metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.168D14, C14.792+ 1+4, C4⋊1D4⋊8D7, C28⋊2D4⋊38C2, (D4×Dic7)⋊36C2, (C2×D4).179D14, C42⋊D7⋊24C2, C28.6Q8⋊23C2, Dic7⋊D4⋊38C2, C28.134(C4○D4), C4.40(D4⋊2D7), (C2×C28).637C23, (C4×C28).205C22, (C2×C14).263C24, C2.83(D4⋊6D14), C23.69(C22×D7), D14⋊C4.150C22, (D4×C14).215C22, Dic7⋊C4.87C22, C4⋊Dic7.249C22, (C22×C14).77C23, C22.284(C23×D7), C23.D7.74C22, C23.18D14⋊27C2, C7⋊7(C22.34C24), (C4×Dic7).156C22, (C2×Dic7).137C23, (C22×D7).117C23, (C22×Dic7).159C22, (C7×C4⋊1D4)⋊10C2, C14.98(C2×C4○D4), C2.62(C2×D4⋊2D7), (C2×C4×D7).140C22, (C2×C4).215(C22×D7), (C2×C7⋊D4).79C22, SmallGroup(448,1172)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.168D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=b2c-1 >
Subgroups: 1068 in 240 conjugacy classes, 95 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C4⋊1D4, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.34C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C2×C4×D7, C22×Dic7, C2×C7⋊D4, D4×C14, C28.6Q8, C42⋊D7, D4×Dic7, C23.18D14, C28⋊2D4, Dic7⋊D4, C7×C4⋊1D4, C42.168D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.34C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D4⋊6D14, C42.168D14
►On 224 points
Generators in S224
(1 145 62 86)(2 87 63 146)(3 147 64 88)(4 89 65 148)(5 149 66 90)(6 91 67 150)(7 151 68 92)(8 93 69 152)(9 153 70 94)(10 95 57 154)(11 141 58 96)(12 97 59 142)(13 143 60 98)(14 85 61 144)(15 167 133 195)(16 196 134 168)(17 155 135 183)(18 184 136 156)(19 157 137 185)(20 186 138 158)(21 159 139 187)(22 188 140 160)(23 161 127 189)(24 190 128 162)(25 163 129 191)(26 192 130 164)(27 165 131 193)(28 194 132 166)(29 181 75 121)(30 122 76 182)(31 169 77 123)(32 124 78 170)(33 171 79 125)(34 126 80 172)(35 173 81 113)(36 114 82 174)(37 175 83 115)(38 116 84 176)(39 177 71 117)(40 118 72 178)(41 179 73 119)(42 120 74 180)(43 216 203 110)(44 111 204 217)(45 218 205 112)(46 99 206 219)(47 220 207 100)(48 101 208 221)(49 222 209 102)(50 103 210 223)(51 224 197 104)(52 105 198 211)(53 212 199 106)(54 107 200 213)(55 214 201 108)(56 109 202 215)
(1 152 38 123)(2 124 39 153)(3 154 40 125)(4 126 41 141)(5 142 42 113)(6 114 29 143)(7 144 30 115)(8 116 31 145)(9 146 32 117)(10 118 33 147)(11 148 34 119)(12 120 35 149)(13 150 36 121)(14 122 37 151)(15 188 216 50)(16 51 217 189)(17 190 218 52)(18 53 219 191)(19 192 220 54)(20 55 221 193)(21 194 222 56)(22 43 223 195)(23 196 224 44)(24 45 211 183)(25 184 212 46)(26 47 213 185)(27 186 214 48)(28 49 215 187)(57 178 79 88)(58 89 80 179)(59 180 81 90)(60 91 82 181)(61 182 83 92)(62 93 84 169)(63 170 71 94)(64 95 72 171)(65 172 73 96)(66 97 74 173)(67 174 75 98)(68 85 76 175)(69 176 77 86)(70 87 78 177)(99 163 136 199)(100 200 137 164)(101 165 138 201)(102 202 139 166)(103 167 140 203)(104 204 127 168)(105 155 128 205)(106 206 129 156)(107 157 130 207)(108 208 131 158)(109 159 132 209)(110 210 133 160)(111 161 134 197)(112 198 135 162)
(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)
(1 165 38 201)(2 200 39 164)(3 163 40 199)(4 198 41 162)(5 161 42 197)(6 210 29 160)(7 159 30 209)(8 208 31 158)(9 157 32 207)(10 206 33 156)(11 155 34 205)(12 204 35 168)(13 167 36 203)(14 202 37 166)(15 114 216 143)(16 142 217 113)(17 126 218 141)(18 154 219 125)(19 124 220 153)(20 152 221 123)(21 122 222 151)(22 150 223 121)(23 120 224 149)(24 148 211 119)(25 118 212 147)(26 146 213 117)(27 116 214 145)(28 144 215 115)(43 60 195 82)(44 81 196 59)(45 58 183 80)(46 79 184 57)(47 70 185 78)(48 77 186 69)(49 68 187 76)(50 75 188 67)(51 66 189 74)(52 73 190 65)(53 64 191 72)(54 71 192 63)(55 62 193 84)(56 83 194 61)(85 109 175 132)(86 131 176 108)(87 107 177 130)(88 129 178 106)(89 105 179 128)(90 127 180 104)(91 103 181 140)(92 139 182 102)(93 101 169 138)(94 137 170 100)(95 99 171 136)(96 135 172 112)(97 111 173 134)(98 133 174 110)
G:=sub<Sym(224)| (1,145,62,86)(2,87,63,146)(3,147,64,88)(4,89,65,148)(5,149,66,90)(6,91,67,150)(7,151,68,92)(8,93,69,152)(9,153,70,94)(10,95,57,154)(11,141,58,96)(12,97,59,142)(13,143,60,98)(14,85,61,144)(15,167,133,195)(16,196,134,168)(17,155,135,183)(18,184,136,156)(19,157,137,185)(20,186,138,158)(21,159,139,187)(22,188,140,160)(23,161,127,189)(24,190,128,162)(25,163,129,191)(26,192,130,164)(27,165,131,193)(28,194,132,166)(29,181,75,121)(30,122,76,182)(31,169,77,123)(32,124,78,170)(33,171,79,125)(34,126,80,172)(35,173,81,113)(36,114,82,174)(37,175,83,115)(38,116,84,176)(39,177,71,117)(40,118,72,178)(41,179,73,119)(42,120,74,180)(43,216,203,110)(44,111,204,217)(45,218,205,112)(46,99,206,219)(47,220,207,100)(48,101,208,221)(49,222,209,102)(50,103,210,223)(51,224,197,104)(52,105,198,211)(53,212,199,106)(54,107,200,213)(55,214,201,108)(56,109,202,215), (1,152,38,123)(2,124,39,153)(3,154,40,125)(4,126,41,141)(5,142,42,113)(6,114,29,143)(7,144,30,115)(8,116,31,145)(9,146,32,117)(10,118,33,147)(11,148,34,119)(12,120,35,149)(13,150,36,121)(14,122,37,151)(15,188,216,50)(16,51,217,189)(17,190,218,52)(18,53,219,191)(19,192,220,54)(20,55,221,193)(21,194,222,56)(22,43,223,195)(23,196,224,44)(24,45,211,183)(25,184,212,46)(26,47,213,185)(27,186,214,48)(28,49,215,187)(57,178,79,88)(58,89,80,179)(59,180,81,90)(60,91,82,181)(61,182,83,92)(62,93,84,169)(63,170,71,94)(64,95,72,171)(65,172,73,96)(66,97,74,173)(67,174,75,98)(68,85,76,175)(69,176,77,86)(70,87,78,177)(99,163,136,199)(100,200,137,164)(101,165,138,201)(102,202,139,166)(103,167,140,203)(104,204,127,168)(105,155,128,205)(106,206,129,156)(107,157,130,207)(108,208,131,158)(109,159,132,209)(110,210,133,160)(111,161,134,197)(112,198,135,162), (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), (1,165,38,201)(2,200,39,164)(3,163,40,199)(4,198,41,162)(5,161,42,197)(6,210,29,160)(7,159,30,209)(8,208,31,158)(9,157,32,207)(10,206,33,156)(11,155,34,205)(12,204,35,168)(13,167,36,203)(14,202,37,166)(15,114,216,143)(16,142,217,113)(17,126,218,141)(18,154,219,125)(19,124,220,153)(20,152,221,123)(21,122,222,151)(22,150,223,121)(23,120,224,149)(24,148,211,119)(25,118,212,147)(26,146,213,117)(27,116,214,145)(28,144,215,115)(43,60,195,82)(44,81,196,59)(45,58,183,80)(46,79,184,57)(47,70,185,78)(48,77,186,69)(49,68,187,76)(50,75,188,67)(51,66,189,74)(52,73,190,65)(53,64,191,72)(54,71,192,63)(55,62,193,84)(56,83,194,61)(85,109,175,132)(86,131,176,108)(87,107,177,130)(88,129,178,106)(89,105,179,128)(90,127,180,104)(91,103,181,140)(92,139,182,102)(93,101,169,138)(94,137,170,100)(95,99,171,136)(96,135,172,112)(97,111,173,134)(98,133,174,110)>;
G:=Group( (1,145,62,86)(2,87,63,146)(3,147,64,88)(4,89,65,148)(5,149,66,90)(6,91,67,150)(7,151,68,92)(8,93,69,152)(9,153,70,94)(10,95,57,154)(11,141,58,96)(12,97,59,142)(13,143,60,98)(14,85,61,144)(15,167,133,195)(16,196,134,168)(17,155,135,183)(18,184,136,156)(19,157,137,185)(20,186,138,158)(21,159,139,187)(22,188,140,160)(23,161,127,189)(24,190,128,162)(25,163,129,191)(26,192,130,164)(27,165,131,193)(28,194,132,166)(29,181,75,121)(30,122,76,182)(31,169,77,123)(32,124,78,170)(33,171,79,125)(34,126,80,172)(35,173,81,113)(36,114,82,174)(37,175,83,115)(38,116,84,176)(39,177,71,117)(40,118,72,178)(41,179,73,119)(42,120,74,180)(43,216,203,110)(44,111,204,217)(45,218,205,112)(46,99,206,219)(47,220,207,100)(48,101,208,221)(49,222,209,102)(50,103,210,223)(51,224,197,104)(52,105,198,211)(53,212,199,106)(54,107,200,213)(55,214,201,108)(56,109,202,215), (1,152,38,123)(2,124,39,153)(3,154,40,125)(4,126,41,141)(5,142,42,113)(6,114,29,143)(7,144,30,115)(8,116,31,145)(9,146,32,117)(10,118,33,147)(11,148,34,119)(12,120,35,149)(13,150,36,121)(14,122,37,151)(15,188,216,50)(16,51,217,189)(17,190,218,52)(18,53,219,191)(19,192,220,54)(20,55,221,193)(21,194,222,56)(22,43,223,195)(23,196,224,44)(24,45,211,183)(25,184,212,46)(26,47,213,185)(27,186,214,48)(28,49,215,187)(57,178,79,88)(58,89,80,179)(59,180,81,90)(60,91,82,181)(61,182,83,92)(62,93,84,169)(63,170,71,94)(64,95,72,171)(65,172,73,96)(66,97,74,173)(67,174,75,98)(68,85,76,175)(69,176,77,86)(70,87,78,177)(99,163,136,199)(100,200,137,164)(101,165,138,201)(102,202,139,166)(103,167,140,203)(104,204,127,168)(105,155,128,205)(106,206,129,156)(107,157,130,207)(108,208,131,158)(109,159,132,209)(110,210,133,160)(111,161,134,197)(112,198,135,162), (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), (1,165,38,201)(2,200,39,164)(3,163,40,199)(4,198,41,162)(5,161,42,197)(6,210,29,160)(7,159,30,209)(8,208,31,158)(9,157,32,207)(10,206,33,156)(11,155,34,205)(12,204,35,168)(13,167,36,203)(14,202,37,166)(15,114,216,143)(16,142,217,113)(17,126,218,141)(18,154,219,125)(19,124,220,153)(20,152,221,123)(21,122,222,151)(22,150,223,121)(23,120,224,149)(24,148,211,119)(25,118,212,147)(26,146,213,117)(27,116,214,145)(28,144,215,115)(43,60,195,82)(44,81,196,59)(45,58,183,80)(46,79,184,57)(47,70,185,78)(48,77,186,69)(49,68,187,76)(50,75,188,67)(51,66,189,74)(52,73,190,65)(53,64,191,72)(54,71,192,63)(55,62,193,84)(56,83,194,61)(85,109,175,132)(86,131,176,108)(87,107,177,130)(88,129,178,106)(89,105,179,128)(90,127,180,104)(91,103,181,140)(92,139,182,102)(93,101,169,138)(94,137,170,100)(95,99,171,136)(96,135,172,112)(97,111,173,134)(98,133,174,110) );
G=PermutationGroup([[(1,145,62,86),(2,87,63,146),(3,147,64,88),(4,89,65,148),(5,149,66,90),(6,91,67,150),(7,151,68,92),(8,93,69,152),(9,153,70,94),(10,95,57,154),(11,141,58,96),(12,97,59,142),(13,143,60,98),(14,85,61,144),(15,167,133,195),(16,196,134,168),(17,155,135,183),(18,184,136,156),(19,157,137,185),(20,186,138,158),(21,159,139,187),(22,188,140,160),(23,161,127,189),(24,190,128,162),(25,163,129,191),(26,192,130,164),(27,165,131,193),(28,194,132,166),(29,181,75,121),(30,122,76,182),(31,169,77,123),(32,124,78,170),(33,171,79,125),(34,126,80,172),(35,173,81,113),(36,114,82,174),(37,175,83,115),(38,116,84,176),(39,177,71,117),(40,118,72,178),(41,179,73,119),(42,120,74,180),(43,216,203,110),(44,111,204,217),(45,218,205,112),(46,99,206,219),(47,220,207,100),(48,101,208,221),(49,222,209,102),(50,103,210,223),(51,224,197,104),(52,105,198,211),(53,212,199,106),(54,107,200,213),(55,214,201,108),(56,109,202,215)], [(1,152,38,123),(2,124,39,153),(3,154,40,125),(4,126,41,141),(5,142,42,113),(6,114,29,143),(7,144,30,115),(8,116,31,145),(9,146,32,117),(10,118,33,147),(11,148,34,119),(12,120,35,149),(13,150,36,121),(14,122,37,151),(15,188,216,50),(16,51,217,189),(17,190,218,52),(18,53,219,191),(19,192,220,54),(20,55,221,193),(21,194,222,56),(22,43,223,195),(23,196,224,44),(24,45,211,183),(25,184,212,46),(26,47,213,185),(27,186,214,48),(28,49,215,187),(57,178,79,88),(58,89,80,179),(59,180,81,90),(60,91,82,181),(61,182,83,92),(62,93,84,169),(63,170,71,94),(64,95,72,171),(65,172,73,96),(66,97,74,173),(67,174,75,98),(68,85,76,175),(69,176,77,86),(70,87,78,177),(99,163,136,199),(100,200,137,164),(101,165,138,201),(102,202,139,166),(103,167,140,203),(104,204,127,168),(105,155,128,205),(106,206,129,156),(107,157,130,207),(108,208,131,158),(109,159,132,209),(110,210,133,160),(111,161,134,197),(112,198,135,162)], [(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)], [(1,165,38,201),(2,200,39,164),(3,163,40,199),(4,198,41,162),(5,161,42,197),(6,210,29,160),(7,159,30,209),(8,208,31,158),(9,157,32,207),(10,206,33,156),(11,155,34,205),(12,204,35,168),(13,167,36,203),(14,202,37,166),(15,114,216,143),(16,142,217,113),(17,126,218,141),(18,154,219,125),(19,124,220,153),(20,152,221,123),(21,122,222,151),(22,150,223,121),(23,120,224,149),(24,148,211,119),(25,118,212,147),(26,146,213,117),(27,116,214,145),(28,144,215,115),(43,60,195,82),(44,81,196,59),(45,58,183,80),(46,79,184,57),(47,70,185,78),(48,77,186,69),(49,68,187,76),(50,75,188,67),(51,66,189,74),(52,73,190,65),(53,64,191,72),(54,71,192,63),(55,62,193,84),(56,83,194,61),(85,109,175,132),(86,131,176,108),(87,107,177,130),(88,129,178,106),(89,105,179,128),(90,127,180,104),(91,103,181,140),(92,139,182,102),(93,101,169,138),(94,137,170,100),(95,99,171,136),(96,135,172,112),(97,111,173,134),(98,133,174,110)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 28 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | D4⋊6D14 |
| kernel | C42.168D14 | C28.6Q8 | C42⋊D7 | D4×Dic7 | C23.18D14 | C28⋊2D4 | Dic7⋊D4 | C7×C4⋊1D4 | C4⋊1D4 | C28 | C42 | C2×D4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 4 | 2 | 4 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 12 |
Matrix representation of C42.168D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 27 |
| 0 | 0 | 0 | 0 | 2 | 18 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 7 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 2 |
| 0 | 0 | 0 | 0 | 27 | 11 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 5 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 25 |
| 0 | 0 | 0 | 0 | 4 | 25 |
| 0 | 0 | 11 | 25 | 0 | 0 |
| 0 | 0 | 4 | 25 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 18 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 16 | 0 | 0 |
| 0 | 0 | 26 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 16 |
| 0 | 0 | 0 | 0 | 26 | 7 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,18,27,0,0,0,0,2,11,0,0,11,2,0,0,0,0,27,18,0,0],[8,7,0,0,0,0,28,21,0,0,0,0,0,0,18,27,0,0,0,0,2,11,0,0,0,0,0,0,18,27,0,0,0,0,2,11],[8,5,0,0,0,0,28,21,0,0,0,0,0,0,0,0,11,4,0,0,0,0,25,25,0,0,11,4,0,0,0,0,25,25,0,0],[12,18,0,0,0,0,0,17,0,0,0,0,0,0,22,26,0,0,0,0,16,7,0,0,0,0,0,0,22,26,0,0,0,0,16,7] >;
C42.168D14 in GAP, Magma, Sage, TeX
C_4^2._{168}D_{14} % in TeX
G:=Group("C4^2.168D14"); // GroupNames label
G:=SmallGroup(448,1172);
// by ID
G=gap.SmallGroup(448,1172);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,185,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations