metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.165D14, C14.1032- 1+4, C14.1432+ 1+4, C28⋊Q8⋊42C2, C28⋊2Q8⋊9C2, C4⋊C4.120D14, C42⋊2D7⋊2C2, C42⋊2C2⋊9D7, (C4×C28).9C22, D14⋊2Q8⋊43C2, D14⋊Q8⋊46C2, Dic7.Q8⋊40C2, (C2×C28).97C23, C22⋊C4.42D14, C28.3Q8⋊41C2, (C2×C14).256C24, D14⋊C4.48C22, D14.D4.5C2, C4⋊Dic7.55C22, C2.68(D4⋊8D14), C23.62(C22×D7), C22⋊Dic14⋊48C2, C23.D14⋊47C2, Dic7⋊C4.11C22, (C22×C14).70C23, Dic7.D4.5C2, C22.D28.3C2, C22.277(C23×D7), C23.D7.70C22, C7⋊5(C22.57C24), (C4×Dic7).153C22, (C2×Dic14).43C22, (C2×Dic7).132C23, (C22×D7).115C23, C2.67(D4.10D14), (C22×Dic7).155C22, C4⋊C4⋊D7⋊45C2, (C2×C4×D7).137C22, (C7×C42⋊2C2)⋊11C2, (C7×C4⋊C4).207C22, (C2×C4).212(C22×D7), (C2×C7⋊D4).76C22, (C7×C22⋊C4).81C22, SmallGroup(448,1165)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.165D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=ab2, dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=c13 >
Subgroups: 876 in 196 conjugacy classes, 91 normal (all characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C22×D7, C22×C14, C22.57C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C28⋊2Q8, C42⋊2D7, C22⋊Dic14, C23.D14, D14.D4, Dic7.D4, C22.D28, C28⋊Q8, Dic7.Q8, C28.3Q8, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42⋊2C2, C42.165D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.57C24, C23×D7, D4⋊8D14, D4.10D14, C42.165D14
►On 224 points
Generators in S224
(1 139 132 8)(2 23 133 126)(3 113 134 10)(4 25 135 128)(5 115 136 12)(6 27 137 130)(7 117 138 14)(9 119 140 16)(11 121 114 18)(13 123 116 20)(15 125 118 22)(17 127 120 24)(19 129 122 26)(21 131 124 28)(29 162 141 50)(30 37 142 149)(31 164 143 52)(32 39 144 151)(33 166 145 54)(34 41 146 153)(35 168 147 56)(36 43 148 155)(38 45 150 157)(40 47 152 159)(42 49 154 161)(44 51 156 163)(46 53 158 165)(48 55 160 167)(57 78 181 174)(58 189 182 65)(59 80 183 176)(60 191 184 67)(61 82 185 178)(62 193 186 69)(63 84 187 180)(64 195 188 71)(66 169 190 73)(68 171 192 75)(70 173 194 77)(72 175 196 79)(74 177 170 81)(76 179 172 83)(85 211 218 106)(86 93 219 198)(87 213 220 108)(88 95 221 200)(89 215 222 110)(90 97 223 202)(91 217 224 112)(92 99 197 204)(94 101 199 206)(96 103 201 208)(98 105 203 210)(100 107 205 212)(102 109 207 214)(104 111 209 216)
(1 151 118 53)(2 166 119 40)(3 153 120 55)(4 168 121 42)(5 155 122 29)(6 142 123 44)(7 157 124 31)(8 144 125 46)(9 159 126 33)(10 146 127 48)(11 161 128 35)(12 148 129 50)(13 163 130 37)(14 150 131 52)(15 165 132 39)(16 152 133 54)(17 167 134 41)(18 154 135 56)(19 141 136 43)(20 156 137 30)(21 143 138 45)(22 158 139 32)(23 145 140 47)(24 160 113 34)(25 147 114 49)(26 162 115 36)(27 149 116 51)(28 164 117 38)(57 209 195 90)(58 224 196 105)(59 211 169 92)(60 198 170 107)(61 213 171 94)(62 200 172 109)(63 215 173 96)(64 202 174 111)(65 217 175 98)(66 204 176 85)(67 219 177 100)(68 206 178 87)(69 221 179 102)(70 208 180 89)(71 223 181 104)(72 210 182 91)(73 197 183 106)(74 212 184 93)(75 199 185 108)(76 214 186 95)(77 201 187 110)(78 216 188 97)(79 203 189 112)(80 218 190 99)(81 205 191 86)(82 220 192 101)(83 207 193 88)(84 222 194 103)
(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)
(1 197 15 211)(2 210 16 224)(3 223 17 209)(4 208 18 222)(5 221 19 207)(6 206 20 220)(7 219 21 205)(8 204 22 218)(9 217 23 203)(10 202 24 216)(11 215 25 201)(12 200 26 214)(13 213 27 199)(14 198 28 212)(29 179 43 193)(30 192 44 178)(31 177 45 191)(32 190 46 176)(33 175 47 189)(34 188 48 174)(35 173 49 187)(36 186 50 172)(37 171 51 185)(38 184 52 170)(39 169 53 183)(40 182 54 196)(41 195 55 181)(42 180 56 194)(57 153 71 167)(58 166 72 152)(59 151 73 165)(60 164 74 150)(61 149 75 163)(62 162 76 148)(63 147 77 161)(64 160 78 146)(65 145 79 159)(66 158 80 144)(67 143 81 157)(68 156 82 142)(69 141 83 155)(70 154 84 168)(85 139 99 125)(86 124 100 138)(87 137 101 123)(88 122 102 136)(89 135 103 121)(90 120 104 134)(91 133 105 119)(92 118 106 132)(93 131 107 117)(94 116 108 130)(95 129 109 115)(96 114 110 128)(97 127 111 113)(98 140 112 126)
G:=sub<Sym(224)| (1,139,132,8)(2,23,133,126)(3,113,134,10)(4,25,135,128)(5,115,136,12)(6,27,137,130)(7,117,138,14)(9,119,140,16)(11,121,114,18)(13,123,116,20)(15,125,118,22)(17,127,120,24)(19,129,122,26)(21,131,124,28)(29,162,141,50)(30,37,142,149)(31,164,143,52)(32,39,144,151)(33,166,145,54)(34,41,146,153)(35,168,147,56)(36,43,148,155)(38,45,150,157)(40,47,152,159)(42,49,154,161)(44,51,156,163)(46,53,158,165)(48,55,160,167)(57,78,181,174)(58,189,182,65)(59,80,183,176)(60,191,184,67)(61,82,185,178)(62,193,186,69)(63,84,187,180)(64,195,188,71)(66,169,190,73)(68,171,192,75)(70,173,194,77)(72,175,196,79)(74,177,170,81)(76,179,172,83)(85,211,218,106)(86,93,219,198)(87,213,220,108)(88,95,221,200)(89,215,222,110)(90,97,223,202)(91,217,224,112)(92,99,197,204)(94,101,199,206)(96,103,201,208)(98,105,203,210)(100,107,205,212)(102,109,207,214)(104,111,209,216), (1,151,118,53)(2,166,119,40)(3,153,120,55)(4,168,121,42)(5,155,122,29)(6,142,123,44)(7,157,124,31)(8,144,125,46)(9,159,126,33)(10,146,127,48)(11,161,128,35)(12,148,129,50)(13,163,130,37)(14,150,131,52)(15,165,132,39)(16,152,133,54)(17,167,134,41)(18,154,135,56)(19,141,136,43)(20,156,137,30)(21,143,138,45)(22,158,139,32)(23,145,140,47)(24,160,113,34)(25,147,114,49)(26,162,115,36)(27,149,116,51)(28,164,117,38)(57,209,195,90)(58,224,196,105)(59,211,169,92)(60,198,170,107)(61,213,171,94)(62,200,172,109)(63,215,173,96)(64,202,174,111)(65,217,175,98)(66,204,176,85)(67,219,177,100)(68,206,178,87)(69,221,179,102)(70,208,180,89)(71,223,181,104)(72,210,182,91)(73,197,183,106)(74,212,184,93)(75,199,185,108)(76,214,186,95)(77,201,187,110)(78,216,188,97)(79,203,189,112)(80,218,190,99)(81,205,191,86)(82,220,192,101)(83,207,193,88)(84,222,194,103), (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), (1,197,15,211)(2,210,16,224)(3,223,17,209)(4,208,18,222)(5,221,19,207)(6,206,20,220)(7,219,21,205)(8,204,22,218)(9,217,23,203)(10,202,24,216)(11,215,25,201)(12,200,26,214)(13,213,27,199)(14,198,28,212)(29,179,43,193)(30,192,44,178)(31,177,45,191)(32,190,46,176)(33,175,47,189)(34,188,48,174)(35,173,49,187)(36,186,50,172)(37,171,51,185)(38,184,52,170)(39,169,53,183)(40,182,54,196)(41,195,55,181)(42,180,56,194)(57,153,71,167)(58,166,72,152)(59,151,73,165)(60,164,74,150)(61,149,75,163)(62,162,76,148)(63,147,77,161)(64,160,78,146)(65,145,79,159)(66,158,80,144)(67,143,81,157)(68,156,82,142)(69,141,83,155)(70,154,84,168)(85,139,99,125)(86,124,100,138)(87,137,101,123)(88,122,102,136)(89,135,103,121)(90,120,104,134)(91,133,105,119)(92,118,106,132)(93,131,107,117)(94,116,108,130)(95,129,109,115)(96,114,110,128)(97,127,111,113)(98,140,112,126)>;
G:=Group( (1,139,132,8)(2,23,133,126)(3,113,134,10)(4,25,135,128)(5,115,136,12)(6,27,137,130)(7,117,138,14)(9,119,140,16)(11,121,114,18)(13,123,116,20)(15,125,118,22)(17,127,120,24)(19,129,122,26)(21,131,124,28)(29,162,141,50)(30,37,142,149)(31,164,143,52)(32,39,144,151)(33,166,145,54)(34,41,146,153)(35,168,147,56)(36,43,148,155)(38,45,150,157)(40,47,152,159)(42,49,154,161)(44,51,156,163)(46,53,158,165)(48,55,160,167)(57,78,181,174)(58,189,182,65)(59,80,183,176)(60,191,184,67)(61,82,185,178)(62,193,186,69)(63,84,187,180)(64,195,188,71)(66,169,190,73)(68,171,192,75)(70,173,194,77)(72,175,196,79)(74,177,170,81)(76,179,172,83)(85,211,218,106)(86,93,219,198)(87,213,220,108)(88,95,221,200)(89,215,222,110)(90,97,223,202)(91,217,224,112)(92,99,197,204)(94,101,199,206)(96,103,201,208)(98,105,203,210)(100,107,205,212)(102,109,207,214)(104,111,209,216), (1,151,118,53)(2,166,119,40)(3,153,120,55)(4,168,121,42)(5,155,122,29)(6,142,123,44)(7,157,124,31)(8,144,125,46)(9,159,126,33)(10,146,127,48)(11,161,128,35)(12,148,129,50)(13,163,130,37)(14,150,131,52)(15,165,132,39)(16,152,133,54)(17,167,134,41)(18,154,135,56)(19,141,136,43)(20,156,137,30)(21,143,138,45)(22,158,139,32)(23,145,140,47)(24,160,113,34)(25,147,114,49)(26,162,115,36)(27,149,116,51)(28,164,117,38)(57,209,195,90)(58,224,196,105)(59,211,169,92)(60,198,170,107)(61,213,171,94)(62,200,172,109)(63,215,173,96)(64,202,174,111)(65,217,175,98)(66,204,176,85)(67,219,177,100)(68,206,178,87)(69,221,179,102)(70,208,180,89)(71,223,181,104)(72,210,182,91)(73,197,183,106)(74,212,184,93)(75,199,185,108)(76,214,186,95)(77,201,187,110)(78,216,188,97)(79,203,189,112)(80,218,190,99)(81,205,191,86)(82,220,192,101)(83,207,193,88)(84,222,194,103), (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), (1,197,15,211)(2,210,16,224)(3,223,17,209)(4,208,18,222)(5,221,19,207)(6,206,20,220)(7,219,21,205)(8,204,22,218)(9,217,23,203)(10,202,24,216)(11,215,25,201)(12,200,26,214)(13,213,27,199)(14,198,28,212)(29,179,43,193)(30,192,44,178)(31,177,45,191)(32,190,46,176)(33,175,47,189)(34,188,48,174)(35,173,49,187)(36,186,50,172)(37,171,51,185)(38,184,52,170)(39,169,53,183)(40,182,54,196)(41,195,55,181)(42,180,56,194)(57,153,71,167)(58,166,72,152)(59,151,73,165)(60,164,74,150)(61,149,75,163)(62,162,76,148)(63,147,77,161)(64,160,78,146)(65,145,79,159)(66,158,80,144)(67,143,81,157)(68,156,82,142)(69,141,83,155)(70,154,84,168)(85,139,99,125)(86,124,100,138)(87,137,101,123)(88,122,102,136)(89,135,103,121)(90,120,104,134)(91,133,105,119)(92,118,106,132)(93,131,107,117)(94,116,108,130)(95,129,109,115)(96,114,110,128)(97,127,111,113)(98,140,112,126) );
G=PermutationGroup([[(1,139,132,8),(2,23,133,126),(3,113,134,10),(4,25,135,128),(5,115,136,12),(6,27,137,130),(7,117,138,14),(9,119,140,16),(11,121,114,18),(13,123,116,20),(15,125,118,22),(17,127,120,24),(19,129,122,26),(21,131,124,28),(29,162,141,50),(30,37,142,149),(31,164,143,52),(32,39,144,151),(33,166,145,54),(34,41,146,153),(35,168,147,56),(36,43,148,155),(38,45,150,157),(40,47,152,159),(42,49,154,161),(44,51,156,163),(46,53,158,165),(48,55,160,167),(57,78,181,174),(58,189,182,65),(59,80,183,176),(60,191,184,67),(61,82,185,178),(62,193,186,69),(63,84,187,180),(64,195,188,71),(66,169,190,73),(68,171,192,75),(70,173,194,77),(72,175,196,79),(74,177,170,81),(76,179,172,83),(85,211,218,106),(86,93,219,198),(87,213,220,108),(88,95,221,200),(89,215,222,110),(90,97,223,202),(91,217,224,112),(92,99,197,204),(94,101,199,206),(96,103,201,208),(98,105,203,210),(100,107,205,212),(102,109,207,214),(104,111,209,216)], [(1,151,118,53),(2,166,119,40),(3,153,120,55),(4,168,121,42),(5,155,122,29),(6,142,123,44),(7,157,124,31),(8,144,125,46),(9,159,126,33),(10,146,127,48),(11,161,128,35),(12,148,129,50),(13,163,130,37),(14,150,131,52),(15,165,132,39),(16,152,133,54),(17,167,134,41),(18,154,135,56),(19,141,136,43),(20,156,137,30),(21,143,138,45),(22,158,139,32),(23,145,140,47),(24,160,113,34),(25,147,114,49),(26,162,115,36),(27,149,116,51),(28,164,117,38),(57,209,195,90),(58,224,196,105),(59,211,169,92),(60,198,170,107),(61,213,171,94),(62,200,172,109),(63,215,173,96),(64,202,174,111),(65,217,175,98),(66,204,176,85),(67,219,177,100),(68,206,178,87),(69,221,179,102),(70,208,180,89),(71,223,181,104),(72,210,182,91),(73,197,183,106),(74,212,184,93),(75,199,185,108),(76,214,186,95),(77,201,187,110),(78,216,188,97),(79,203,189,112),(80,218,190,99),(81,205,191,86),(82,220,192,101),(83,207,193,88),(84,222,194,103)], [(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)], [(1,197,15,211),(2,210,16,224),(3,223,17,209),(4,208,18,222),(5,221,19,207),(6,206,20,220),(7,219,21,205),(8,204,22,218),(9,217,23,203),(10,202,24,216),(11,215,25,201),(12,200,26,214),(13,213,27,199),(14,198,28,212),(29,179,43,193),(30,192,44,178),(31,177,45,191),(32,190,46,176),(33,175,47,189),(34,188,48,174),(35,173,49,187),(36,186,50,172),(37,171,51,185),(38,184,52,170),(39,169,53,183),(40,182,54,196),(41,195,55,181),(42,180,56,194),(57,153,71,167),(58,166,72,152),(59,151,73,165),(60,164,74,150),(61,149,75,163),(62,162,76,148),(63,147,77,161),(64,160,78,146),(65,145,79,159),(66,158,80,144),(67,143,81,157),(68,156,82,142),(69,141,83,155),(70,154,84,168),(85,139,99,125),(86,124,100,138),(87,137,101,123),(88,122,102,136),(89,135,103,121),(90,120,104,134),(91,133,105,119),(92,118,106,132),(93,131,107,117),(94,116,108,130),(95,129,109,115),(96,114,110,128),(97,127,111,113),(98,140,112,126)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.165D14 | C28⋊2Q8 | C42⋊2D7 | C22⋊Dic14 | C23.D14 | D14.D4 | Dic7.D4 | C22.D28 | C28⋊Q8 | Dic7.Q8 | C28.3Q8 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | C42 | C22⋊C4 | C4⋊C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 9 | 9 | 1 | 2 | 6 | 12 |
Matrix representation of C42.165D14 ►in GL8(𝔽29)
| 3 | 11 | 23 | 7 | 0 | 0 | 0 | 0 |
| 7 | 26 | 15 | 6 | 0 | 0 | 0 | 0 |
| 3 | 11 | 26 | 18 | 0 | 0 | 0 | 0 |
| 7 | 26 | 22 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 5 | 25 | 0 |
| 0 | 0 | 0 | 0 | 24 | 16 | 0 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 5 | 13 |
| 1 | 0 | 27 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 27 | 0 | 0 | 0 | 0 |
| 1 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 5 |
| 0 | 0 | 0 | 0 | 0 | 0 | 24 | 16 |
| 4 | 12 | 21 | 5 | 0 | 0 | 0 | 0 |
| 5 | 8 | 19 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 3 | 16 | 16 |
| 0 | 0 | 0 | 0 | 26 | 22 | 13 | 14 |
| 0 | 0 | 0 | 0 | 2 | 2 | 3 | 26 |
| 0 | 0 | 0 | 0 | 27 | 9 | 3 | 7 |
| 22 | 13 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 22 | 13 | 7 | 16 | 0 | 0 | 0 | 0 |
| 14 | 7 | 15 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 25 | 17 | 12 |
| 0 | 0 | 0 | 0 | 11 | 4 | 28 | 12 |
| 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 11 | 4 |
G:=sub<GL(8,GF(29))| [3,7,3,7,0,0,0,0,11,26,11,26,0,0,0,0,23,15,26,22,0,0,0,0,7,6,18,3,0,0,0,0,0,0,0,0,13,24,0,0,0,0,0,0,5,16,0,0,0,0,0,0,25,0,16,5,0,0,0,0,0,25,24,13],[1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,27,0,28,0,0,0,0,0,0,27,0,28,0,0,0,0,0,0,0,0,13,24,0,0,0,0,0,0,5,16,0,0,0,0,0,0,0,0,13,24,0,0,0,0,0,0,5,16],[4,5,0,0,0,0,0,0,12,8,0,0,0,0,0,0,21,19,25,24,0,0,0,0,5,13,17,21,0,0,0,0,0,0,0,0,26,26,2,27,0,0,0,0,3,22,2,9,0,0,0,0,16,13,3,3,0,0,0,0,16,14,26,7],[22,14,22,14,0,0,0,0,13,7,13,7,0,0,0,0,0,0,7,15,0,0,0,0,0,0,16,22,0,0,0,0,0,0,0,0,25,11,0,0,0,0,0,0,25,4,0,0,0,0,0,0,17,28,25,11,0,0,0,0,12,12,25,4] >;
C42.165D14 in GAP, Magma, Sage, TeX
C_4^2._{165}D_{14} % in TeX
G:=Group("C4^2.165D14"); // GroupNames label
G:=SmallGroup(448,1165);
// by ID
G=gap.SmallGroup(448,1165);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,570,297,80,18822]);
// 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=a*b^2,d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations