metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.92D14, C14.502- 1+4, C28⋊2Q8⋊7C2, (C2×C4).56D28, C4.72(C2×D28), C4⋊C4.269D14, (C2×C28).202D4, C4.D28⋊4C2, C28.288(C2×D4), (C4×C28).8C22, D14⋊2Q8⋊11C2, C42⋊C2⋊10D7, (C2×C14).70C24, D14⋊C4.2C22, C22⋊C4.94D14, C2.16(C22×D28), C14.14(C22×D4), C22.21(C2×D28), (C2×C28).145C23, C22.D28⋊4C2, (C22×C4).191D14, C4⋊Dic7.33C22, C22.99(C23×D7), (C22×Dic14)⋊15C2, (C2×D28).206C22, (C2×Dic7).24C23, (C22×D7).20C23, C23.158(C22×D7), C2.8(D4.10D14), (C22×C14).140C23, (C22×C28).230C22, C7⋊1(C23.38C23), (C2×Dic14).285C22, (C22×Dic7).87C22, (C2×C14).51(C2×D4), (C2×C4×D7).59C22, (C2×C4○D28).19C2, (C7×C42⋊C2)⋊12C2, (C7×C4⋊C4).307C22, (C2×C4).576(C22×D7), (C2×C7⋊D4).101C22, (C7×C22⋊C4).102C22, SmallGroup(448,979)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.92D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, ac=ca, dad-1=a-1, cbc-1=a2b, dbd-1=b-1, dcd-1=c13 >
Subgroups: 1268 in 270 conjugacy classes, 111 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.38C23, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C22×Dic7, C2×C7⋊D4, C22×C28, C28⋊2Q8, C4.D28, C22.D28, D14⋊2Q8, C7×C42⋊C2, C22×Dic14, C2×C4○D28, C42.92D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2- 1+4, D28, C22×D7, C23.38C23, C2×D28, C23×D7, C22×D28, D4.10D14, C42.92D14
►On 224 points
Generators in S224
(1 22 15 8)(2 23 16 9)(3 24 17 10)(4 25 18 11)(5 26 19 12)(6 27 20 13)(7 28 21 14)(29 36 43 50)(30 37 44 51)(31 38 45 52)(32 39 46 53)(33 40 47 54)(34 41 48 55)(35 42 49 56)(57 78 71 64)(58 79 72 65)(59 80 73 66)(60 81 74 67)(61 82 75 68)(62 83 76 69)(63 84 77 70)(85 106 99 92)(86 107 100 93)(87 108 101 94)(88 109 102 95)(89 110 103 96)(90 111 104 97)(91 112 105 98)(113 120 127 134)(114 121 128 135)(115 122 129 136)(116 123 130 137)(117 124 131 138)(118 125 132 139)(119 126 133 140)(141 148 155 162)(142 149 156 163)(143 150 157 164)(144 151 158 165)(145 152 159 166)(146 153 160 167)(147 154 161 168)(169 190 183 176)(170 191 184 177)(171 192 185 178)(172 193 186 179)(173 194 187 180)(174 195 188 181)(175 196 189 182)(197 204 211 218)(198 205 212 219)(199 206 213 220)(200 207 214 221)(201 208 215 222)(202 209 216 223)(203 210 217 224)
(1 137 89 216)(2 124 90 203)(3 139 91 218)(4 126 92 205)(5 113 93 220)(6 128 94 207)(7 115 95 222)(8 130 96 209)(9 117 97 224)(10 132 98 211)(11 119 99 198)(12 134 100 213)(13 121 101 200)(14 136 102 215)(15 123 103 202)(16 138 104 217)(17 125 105 204)(18 140 106 219)(19 127 107 206)(20 114 108 221)(21 129 109 208)(22 116 110 223)(23 131 111 210)(24 118 112 197)(25 133 85 212)(26 120 86 199)(27 135 87 214)(28 122 88 201)(29 57 166 178)(30 72 167 193)(31 59 168 180)(32 74 141 195)(33 61 142 182)(34 76 143 169)(35 63 144 184)(36 78 145 171)(37 65 146 186)(38 80 147 173)(39 67 148 188)(40 82 149 175)(41 69 150 190)(42 84 151 177)(43 71 152 192)(44 58 153 179)(45 73 154 194)(46 60 155 181)(47 75 156 196)(48 62 157 183)(49 77 158 170)(50 64 159 185)(51 79 160 172)(52 66 161 187)(53 81 162 174)(54 68 163 189)(55 83 164 176)(56 70 165 191)
(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 41 15 55)(2 54 16 40)(3 39 17 53)(4 52 18 38)(5 37 19 51)(6 50 20 36)(7 35 21 49)(8 48 22 34)(9 33 23 47)(10 46 24 32)(11 31 25 45)(12 44 26 30)(13 29 27 43)(14 42 28 56)(57 214 71 200)(58 199 72 213)(59 212 73 198)(60 197 74 211)(61 210 75 224)(62 223 76 209)(63 208 77 222)(64 221 78 207)(65 206 79 220)(66 219 80 205)(67 204 81 218)(68 217 82 203)(69 202 83 216)(70 215 84 201)(85 154 99 168)(86 167 100 153)(87 152 101 166)(88 165 102 151)(89 150 103 164)(90 163 104 149)(91 148 105 162)(92 161 106 147)(93 146 107 160)(94 159 108 145)(95 144 109 158)(96 157 110 143)(97 142 111 156)(98 155 112 141)(113 186 127 172)(114 171 128 185)(115 184 129 170)(116 169 130 183)(117 182 131 196)(118 195 132 181)(119 180 133 194)(120 193 134 179)(121 178 135 192)(122 191 136 177)(123 176 137 190)(124 189 138 175)(125 174 139 188)(126 187 140 173)
G:=sub<Sym(224)| (1,22,15,8)(2,23,16,9)(3,24,17,10)(4,25,18,11)(5,26,19,12)(6,27,20,13)(7,28,21,14)(29,36,43,50)(30,37,44,51)(31,38,45,52)(32,39,46,53)(33,40,47,54)(34,41,48,55)(35,42,49,56)(57,78,71,64)(58,79,72,65)(59,80,73,66)(60,81,74,67)(61,82,75,68)(62,83,76,69)(63,84,77,70)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(113,120,127,134)(114,121,128,135)(115,122,129,136)(116,123,130,137)(117,124,131,138)(118,125,132,139)(119,126,133,140)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,137,89,216)(2,124,90,203)(3,139,91,218)(4,126,92,205)(5,113,93,220)(6,128,94,207)(7,115,95,222)(8,130,96,209)(9,117,97,224)(10,132,98,211)(11,119,99,198)(12,134,100,213)(13,121,101,200)(14,136,102,215)(15,123,103,202)(16,138,104,217)(17,125,105,204)(18,140,106,219)(19,127,107,206)(20,114,108,221)(21,129,109,208)(22,116,110,223)(23,131,111,210)(24,118,112,197)(25,133,85,212)(26,120,86,199)(27,135,87,214)(28,122,88,201)(29,57,166,178)(30,72,167,193)(31,59,168,180)(32,74,141,195)(33,61,142,182)(34,76,143,169)(35,63,144,184)(36,78,145,171)(37,65,146,186)(38,80,147,173)(39,67,148,188)(40,82,149,175)(41,69,150,190)(42,84,151,177)(43,71,152,192)(44,58,153,179)(45,73,154,194)(46,60,155,181)(47,75,156,196)(48,62,157,183)(49,77,158,170)(50,64,159,185)(51,79,160,172)(52,66,161,187)(53,81,162,174)(54,68,163,189)(55,83,164,176)(56,70,165,191), (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), (1,41,15,55)(2,54,16,40)(3,39,17,53)(4,52,18,38)(5,37,19,51)(6,50,20,36)(7,35,21,49)(8,48,22,34)(9,33,23,47)(10,46,24,32)(11,31,25,45)(12,44,26,30)(13,29,27,43)(14,42,28,56)(57,214,71,200)(58,199,72,213)(59,212,73,198)(60,197,74,211)(61,210,75,224)(62,223,76,209)(63,208,77,222)(64,221,78,207)(65,206,79,220)(66,219,80,205)(67,204,81,218)(68,217,82,203)(69,202,83,216)(70,215,84,201)(85,154,99,168)(86,167,100,153)(87,152,101,166)(88,165,102,151)(89,150,103,164)(90,163,104,149)(91,148,105,162)(92,161,106,147)(93,146,107,160)(94,159,108,145)(95,144,109,158)(96,157,110,143)(97,142,111,156)(98,155,112,141)(113,186,127,172)(114,171,128,185)(115,184,129,170)(116,169,130,183)(117,182,131,196)(118,195,132,181)(119,180,133,194)(120,193,134,179)(121,178,135,192)(122,191,136,177)(123,176,137,190)(124,189,138,175)(125,174,139,188)(126,187,140,173)>;
G:=Group( (1,22,15,8)(2,23,16,9)(3,24,17,10)(4,25,18,11)(5,26,19,12)(6,27,20,13)(7,28,21,14)(29,36,43,50)(30,37,44,51)(31,38,45,52)(32,39,46,53)(33,40,47,54)(34,41,48,55)(35,42,49,56)(57,78,71,64)(58,79,72,65)(59,80,73,66)(60,81,74,67)(61,82,75,68)(62,83,76,69)(63,84,77,70)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(113,120,127,134)(114,121,128,135)(115,122,129,136)(116,123,130,137)(117,124,131,138)(118,125,132,139)(119,126,133,140)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,137,89,216)(2,124,90,203)(3,139,91,218)(4,126,92,205)(5,113,93,220)(6,128,94,207)(7,115,95,222)(8,130,96,209)(9,117,97,224)(10,132,98,211)(11,119,99,198)(12,134,100,213)(13,121,101,200)(14,136,102,215)(15,123,103,202)(16,138,104,217)(17,125,105,204)(18,140,106,219)(19,127,107,206)(20,114,108,221)(21,129,109,208)(22,116,110,223)(23,131,111,210)(24,118,112,197)(25,133,85,212)(26,120,86,199)(27,135,87,214)(28,122,88,201)(29,57,166,178)(30,72,167,193)(31,59,168,180)(32,74,141,195)(33,61,142,182)(34,76,143,169)(35,63,144,184)(36,78,145,171)(37,65,146,186)(38,80,147,173)(39,67,148,188)(40,82,149,175)(41,69,150,190)(42,84,151,177)(43,71,152,192)(44,58,153,179)(45,73,154,194)(46,60,155,181)(47,75,156,196)(48,62,157,183)(49,77,158,170)(50,64,159,185)(51,79,160,172)(52,66,161,187)(53,81,162,174)(54,68,163,189)(55,83,164,176)(56,70,165,191), (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), (1,41,15,55)(2,54,16,40)(3,39,17,53)(4,52,18,38)(5,37,19,51)(6,50,20,36)(7,35,21,49)(8,48,22,34)(9,33,23,47)(10,46,24,32)(11,31,25,45)(12,44,26,30)(13,29,27,43)(14,42,28,56)(57,214,71,200)(58,199,72,213)(59,212,73,198)(60,197,74,211)(61,210,75,224)(62,223,76,209)(63,208,77,222)(64,221,78,207)(65,206,79,220)(66,219,80,205)(67,204,81,218)(68,217,82,203)(69,202,83,216)(70,215,84,201)(85,154,99,168)(86,167,100,153)(87,152,101,166)(88,165,102,151)(89,150,103,164)(90,163,104,149)(91,148,105,162)(92,161,106,147)(93,146,107,160)(94,159,108,145)(95,144,109,158)(96,157,110,143)(97,142,111,156)(98,155,112,141)(113,186,127,172)(114,171,128,185)(115,184,129,170)(116,169,130,183)(117,182,131,196)(118,195,132,181)(119,180,133,194)(120,193,134,179)(121,178,135,192)(122,191,136,177)(123,176,137,190)(124,189,138,175)(125,174,139,188)(126,187,140,173) );
G=PermutationGroup([[(1,22,15,8),(2,23,16,9),(3,24,17,10),(4,25,18,11),(5,26,19,12),(6,27,20,13),(7,28,21,14),(29,36,43,50),(30,37,44,51),(31,38,45,52),(32,39,46,53),(33,40,47,54),(34,41,48,55),(35,42,49,56),(57,78,71,64),(58,79,72,65),(59,80,73,66),(60,81,74,67),(61,82,75,68),(62,83,76,69),(63,84,77,70),(85,106,99,92),(86,107,100,93),(87,108,101,94),(88,109,102,95),(89,110,103,96),(90,111,104,97),(91,112,105,98),(113,120,127,134),(114,121,128,135),(115,122,129,136),(116,123,130,137),(117,124,131,138),(118,125,132,139),(119,126,133,140),(141,148,155,162),(142,149,156,163),(143,150,157,164),(144,151,158,165),(145,152,159,166),(146,153,160,167),(147,154,161,168),(169,190,183,176),(170,191,184,177),(171,192,185,178),(172,193,186,179),(173,194,187,180),(174,195,188,181),(175,196,189,182),(197,204,211,218),(198,205,212,219),(199,206,213,220),(200,207,214,221),(201,208,215,222),(202,209,216,223),(203,210,217,224)], [(1,137,89,216),(2,124,90,203),(3,139,91,218),(4,126,92,205),(5,113,93,220),(6,128,94,207),(7,115,95,222),(8,130,96,209),(9,117,97,224),(10,132,98,211),(11,119,99,198),(12,134,100,213),(13,121,101,200),(14,136,102,215),(15,123,103,202),(16,138,104,217),(17,125,105,204),(18,140,106,219),(19,127,107,206),(20,114,108,221),(21,129,109,208),(22,116,110,223),(23,131,111,210),(24,118,112,197),(25,133,85,212),(26,120,86,199),(27,135,87,214),(28,122,88,201),(29,57,166,178),(30,72,167,193),(31,59,168,180),(32,74,141,195),(33,61,142,182),(34,76,143,169),(35,63,144,184),(36,78,145,171),(37,65,146,186),(38,80,147,173),(39,67,148,188),(40,82,149,175),(41,69,150,190),(42,84,151,177),(43,71,152,192),(44,58,153,179),(45,73,154,194),(46,60,155,181),(47,75,156,196),(48,62,157,183),(49,77,158,170),(50,64,159,185),(51,79,160,172),(52,66,161,187),(53,81,162,174),(54,68,163,189),(55,83,164,176),(56,70,165,191)], [(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)], [(1,41,15,55),(2,54,16,40),(3,39,17,53),(4,52,18,38),(5,37,19,51),(6,50,20,36),(7,35,21,49),(8,48,22,34),(9,33,23,47),(10,46,24,32),(11,31,25,45),(12,44,26,30),(13,29,27,43),(14,42,28,56),(57,214,71,200),(58,199,72,213),(59,212,73,198),(60,197,74,211),(61,210,75,224),(62,223,76,209),(63,208,77,222),(64,221,78,207),(65,206,79,220),(66,219,80,205),(67,204,81,218),(68,217,82,203),(69,202,83,216),(70,215,84,201),(85,154,99,168),(86,167,100,153),(87,152,101,166),(88,165,102,151),(89,150,103,164),(90,163,104,149),(91,148,105,162),(92,161,106,147),(93,146,107,160),(94,159,108,145),(95,144,109,158),(96,157,110,143),(97,142,111,156),(98,155,112,141),(113,186,127,172),(114,171,128,185),(115,184,129,170),(116,169,130,183),(117,182,131,196),(118,195,132,181),(119,180,133,194),(120,193,134,179),(121,178,135,192),(122,191,136,177),(123,176,137,190),(124,189,138,175),(125,174,139,188),(126,187,140,173)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 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 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | D14 | D28 | 2- 1+4 | D4.10D14 |
| kernel | C42.92D14 | C28⋊2Q8 | C4.D28 | C22.D28 | D14⋊2Q8 | C7×C42⋊C2 | C22×Dic14 | C2×C4○D28 | C2×C28 | C42⋊C2 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C14 | C2 |
| # reps | 1 | 2 | 2 | 4 | 4 | 1 | 1 | 1 | 4 | 3 | 6 | 6 | 6 | 3 | 24 | 2 | 12 |
Matrix representation of C42.92D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 24 | 0 | 0 |
| 0 | 0 | 5 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 24 |
| 0 | 0 | 0 | 0 | 5 | 13 |
| 10 | 28 | 0 | 0 | 0 | 0 |
| 14 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 26 | 0 | 0 |
| 0 | 0 | 3 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 3 |
| 0 | 0 | 0 | 0 | 26 | 22 |
| 22 | 16 | 0 | 0 | 0 | 0 |
| 26 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 18 |
| 0 | 0 | 0 | 0 | 22 | 3 |
| 0 | 0 | 26 | 18 | 0 | 0 |
| 0 | 0 | 22 | 3 | 0 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,16,5,0,0,0,0,24,13,0,0,0,0,0,0,16,5,0,0,0,0,24,13],[10,14,0,0,0,0,28,19,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,0,0,0,0,26,7,0,0,0,0,0,0,26,26,0,0,0,0,3,22],[22,26,0,0,0,0,16,7,0,0,0,0,0,0,0,0,26,22,0,0,0,0,18,3,0,0,26,22,0,0,0,0,18,3,0,0] >;
C42.92D14 in GAP, Magma, Sage, TeX
C_4^2._{92}D_{14} % in TeX
G:=Group("C4^2.92D14"); // GroupNames label
G:=SmallGroup(448,979);
// by ID
G=gap.SmallGroup(448,979);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,675,570,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=a^2*b,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations