),(24,207,108,129),(25,208,109,130),(26,209,110,131),(27,210,111,132),(28,211,112,133),(29,151,73,187),(30,152,74,188),(31,153,75,189),(32,154,76,190),(33,155,77,191),(34,156,78,192),(35,157,79,193),(36,158,80,194),(37,159,81,195),(38,160,82,196),(39,161,83,169),(40,162,84,170),(41,163,57,171),(42,164,58,172),(43,165,59,173),(44,166,60,174),(45,167,61,175),(46,168,62,176),(47,141,63,177),(48,142,64,178),(49,143,65,179),(50,144,66,180),(51,145,67,181),(52,146,68,182),(53,147,69,183),(54,148,70,184),(55,149,71,185),(56,150,72,186)], [(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)], [(1,98,15,112),(2,111,16,97),(3,96,17,110),(4,109,18,95),(5,94,19,108),(6,107,20,93),(7,92,21,106),(8,105,22,91),(9,90,23,104),(10,103,24,89),(11,88,25,102),(12,101,26,87),(13,86,27,100),(14,99,28,85),(29,66,43,80),(30,79,44,65),(31,64,45,78),(32,77,46,63),(33,62,47,76),(34,75,48,61),(35,60,49,74),(36,73,50,59),(37,58,51,72),(38,71,52,57),(39,84,53,70),(40,69,54,83),(41,82,55,68),(42,67,56,81),(113,218,127,204),(114,203,128,217),(115,216,129,202),(116,201,130,215),(117,214,131,200),(118,199,132,213),(119,212,133,198),(120,197,134,211),(121,210,135,224),(122,223,136,209),(123,208,137,222),(124,221,138,207),(125,206,139,220),(126,219,140,205),(141,176,155,190),(142,189,156,175),(143,174,157,188),(144,187,158,173),(145,172,159,186),(146,185,160,171),(147,170,161,184),(148,183,162,169),(149,196,163,182),(150,181,164,195),(151,194,165,180),(152,179,166,193),(153,192,167,178),(154,177,168,191)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4N | 4O | ··· | 4AB | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| 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 | 14 | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | C4×D7 | 2- 1+4 | Q8.10D14 | D4.10D14 |
| kernel | C42.125D14 | C4×Dic14 | C42⋊D7 | Dic7⋊3Q8 | C4⋊C4⋊7D7 | Q8×Dic7 | Q8×C28 | C2×Q8×D7 | Q8×D7 | C4×Q8 | C42 | C4⋊C4 | C2×Q8 | Q8 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 16 | 3 | 9 | 9 | 3 | 24 | 2 | 6 | 6 |
Matrix representation of C42.125D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 |
| 0 | 0 | 0 | 0 | 11 | 27 |
| 2 | 8 | 0 | 0 | 0 | 0 |
| 13 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 21 |
| 0 | 0 | 0 | 0 | 8 | 26 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 5 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 8 |
| 0 | 0 | 0 | 0 | 3 | 21 |
| 0 | 0 | 21 | 21 | 0 | 0 |
| 0 | 0 | 26 | 8 | 0 | 0 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,12,0,0,0,0,0,0,12,0,0],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,2,11,0,0,0,0,18,27,0,0,0,0,0,0,2,11,0,0,0,0,18,27],[2,13,0,0,0,0,8,9,0,0,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,21,8,0,0,0,0,21,26,0,0],[8,5,0,0,0,0,28,21,0,0,0,0,0,0,0,0,21,26,0,0,0,0,21,8,0,0,8,3,0,0,0,0,8,21,0,0] >;
C42.125D14 in GAP, Magma, Sage, TeX
C_4^2._{125}D_{14} % in TeX
G:=Group("C4^2.125D14"); // GroupNames label
G:=SmallGroup(448,1025);
// by ID
G=gap.SmallGroup(448,1025);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,184,1123,80,18822]);
// 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=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations