metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.150D14, C14.282- 1+4, C14.1322+ 1+4, (C4×D28)⋊47C2, C42.C2⋊6D7, C4⋊C4.207D14, C42⋊2D7⋊9C2, D28⋊C4⋊36C2, D14⋊Q8⋊35C2, D14⋊2Q8⋊37C2, C4⋊D28.12C2, Dic7.Q8⋊33C2, D14.11(C4○D4), D14.5D4⋊34C2, (C2×C28).188C23, (C2×C14).236C24, (C4×C28).196C22, D14⋊C4.10C22, C2.57(D4⋊8D14), (C2×D28).164C22, Dic7⋊C4.52C22, C4⋊Dic7.314C22, C22.257(C23×D7), C7⋊8(C22.33C24), (C2×Dic7).258C23, (C4×Dic7).143C22, (C22×D7).102C23, C2.29(Q8.10D14), (C2×Dic14).180C22, (D7×C4⋊C4)⋊36C2, C2.87(D7×C4○D4), C4⋊C4⋊D7⋊34C2, (C7×C42.C2)⋊9C2, C14.198(C2×C4○D4), (C2×C4×D7).126C22, (C2×C4).80(C22×D7), (C7×C4⋊C4).191C22, SmallGroup(448,1145)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.150D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1084 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, D14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42.C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C22×D7, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4×D28, C42⋊2D7, Dic7.Q8, D7×C4⋊C4, D28⋊C4, D14.5D4, C4⋊D28, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42.C2, C42.150D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.33C24, C23×D7, Q8.10D14, D7×C4○D4, D4⋊8D14, C42.150D14
►On 224 points
Generators in S224
(1 124 160 62)(2 139 161 77)(3 126 162 64)(4 113 163 79)(5 128 164 66)(6 115 165 81)(7 130 166 68)(8 117 167 83)(9 132 168 70)(10 119 141 57)(11 134 142 72)(12 121 143 59)(13 136 144 74)(14 123 145 61)(15 138 146 76)(16 125 147 63)(17 140 148 78)(18 127 149 65)(19 114 150 80)(20 129 151 67)(21 116 152 82)(22 131 153 69)(23 118 154 84)(24 133 155 71)(25 120 156 58)(26 135 157 73)(27 122 158 60)(28 137 159 75)(29 180 217 90)(30 195 218 105)(31 182 219 92)(32 169 220 107)(33 184 221 94)(34 171 222 109)(35 186 223 96)(36 173 224 111)(37 188 197 98)(38 175 198 85)(39 190 199 100)(40 177 200 87)(41 192 201 102)(42 179 202 89)(43 194 203 104)(44 181 204 91)(45 196 205 106)(46 183 206 93)(47 170 207 108)(48 185 208 95)(49 172 209 110)(50 187 210 97)(51 174 211 112)(52 189 212 99)(53 176 213 86)(54 191 214 101)(55 178 215 88)(56 193 216 103)
(1 204 146 30)(2 31 147 205)(3 206 148 32)(4 33 149 207)(5 208 150 34)(6 35 151 209)(7 210 152 36)(8 37 153 211)(9 212 154 38)(10 39 155 213)(11 214 156 40)(12 41 157 215)(13 216 158 42)(14 43 159 217)(15 218 160 44)(16 45 161 219)(17 220 162 46)(18 47 163 221)(19 222 164 48)(20 49 165 223)(21 224 166 50)(22 51 167 197)(23 198 168 52)(24 53 141 199)(25 200 142 54)(26 55 143 201)(27 202 144 56)(28 29 145 203)(57 100 133 176)(58 177 134 101)(59 102 135 178)(60 179 136 103)(61 104 137 180)(62 181 138 105)(63 106 139 182)(64 183 140 107)(65 108 113 184)(66 185 114 109)(67 110 115 186)(68 187 116 111)(69 112 117 188)(70 189 118 85)(71 86 119 190)(72 191 120 87)(73 88 121 192)(74 193 122 89)(75 90 123 194)(76 195 124 91)(77 92 125 196)(78 169 126 93)(79 94 127 170)(80 171 128 95)(81 96 129 172)(82 173 130 97)(83 98 131 174)(84 175 132 99)
(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 44 43 30)(31 42 45 56)(32 55 46 41)(33 40 47 54)(34 53 48 39)(35 38 49 52)(36 51 50 37)(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 96 99 110)(86 109 100 95)(87 94 101 108)(88 107 102 93)(89 92 103 106)(90 105 104 91)(97 112 111 98)(113 134 127 120)(114 119 128 133)(115 132 129 118)(116 117 130 131)(121 126 135 140)(122 139 136 125)(123 124 137 138)(141 150 155 164)(142 163 156 149)(143 148 157 162)(144 161 158 147)(145 146 159 160)(151 168 165 154)(152 153 166 167)(169 192 183 178)(170 177 184 191)(171 190 185 176)(172 175 186 189)(173 188 187 174)(179 182 193 196)(180 195 194 181)(197 224 211 210)(198 209 212 223)(199 222 213 208)(200 207 214 221)(201 220 215 206)(202 205 216 219)(203 218 217 204)
G:=sub<Sym(224)| (1,124,160,62)(2,139,161,77)(3,126,162,64)(4,113,163,79)(5,128,164,66)(6,115,165,81)(7,130,166,68)(8,117,167,83)(9,132,168,70)(10,119,141,57)(11,134,142,72)(12,121,143,59)(13,136,144,74)(14,123,145,61)(15,138,146,76)(16,125,147,63)(17,140,148,78)(18,127,149,65)(19,114,150,80)(20,129,151,67)(21,116,152,82)(22,131,153,69)(23,118,154,84)(24,133,155,71)(25,120,156,58)(26,135,157,73)(27,122,158,60)(28,137,159,75)(29,180,217,90)(30,195,218,105)(31,182,219,92)(32,169,220,107)(33,184,221,94)(34,171,222,109)(35,186,223,96)(36,173,224,111)(37,188,197,98)(38,175,198,85)(39,190,199,100)(40,177,200,87)(41,192,201,102)(42,179,202,89)(43,194,203,104)(44,181,204,91)(45,196,205,106)(46,183,206,93)(47,170,207,108)(48,185,208,95)(49,172,209,110)(50,187,210,97)(51,174,211,112)(52,189,212,99)(53,176,213,86)(54,191,214,101)(55,178,215,88)(56,193,216,103), (1,204,146,30)(2,31,147,205)(3,206,148,32)(4,33,149,207)(5,208,150,34)(6,35,151,209)(7,210,152,36)(8,37,153,211)(9,212,154,38)(10,39,155,213)(11,214,156,40)(12,41,157,215)(13,216,158,42)(14,43,159,217)(15,218,160,44)(16,45,161,219)(17,220,162,46)(18,47,163,221)(19,222,164,48)(20,49,165,223)(21,224,166,50)(22,51,167,197)(23,198,168,52)(24,53,141,199)(25,200,142,54)(26,55,143,201)(27,202,144,56)(28,29,145,203)(57,100,133,176)(58,177,134,101)(59,102,135,178)(60,179,136,103)(61,104,137,180)(62,181,138,105)(63,106,139,182)(64,183,140,107)(65,108,113,184)(66,185,114,109)(67,110,115,186)(68,187,116,111)(69,112,117,188)(70,189,118,85)(71,86,119,190)(72,191,120,87)(73,88,121,192)(74,193,122,89)(75,90,123,194)(76,195,124,91)(77,92,125,196)(78,169,126,93)(79,94,127,170)(80,171,128,95)(81,96,129,172)(82,173,130,97)(83,98,131,174)(84,175,132,99), (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)(29,44,43,30)(31,42,45,56)(32,55,46,41)(33,40,47,54)(34,53,48,39)(35,38,49,52)(36,51,50,37)(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)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,150,155,164)(142,163,156,149)(143,148,157,162)(144,161,158,147)(145,146,159,160)(151,168,165,154)(152,153,166,167)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181)(197,224,211,210)(198,209,212,223)(199,222,213,208)(200,207,214,221)(201,220,215,206)(202,205,216,219)(203,218,217,204)>;
G:=Group( (1,124,160,62)(2,139,161,77)(3,126,162,64)(4,113,163,79)(5,128,164,66)(6,115,165,81)(7,130,166,68)(8,117,167,83)(9,132,168,70)(10,119,141,57)(11,134,142,72)(12,121,143,59)(13,136,144,74)(14,123,145,61)(15,138,146,76)(16,125,147,63)(17,140,148,78)(18,127,149,65)(19,114,150,80)(20,129,151,67)(21,116,152,82)(22,131,153,69)(23,118,154,84)(24,133,155,71)(25,120,156,58)(26,135,157,73)(27,122,158,60)(28,137,159,75)(29,180,217,90)(30,195,218,105)(31,182,219,92)(32,169,220,107)(33,184,221,94)(34,171,222,109)(35,186,223,96)(36,173,224,111)(37,188,197,98)(38,175,198,85)(39,190,199,100)(40,177,200,87)(41,192,201,102)(42,179,202,89)(43,194,203,104)(44,181,204,91)(45,196,205,106)(46,183,206,93)(47,170,207,108)(48,185,208,95)(49,172,209,110)(50,187,210,97)(51,174,211,112)(52,189,212,99)(53,176,213,86)(54,191,214,101)(55,178,215,88)(56,193,216,103), (1,204,146,30)(2,31,147,205)(3,206,148,32)(4,33,149,207)(5,208,150,34)(6,35,151,209)(7,210,152,36)(8,37,153,211)(9,212,154,38)(10,39,155,213)(11,214,156,40)(12,41,157,215)(13,216,158,42)(14,43,159,217)(15,218,160,44)(16,45,161,219)(17,220,162,46)(18,47,163,221)(19,222,164,48)(20,49,165,223)(21,224,166,50)(22,51,167,197)(23,198,168,52)(24,53,141,199)(25,200,142,54)(26,55,143,201)(27,202,144,56)(28,29,145,203)(57,100,133,176)(58,177,134,101)(59,102,135,178)(60,179,136,103)(61,104,137,180)(62,181,138,105)(63,106,139,182)(64,183,140,107)(65,108,113,184)(66,185,114,109)(67,110,115,186)(68,187,116,111)(69,112,117,188)(70,189,118,85)(71,86,119,190)(72,191,120,87)(73,88,121,192)(74,193,122,89)(75,90,123,194)(76,195,124,91)(77,92,125,196)(78,169,126,93)(79,94,127,170)(80,171,128,95)(81,96,129,172)(82,173,130,97)(83,98,131,174)(84,175,132,99), (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)(29,44,43,30)(31,42,45,56)(32,55,46,41)(33,40,47,54)(34,53,48,39)(35,38,49,52)(36,51,50,37)(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)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,150,155,164)(142,163,156,149)(143,148,157,162)(144,161,158,147)(145,146,159,160)(151,168,165,154)(152,153,166,167)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181)(197,224,211,210)(198,209,212,223)(199,222,213,208)(200,207,214,221)(201,220,215,206)(202,205,216,219)(203,218,217,204) );
G=PermutationGroup([[(1,124,160,62),(2,139,161,77),(3,126,162,64),(4,113,163,79),(5,128,164,66),(6,115,165,81),(7,130,166,68),(8,117,167,83),(9,132,168,70),(10,119,141,57),(11,134,142,72),(12,121,143,59),(13,136,144,74),(14,123,145,61),(15,138,146,76),(16,125,147,63),(17,140,148,78),(18,127,149,65),(19,114,150,80),(20,129,151,67),(21,116,152,82),(22,131,153,69),(23,118,154,84),(24,133,155,71),(25,120,156,58),(26,135,157,73),(27,122,158,60),(28,137,159,75),(29,180,217,90),(30,195,218,105),(31,182,219,92),(32,169,220,107),(33,184,221,94),(34,171,222,109),(35,186,223,96),(36,173,224,111),(37,188,197,98),(38,175,198,85),(39,190,199,100),(40,177,200,87),(41,192,201,102),(42,179,202,89),(43,194,203,104),(44,181,204,91),(45,196,205,106),(46,183,206,93),(47,170,207,108),(48,185,208,95),(49,172,209,110),(50,187,210,97),(51,174,211,112),(52,189,212,99),(53,176,213,86),(54,191,214,101),(55,178,215,88),(56,193,216,103)], [(1,204,146,30),(2,31,147,205),(3,206,148,32),(4,33,149,207),(5,208,150,34),(6,35,151,209),(7,210,152,36),(8,37,153,211),(9,212,154,38),(10,39,155,213),(11,214,156,40),(12,41,157,215),(13,216,158,42),(14,43,159,217),(15,218,160,44),(16,45,161,219),(17,220,162,46),(18,47,163,221),(19,222,164,48),(20,49,165,223),(21,224,166,50),(22,51,167,197),(23,198,168,52),(24,53,141,199),(25,200,142,54),(26,55,143,201),(27,202,144,56),(28,29,145,203),(57,100,133,176),(58,177,134,101),(59,102,135,178),(60,179,136,103),(61,104,137,180),(62,181,138,105),(63,106,139,182),(64,183,140,107),(65,108,113,184),(66,185,114,109),(67,110,115,186),(68,187,116,111),(69,112,117,188),(70,189,118,85),(71,86,119,190),(72,191,120,87),(73,88,121,192),(74,193,122,89),(75,90,123,194),(76,195,124,91),(77,92,125,196),(78,169,126,93),(79,94,127,170),(80,171,128,95),(81,96,129,172),(82,173,130,97),(83,98,131,174),(84,175,132,99)], [(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),(29,44,43,30),(31,42,45,56),(32,55,46,41),(33,40,47,54),(34,53,48,39),(35,38,49,52),(36,51,50,37),(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),(85,96,99,110),(86,109,100,95),(87,94,101,108),(88,107,102,93),(89,92,103,106),(90,105,104,91),(97,112,111,98),(113,134,127,120),(114,119,128,133),(115,132,129,118),(116,117,130,131),(121,126,135,140),(122,139,136,125),(123,124,137,138),(141,150,155,164),(142,163,156,149),(143,148,157,162),(144,161,158,147),(145,146,159,160),(151,168,165,154),(152,153,166,167),(169,192,183,178),(170,177,184,191),(171,190,185,176),(172,175,186,189),(173,188,187,174),(179,182,193,196),(180,195,194,181),(197,224,211,210),(198,209,212,223),(199,222,213,208),(200,207,214,221),(201,220,215,206),(202,205,216,219),(203,218,217,204)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | 28 | 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 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8.10D14 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.150D14 | C4×D28 | C42⋊2D7 | Dic7.Q8 | D7×C4⋊C4 | D28⋊C4 | D14.5D4 | C4⋊D28 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | D14 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 18 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.150D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 18 | 22 | 1 |
| 0 | 0 | 27 | 8 | 16 | 0 |
| 0 | 0 | 0 | 11 | 2 | 11 |
| 0 | 0 | 2 | 19 | 18 | 27 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 4 | 8 |
| 0 | 0 | 0 | 1 | 3 | 2 |
| 0 | 0 | 22 | 28 | 28 | 0 |
| 0 | 0 | 25 | 15 | 0 | 28 |
| 9 | 6 | 0 | 0 | 0 | 0 |
| 6 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 20 | 0 | 0 |
| 0 | 0 | 1 | 17 | 0 | 0 |
| 0 | 0 | 27 | 17 | 7 | 9 |
| 0 | 0 | 2 | 1 | 20 | 9 |
| 20 | 23 | 0 | 0 | 0 | 0 |
| 23 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 7 | 0 | 0 |
| 0 | 0 | 11 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 12 | 0 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,21,27,0,2,0,0,18,8,11,19,0,0,22,16,2,18,0,0,1,0,11,27],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,1,0,22,25,0,0,0,1,28,15,0,0,4,3,28,0,0,0,8,2,0,28],[9,6,0,0,0,0,6,20,0,0,0,0,0,0,25,1,27,2,0,0,20,17,17,1,0,0,0,0,7,20,0,0,0,0,9,9],[20,23,0,0,0,0,23,9,0,0,0,0,0,0,26,11,0,0,0,0,7,3,0,0,0,0,0,0,0,12,0,0,0,0,12,0] >;
C42.150D14 in GAP, Magma, Sage, TeX
C_4^2._{150}D_{14} % in TeX
G:=Group("C4^2.150D14"); // GroupNames label
G:=SmallGroup(448,1145);
// by ID
G=gap.SmallGroup(448,1145);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,570,136,18822]);
// 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=d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations