metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.106D14, C14.572- 1+4, (C4×D4).13D7, C4⋊C4.314D14, C28⋊2Q8⋊22C2, (D4×C28).14C2, (C4×Dic14)⋊28C2, (C2×D4).210D14, C4.15(C4○D28), (C2×C14).86C24, Dic7⋊3Q8⋊14C2, C28.109(C4○D4), C28.48D4⋊19C2, (C2×C28).155C23, (C4×C28).148C22, C22⋊C4.107D14, C28.17D4.7C2, C23.D14⋊7C2, (C22×C4).205D14, C4.116(D4⋊2D7), C23.92(C22×D7), (D4×C14).250C22, C23.21D14⋊7C2, C4⋊Dic7.297C22, (C2×Dic7).36C23, (C4×Dic7).73C22, C22.114(C23×D7), Dic7⋊C4.109C22, (C22×C28).105C22, (C22×C14).156C23, C7⋊2(C22.50C24), C23.D7.103C22, C2.15(D4.10D14), (C2×Dic14).237C22, C14.38(C2×C4○D4), C2.42(C2×C4○D28), C2.20(C2×D4⋊2D7), (C7×C4⋊C4).322C22, (C2×C4).281(C22×D7), (C7×C22⋊C4).120C22, SmallGroup(448,995)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.106D14
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=c13 >
Subgroups: 756 in 212 conjugacy classes, 99 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C22×C14, C22.50C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×C28, D4×C14, C4×Dic14, C28⋊2Q8, C23.D14, Dic7⋊3Q8, C28.48D4, C23.21D14, C28.17D4, D4×C28, C42.106D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D4.10D14, C42.106D14
►On 224 points
Generators in S224
(1 183 219 134)(2 135 220 184)(3 185 221 136)(4 137 222 186)(5 187 223 138)(6 139 224 188)(7 189 197 140)(8 113 198 190)(9 191 199 114)(10 115 200 192)(11 193 201 116)(12 117 202 194)(13 195 203 118)(14 119 204 196)(15 169 205 120)(16 121 206 170)(17 171 207 122)(18 123 208 172)(19 173 209 124)(20 125 210 174)(21 175 211 126)(22 127 212 176)(23 177 213 128)(24 129 214 178)(25 179 215 130)(26 131 216 180)(27 181 217 132)(28 133 218 182)(29 89 61 146)(30 147 62 90)(31 91 63 148)(32 149 64 92)(33 93 65 150)(34 151 66 94)(35 95 67 152)(36 153 68 96)(37 97 69 154)(38 155 70 98)(39 99 71 156)(40 157 72 100)(41 101 73 158)(42 159 74 102)(43 103 75 160)(44 161 76 104)(45 105 77 162)(46 163 78 106)(47 107 79 164)(48 165 80 108)(49 109 81 166)(50 167 82 110)(51 111 83 168)(52 141 84 112)(53 85 57 142)(54 143 58 86)(55 87 59 144)(56 145 60 88)
(1 190 15 176)(2 191 16 177)(3 192 17 178)(4 193 18 179)(5 194 19 180)(6 195 20 181)(7 196 21 182)(8 169 22 183)(9 170 23 184)(10 171 24 185)(11 172 25 186)(12 173 26 187)(13 174 27 188)(14 175 28 189)(29 167 43 153)(30 168 44 154)(31 141 45 155)(32 142 46 156)(33 143 47 157)(34 144 48 158)(35 145 49 159)(36 146 50 160)(37 147 51 161)(38 148 52 162)(39 149 53 163)(40 150 54 164)(41 151 55 165)(42 152 56 166)(57 106 71 92)(58 107 72 93)(59 108 73 94)(60 109 74 95)(61 110 75 96)(62 111 76 97)(63 112 77 98)(64 85 78 99)(65 86 79 100)(66 87 80 101)(67 88 81 102)(68 89 82 103)(69 90 83 104)(70 91 84 105)(113 205 127 219)(114 206 128 220)(115 207 129 221)(116 208 130 222)(117 209 131 223)(118 210 132 224)(119 211 133 197)(120 212 134 198)(121 213 135 199)(122 214 136 200)(123 215 137 201)(124 216 138 202)(125 217 139 203)(126 218 140 204)
(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 57 219 53)(2 70 220 38)(3 83 221 51)(4 68 222 36)(5 81 223 49)(6 66 224 34)(7 79 197 47)(8 64 198 32)(9 77 199 45)(10 62 200 30)(11 75 201 43)(12 60 202 56)(13 73 203 41)(14 58 204 54)(15 71 205 39)(16 84 206 52)(17 69 207 37)(18 82 208 50)(19 67 209 35)(20 80 210 48)(21 65 211 33)(22 78 212 46)(23 63 213 31)(24 76 214 44)(25 61 215 29)(26 74 216 42)(27 59 217 55)(28 72 218 40)(85 134 142 183)(86 119 143 196)(87 132 144 181)(88 117 145 194)(89 130 146 179)(90 115 147 192)(91 128 148 177)(92 113 149 190)(93 126 150 175)(94 139 151 188)(95 124 152 173)(96 137 153 186)(97 122 154 171)(98 135 155 184)(99 120 156 169)(100 133 157 182)(101 118 158 195)(102 131 159 180)(103 116 160 193)(104 129 161 178)(105 114 162 191)(106 127 163 176)(107 140 164 189)(108 125 165 174)(109 138 166 187)(110 123 167 172)(111 136 168 185)(112 121 141 170)
G:=sub<Sym(224)| (1,183,219,134)(2,135,220,184)(3,185,221,136)(4,137,222,186)(5,187,223,138)(6,139,224,188)(7,189,197,140)(8,113,198,190)(9,191,199,114)(10,115,200,192)(11,193,201,116)(12,117,202,194)(13,195,203,118)(14,119,204,196)(15,169,205,120)(16,121,206,170)(17,171,207,122)(18,123,208,172)(19,173,209,124)(20,125,210,174)(21,175,211,126)(22,127,212,176)(23,177,213,128)(24,129,214,178)(25,179,215,130)(26,131,216,180)(27,181,217,132)(28,133,218,182)(29,89,61,146)(30,147,62,90)(31,91,63,148)(32,149,64,92)(33,93,65,150)(34,151,66,94)(35,95,67,152)(36,153,68,96)(37,97,69,154)(38,155,70,98)(39,99,71,156)(40,157,72,100)(41,101,73,158)(42,159,74,102)(43,103,75,160)(44,161,76,104)(45,105,77,162)(46,163,78,106)(47,107,79,164)(48,165,80,108)(49,109,81,166)(50,167,82,110)(51,111,83,168)(52,141,84,112)(53,85,57,142)(54,143,58,86)(55,87,59,144)(56,145,60,88), (1,190,15,176)(2,191,16,177)(3,192,17,178)(4,193,18,179)(5,194,19,180)(6,195,20,181)(7,196,21,182)(8,169,22,183)(9,170,23,184)(10,171,24,185)(11,172,25,186)(12,173,26,187)(13,174,27,188)(14,175,28,189)(29,167,43,153)(30,168,44,154)(31,141,45,155)(32,142,46,156)(33,143,47,157)(34,144,48,158)(35,145,49,159)(36,146,50,160)(37,147,51,161)(38,148,52,162)(39,149,53,163)(40,150,54,164)(41,151,55,165)(42,152,56,166)(57,106,71,92)(58,107,72,93)(59,108,73,94)(60,109,74,95)(61,110,75,96)(62,111,76,97)(63,112,77,98)(64,85,78,99)(65,86,79,100)(66,87,80,101)(67,88,81,102)(68,89,82,103)(69,90,83,104)(70,91,84,105)(113,205,127,219)(114,206,128,220)(115,207,129,221)(116,208,130,222)(117,209,131,223)(118,210,132,224)(119,211,133,197)(120,212,134,198)(121,213,135,199)(122,214,136,200)(123,215,137,201)(124,216,138,202)(125,217,139,203)(126,218,140,204), (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), (1,57,219,53)(2,70,220,38)(3,83,221,51)(4,68,222,36)(5,81,223,49)(6,66,224,34)(7,79,197,47)(8,64,198,32)(9,77,199,45)(10,62,200,30)(11,75,201,43)(12,60,202,56)(13,73,203,41)(14,58,204,54)(15,71,205,39)(16,84,206,52)(17,69,207,37)(18,82,208,50)(19,67,209,35)(20,80,210,48)(21,65,211,33)(22,78,212,46)(23,63,213,31)(24,76,214,44)(25,61,215,29)(26,74,216,42)(27,59,217,55)(28,72,218,40)(85,134,142,183)(86,119,143,196)(87,132,144,181)(88,117,145,194)(89,130,146,179)(90,115,147,192)(91,128,148,177)(92,113,149,190)(93,126,150,175)(94,139,151,188)(95,124,152,173)(96,137,153,186)(97,122,154,171)(98,135,155,184)(99,120,156,169)(100,133,157,182)(101,118,158,195)(102,131,159,180)(103,116,160,193)(104,129,161,178)(105,114,162,191)(106,127,163,176)(107,140,164,189)(108,125,165,174)(109,138,166,187)(110,123,167,172)(111,136,168,185)(112,121,141,170)>;
G:=Group( (1,183,219,134)(2,135,220,184)(3,185,221,136)(4,137,222,186)(5,187,223,138)(6,139,224,188)(7,189,197,140)(8,113,198,190)(9,191,199,114)(10,115,200,192)(11,193,201,116)(12,117,202,194)(13,195,203,118)(14,119,204,196)(15,169,205,120)(16,121,206,170)(17,171,207,122)(18,123,208,172)(19,173,209,124)(20,125,210,174)(21,175,211,126)(22,127,212,176)(23,177,213,128)(24,129,214,178)(25,179,215,130)(26,131,216,180)(27,181,217,132)(28,133,218,182)(29,89,61,146)(30,147,62,90)(31,91,63,148)(32,149,64,92)(33,93,65,150)(34,151,66,94)(35,95,67,152)(36,153,68,96)(37,97,69,154)(38,155,70,98)(39,99,71,156)(40,157,72,100)(41,101,73,158)(42,159,74,102)(43,103,75,160)(44,161,76,104)(45,105,77,162)(46,163,78,106)(47,107,79,164)(48,165,80,108)(49,109,81,166)(50,167,82,110)(51,111,83,168)(52,141,84,112)(53,85,57,142)(54,143,58,86)(55,87,59,144)(56,145,60,88), (1,190,15,176)(2,191,16,177)(3,192,17,178)(4,193,18,179)(5,194,19,180)(6,195,20,181)(7,196,21,182)(8,169,22,183)(9,170,23,184)(10,171,24,185)(11,172,25,186)(12,173,26,187)(13,174,27,188)(14,175,28,189)(29,167,43,153)(30,168,44,154)(31,141,45,155)(32,142,46,156)(33,143,47,157)(34,144,48,158)(35,145,49,159)(36,146,50,160)(37,147,51,161)(38,148,52,162)(39,149,53,163)(40,150,54,164)(41,151,55,165)(42,152,56,166)(57,106,71,92)(58,107,72,93)(59,108,73,94)(60,109,74,95)(61,110,75,96)(62,111,76,97)(63,112,77,98)(64,85,78,99)(65,86,79,100)(66,87,80,101)(67,88,81,102)(68,89,82,103)(69,90,83,104)(70,91,84,105)(113,205,127,219)(114,206,128,220)(115,207,129,221)(116,208,130,222)(117,209,131,223)(118,210,132,224)(119,211,133,197)(120,212,134,198)(121,213,135,199)(122,214,136,200)(123,215,137,201)(124,216,138,202)(125,217,139,203)(126,218,140,204), (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), (1,57,219,53)(2,70,220,38)(3,83,221,51)(4,68,222,36)(5,81,223,49)(6,66,224,34)(7,79,197,47)(8,64,198,32)(9,77,199,45)(10,62,200,30)(11,75,201,43)(12,60,202,56)(13,73,203,41)(14,58,204,54)(15,71,205,39)(16,84,206,52)(17,69,207,37)(18,82,208,50)(19,67,209,35)(20,80,210,48)(21,65,211,33)(22,78,212,46)(23,63,213,31)(24,76,214,44)(25,61,215,29)(26,74,216,42)(27,59,217,55)(28,72,218,40)(85,134,142,183)(86,119,143,196)(87,132,144,181)(88,117,145,194)(89,130,146,179)(90,115,147,192)(91,128,148,177)(92,113,149,190)(93,126,150,175)(94,139,151,188)(95,124,152,173)(96,137,153,186)(97,122,154,171)(98,135,155,184)(99,120,156,169)(100,133,157,182)(101,118,158,195)(102,131,159,180)(103,116,160,193)(104,129,161,178)(105,114,162,191)(106,127,163,176)(107,140,164,189)(108,125,165,174)(109,138,166,187)(110,123,167,172)(111,136,168,185)(112,121,141,170) );
G=PermutationGroup([[(1,183,219,134),(2,135,220,184),(3,185,221,136),(4,137,222,186),(5,187,223,138),(6,139,224,188),(7,189,197,140),(8,113,198,190),(9,191,199,114),(10,115,200,192),(11,193,201,116),(12,117,202,194),(13,195,203,118),(14,119,204,196),(15,169,205,120),(16,121,206,170),(17,171,207,122),(18,123,208,172),(19,173,209,124),(20,125,210,174),(21,175,211,126),(22,127,212,176),(23,177,213,128),(24,129,214,178),(25,179,215,130),(26,131,216,180),(27,181,217,132),(28,133,218,182),(29,89,61,146),(30,147,62,90),(31,91,63,148),(32,149,64,92),(33,93,65,150),(34,151,66,94),(35,95,67,152),(36,153,68,96),(37,97,69,154),(38,155,70,98),(39,99,71,156),(40,157,72,100),(41,101,73,158),(42,159,74,102),(43,103,75,160),(44,161,76,104),(45,105,77,162),(46,163,78,106),(47,107,79,164),(48,165,80,108),(49,109,81,166),(50,167,82,110),(51,111,83,168),(52,141,84,112),(53,85,57,142),(54,143,58,86),(55,87,59,144),(56,145,60,88)], [(1,190,15,176),(2,191,16,177),(3,192,17,178),(4,193,18,179),(5,194,19,180),(6,195,20,181),(7,196,21,182),(8,169,22,183),(9,170,23,184),(10,171,24,185),(11,172,25,186),(12,173,26,187),(13,174,27,188),(14,175,28,189),(29,167,43,153),(30,168,44,154),(31,141,45,155),(32,142,46,156),(33,143,47,157),(34,144,48,158),(35,145,49,159),(36,146,50,160),(37,147,51,161),(38,148,52,162),(39,149,53,163),(40,150,54,164),(41,151,55,165),(42,152,56,166),(57,106,71,92),(58,107,72,93),(59,108,73,94),(60,109,74,95),(61,110,75,96),(62,111,76,97),(63,112,77,98),(64,85,78,99),(65,86,79,100),(66,87,80,101),(67,88,81,102),(68,89,82,103),(69,90,83,104),(70,91,84,105),(113,205,127,219),(114,206,128,220),(115,207,129,221),(116,208,130,222),(117,209,131,223),(118,210,132,224),(119,211,133,197),(120,212,134,198),(121,213,135,199),(122,214,136,200),(123,215,137,201),(124,216,138,202),(125,217,139,203),(126,218,140,204)], [(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)], [(1,57,219,53),(2,70,220,38),(3,83,221,51),(4,68,222,36),(5,81,223,49),(6,66,224,34),(7,79,197,47),(8,64,198,32),(9,77,199,45),(10,62,200,30),(11,75,201,43),(12,60,202,56),(13,73,203,41),(14,58,204,54),(15,71,205,39),(16,84,206,52),(17,69,207,37),(18,82,208,50),(19,67,209,35),(20,80,210,48),(21,65,211,33),(22,78,212,46),(23,63,213,31),(24,76,214,44),(25,61,215,29),(26,74,216,42),(27,59,217,55),(28,72,218,40),(85,134,142,183),(86,119,143,196),(87,132,144,181),(88,117,145,194),(89,130,146,179),(90,115,147,192),(91,128,148,177),(92,113,149,190),(93,126,150,175),(94,139,151,188),(95,124,152,173),(96,137,153,186),(97,122,154,171),(98,135,155,184),(99,120,156,169),(100,133,157,182),(101,118,158,195),(102,131,159,180),(103,116,160,193),(104,129,161,178),(105,114,162,191),(106,127,163,176),(107,140,164,189),(108,125,165,174),(109,138,166,187),(110,123,167,172),(111,136,168,185),(112,121,141,170)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | ··· | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 4 | 2 | ··· | 2 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | D4⋊2D7 | D4.10D14 |
| kernel | C42.106D14 | C4×Dic14 | C28⋊2Q8 | C23.D14 | Dic7⋊3Q8 | C28.48D4 | C23.21D14 | C28.17D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 2 | 1 | 3 | 8 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.106D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 4 | 0 | 0 | 0 | 0 | 0 |
| 9 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 27 |
| 0 | 0 | 0 | 0 | 28 | 12 |
| 14 | 28 | 0 | 0 | 0 | 0 |
| 21 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 24 |
| 0 | 0 | 0 | 0 | 12 | 1 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,2,17],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[4,9,0,0,0,0,0,22,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,28,0,0,0,0,27,12],[14,21,0,0,0,0,28,15,0,0,0,0,0,0,0,12,0,0,0,0,17,0,0,0,0,0,0,0,28,12,0,0,0,0,24,1] >;
C42.106D14 in GAP, Magma, Sage, TeX
C_4^2._{106}D_{14} % in TeX
G:=Group("C4^2.106D14"); // GroupNames label
G:=SmallGroup(448,995);
// by ID
G=gap.SmallGroup(448,995);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,219,268,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,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=b^-1,d*c*d^-1=c^13>;
// generators/relations