metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.99D14, C14.992+ 1+4, C14.542- 1+4, (C4×D28)⋊11C2, C28⋊2Q8⋊8C2, C4⋊C4.274D14, D14⋊Q8⋊6C2, C4.D28⋊5C2, (C4×Dic14)⋊12C2, D14.D4⋊5C2, C28⋊7D4.18C2, C42⋊C2⋊18D7, (C2×C14).78C24, (C4×C28).29C22, D14⋊C4.4C22, C4.120(C4○D28), C28.236(C4○D4), C28.48D4⋊42C2, (C2×C28).151C23, C22⋊C4.102D14, Dic7.D4⋊5C2, (C22×C4).199D14, C4⋊Dic7.36C22, C2.11(D4⋊8D14), C23.89(C22×D7), C23.D7.6C22, (C2×D28).208C22, Dic7⋊C4.75C22, (C2×Dic7).31C23, (C22×D7).26C23, C22.107(C23×D7), (C22×C28).308C22, (C22×C14).148C23, C7⋊1(C22.36C24), (C4×Dic7).200C22, C2.12(D4.10D14), (C2×Dic14).233C22, C4⋊C4⋊D7⋊6C2, C2.37(C2×C4○D28), C14.34(C2×C4○D4), (C2×C4×D7).195C22, (C7×C42⋊C2)⋊20C2, (C7×C4⋊C4).314C22, (C2×C4).151(C22×D7), (C2×C7⋊D4).11C22, (C7×C22⋊C4).117C22, SmallGroup(448,987)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.99D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, ac=ca, dad-1=a-1, cbc-1=dbd-1=a2b, dcd-1=b2c-1 >
Subgroups: 1012 in 216 conjugacy classes, 95 normal (51 characteristic)
C1, C2, C2, C4, 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, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C22.36C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, C4×Dic14, C28⋊2Q8, C4×D28, C4.D28, D14.D4, Dic7.D4, D14⋊Q8, C4⋊C4⋊D7, C28.48D4, C28⋊7D4, C7×C42⋊C2, C42.99D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, C4○D28, C23×D7, C2×C4○D28, D4⋊8D14, D4.10D14, C42.99D14
►On 224 points
Generators in S224
(1 14 28 32)(2 8 22 33)(3 9 23 34)(4 10 24 35)(5 11 25 29)(6 12 26 30)(7 13 27 31)(15 44 42 54)(16 45 36 55)(17 46 37 56)(18 47 38 50)(19 48 39 51)(20 49 40 52)(21 43 41 53)(57 216 199 182)(58 217 200 169)(59 218 201 170)(60 219 202 171)(61 220 203 172)(62 221 204 173)(63 222 205 174)(64 223 206 175)(65 224 207 176)(66 211 208 177)(67 212 209 178)(68 213 210 179)(69 214 197 180)(70 215 198 181)(71 85 78 92)(72 86 79 93)(73 87 80 94)(74 88 81 95)(75 89 82 96)(76 90 83 97)(77 91 84 98)(99 159 106 166)(100 160 107 167)(101 161 108 168)(102 162 109 155)(103 163 110 156)(104 164 111 157)(105 165 112 158)(113 191 153 140)(114 192 154 127)(115 193 141 128)(116 194 142 129)(117 195 143 130)(118 196 144 131)(119 183 145 132)(120 184 146 133)(121 185 147 134)(122 186 148 135)(123 187 149 136)(124 188 150 137)(125 189 151 138)(126 190 152 139)
(1 78 43 111)(2 72 44 105)(3 80 45 99)(4 74 46 107)(5 82 47 101)(6 76 48 109)(7 84 49 103)(8 86 42 165)(9 94 36 159)(10 88 37 167)(11 96 38 161)(12 90 39 155)(13 98 40 163)(14 92 41 157)(15 158 33 93)(16 166 34 87)(17 160 35 95)(18 168 29 89)(19 162 30 97)(20 156 31 91)(21 164 32 85)(22 79 54 112)(23 73 55 106)(24 81 56 100)(25 75 50 108)(26 83 51 102)(27 77 52 110)(28 71 53 104)(57 145 206 152)(58 120 207 113)(59 147 208 154)(60 122 209 115)(61 149 210 142)(62 124 197 117)(63 151 198 144)(64 126 199 119)(65 153 200 146)(66 114 201 121)(67 141 202 148)(68 116 203 123)(69 143 204 150)(70 118 205 125)(127 218 134 177)(128 171 135 212)(129 220 136 179)(130 173 137 214)(131 222 138 181)(132 175 139 216)(133 224 140 169)(170 185 211 192)(172 187 213 194)(174 189 215 196)(176 191 217 184)(178 193 219 186)(180 195 221 188)(182 183 223 190)
(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)
(1 136 43 129)(2 128 44 135)(3 134 45 127)(4 140 46 133)(5 132 47 139)(6 138 48 131)(7 130 49 137)(8 141 42 148)(9 147 36 154)(10 153 37 146)(11 145 38 152)(12 151 39 144)(13 143 40 150)(14 149 41 142)(15 122 33 115)(16 114 34 121)(17 120 35 113)(18 126 29 119)(19 118 30 125)(20 124 31 117)(21 116 32 123)(22 193 54 186)(23 185 55 192)(24 191 56 184)(25 183 50 190)(26 189 51 196)(27 195 52 188)(28 187 53 194)(57 89 206 168)(58 167 207 88)(59 87 208 166)(60 165 209 86)(61 85 210 164)(62 163 197 98)(63 97 198 162)(64 161 199 96)(65 95 200 160)(66 159 201 94)(67 93 202 158)(68 157 203 92)(69 91 204 156)(70 155 205 90)(71 179 104 220)(72 219 105 178)(73 177 106 218)(74 217 107 176)(75 175 108 216)(76 215 109 174)(77 173 110 214)(78 213 111 172)(79 171 112 212)(80 211 99 170)(81 169 100 224)(82 223 101 182)(83 181 102 222)(84 221 103 180)
G:=sub<Sym(224)| (1,14,28,32)(2,8,22,33)(3,9,23,34)(4,10,24,35)(5,11,25,29)(6,12,26,30)(7,13,27,31)(15,44,42,54)(16,45,36,55)(17,46,37,56)(18,47,38,50)(19,48,39,51)(20,49,40,52)(21,43,41,53)(57,216,199,182)(58,217,200,169)(59,218,201,170)(60,219,202,171)(61,220,203,172)(62,221,204,173)(63,222,205,174)(64,223,206,175)(65,224,207,176)(66,211,208,177)(67,212,209,178)(68,213,210,179)(69,214,197,180)(70,215,198,181)(71,85,78,92)(72,86,79,93)(73,87,80,94)(74,88,81,95)(75,89,82,96)(76,90,83,97)(77,91,84,98)(99,159,106,166)(100,160,107,167)(101,161,108,168)(102,162,109,155)(103,163,110,156)(104,164,111,157)(105,165,112,158)(113,191,153,140)(114,192,154,127)(115,193,141,128)(116,194,142,129)(117,195,143,130)(118,196,144,131)(119,183,145,132)(120,184,146,133)(121,185,147,134)(122,186,148,135)(123,187,149,136)(124,188,150,137)(125,189,151,138)(126,190,152,139), (1,78,43,111)(2,72,44,105)(3,80,45,99)(4,74,46,107)(5,82,47,101)(6,76,48,109)(7,84,49,103)(8,86,42,165)(9,94,36,159)(10,88,37,167)(11,96,38,161)(12,90,39,155)(13,98,40,163)(14,92,41,157)(15,158,33,93)(16,166,34,87)(17,160,35,95)(18,168,29,89)(19,162,30,97)(20,156,31,91)(21,164,32,85)(22,79,54,112)(23,73,55,106)(24,81,56,100)(25,75,50,108)(26,83,51,102)(27,77,52,110)(28,71,53,104)(57,145,206,152)(58,120,207,113)(59,147,208,154)(60,122,209,115)(61,149,210,142)(62,124,197,117)(63,151,198,144)(64,126,199,119)(65,153,200,146)(66,114,201,121)(67,141,202,148)(68,116,203,123)(69,143,204,150)(70,118,205,125)(127,218,134,177)(128,171,135,212)(129,220,136,179)(130,173,137,214)(131,222,138,181)(132,175,139,216)(133,224,140,169)(170,185,211,192)(172,187,213,194)(174,189,215,196)(176,191,217,184)(178,193,219,186)(180,195,221,188)(182,183,223,190), (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), (1,136,43,129)(2,128,44,135)(3,134,45,127)(4,140,46,133)(5,132,47,139)(6,138,48,131)(7,130,49,137)(8,141,42,148)(9,147,36,154)(10,153,37,146)(11,145,38,152)(12,151,39,144)(13,143,40,150)(14,149,41,142)(15,122,33,115)(16,114,34,121)(17,120,35,113)(18,126,29,119)(19,118,30,125)(20,124,31,117)(21,116,32,123)(22,193,54,186)(23,185,55,192)(24,191,56,184)(25,183,50,190)(26,189,51,196)(27,195,52,188)(28,187,53,194)(57,89,206,168)(58,167,207,88)(59,87,208,166)(60,165,209,86)(61,85,210,164)(62,163,197,98)(63,97,198,162)(64,161,199,96)(65,95,200,160)(66,159,201,94)(67,93,202,158)(68,157,203,92)(69,91,204,156)(70,155,205,90)(71,179,104,220)(72,219,105,178)(73,177,106,218)(74,217,107,176)(75,175,108,216)(76,215,109,174)(77,173,110,214)(78,213,111,172)(79,171,112,212)(80,211,99,170)(81,169,100,224)(82,223,101,182)(83,181,102,222)(84,221,103,180)>;
G:=Group( (1,14,28,32)(2,8,22,33)(3,9,23,34)(4,10,24,35)(5,11,25,29)(6,12,26,30)(7,13,27,31)(15,44,42,54)(16,45,36,55)(17,46,37,56)(18,47,38,50)(19,48,39,51)(20,49,40,52)(21,43,41,53)(57,216,199,182)(58,217,200,169)(59,218,201,170)(60,219,202,171)(61,220,203,172)(62,221,204,173)(63,222,205,174)(64,223,206,175)(65,224,207,176)(66,211,208,177)(67,212,209,178)(68,213,210,179)(69,214,197,180)(70,215,198,181)(71,85,78,92)(72,86,79,93)(73,87,80,94)(74,88,81,95)(75,89,82,96)(76,90,83,97)(77,91,84,98)(99,159,106,166)(100,160,107,167)(101,161,108,168)(102,162,109,155)(103,163,110,156)(104,164,111,157)(105,165,112,158)(113,191,153,140)(114,192,154,127)(115,193,141,128)(116,194,142,129)(117,195,143,130)(118,196,144,131)(119,183,145,132)(120,184,146,133)(121,185,147,134)(122,186,148,135)(123,187,149,136)(124,188,150,137)(125,189,151,138)(126,190,152,139), (1,78,43,111)(2,72,44,105)(3,80,45,99)(4,74,46,107)(5,82,47,101)(6,76,48,109)(7,84,49,103)(8,86,42,165)(9,94,36,159)(10,88,37,167)(11,96,38,161)(12,90,39,155)(13,98,40,163)(14,92,41,157)(15,158,33,93)(16,166,34,87)(17,160,35,95)(18,168,29,89)(19,162,30,97)(20,156,31,91)(21,164,32,85)(22,79,54,112)(23,73,55,106)(24,81,56,100)(25,75,50,108)(26,83,51,102)(27,77,52,110)(28,71,53,104)(57,145,206,152)(58,120,207,113)(59,147,208,154)(60,122,209,115)(61,149,210,142)(62,124,197,117)(63,151,198,144)(64,126,199,119)(65,153,200,146)(66,114,201,121)(67,141,202,148)(68,116,203,123)(69,143,204,150)(70,118,205,125)(127,218,134,177)(128,171,135,212)(129,220,136,179)(130,173,137,214)(131,222,138,181)(132,175,139,216)(133,224,140,169)(170,185,211,192)(172,187,213,194)(174,189,215,196)(176,191,217,184)(178,193,219,186)(180,195,221,188)(182,183,223,190), (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), (1,136,43,129)(2,128,44,135)(3,134,45,127)(4,140,46,133)(5,132,47,139)(6,138,48,131)(7,130,49,137)(8,141,42,148)(9,147,36,154)(10,153,37,146)(11,145,38,152)(12,151,39,144)(13,143,40,150)(14,149,41,142)(15,122,33,115)(16,114,34,121)(17,120,35,113)(18,126,29,119)(19,118,30,125)(20,124,31,117)(21,116,32,123)(22,193,54,186)(23,185,55,192)(24,191,56,184)(25,183,50,190)(26,189,51,196)(27,195,52,188)(28,187,53,194)(57,89,206,168)(58,167,207,88)(59,87,208,166)(60,165,209,86)(61,85,210,164)(62,163,197,98)(63,97,198,162)(64,161,199,96)(65,95,200,160)(66,159,201,94)(67,93,202,158)(68,157,203,92)(69,91,204,156)(70,155,205,90)(71,179,104,220)(72,219,105,178)(73,177,106,218)(74,217,107,176)(75,175,108,216)(76,215,109,174)(77,173,110,214)(78,213,111,172)(79,171,112,212)(80,211,99,170)(81,169,100,224)(82,223,101,182)(83,181,102,222)(84,221,103,180) );
G=PermutationGroup([[(1,14,28,32),(2,8,22,33),(3,9,23,34),(4,10,24,35),(5,11,25,29),(6,12,26,30),(7,13,27,31),(15,44,42,54),(16,45,36,55),(17,46,37,56),(18,47,38,50),(19,48,39,51),(20,49,40,52),(21,43,41,53),(57,216,199,182),(58,217,200,169),(59,218,201,170),(60,219,202,171),(61,220,203,172),(62,221,204,173),(63,222,205,174),(64,223,206,175),(65,224,207,176),(66,211,208,177),(67,212,209,178),(68,213,210,179),(69,214,197,180),(70,215,198,181),(71,85,78,92),(72,86,79,93),(73,87,80,94),(74,88,81,95),(75,89,82,96),(76,90,83,97),(77,91,84,98),(99,159,106,166),(100,160,107,167),(101,161,108,168),(102,162,109,155),(103,163,110,156),(104,164,111,157),(105,165,112,158),(113,191,153,140),(114,192,154,127),(115,193,141,128),(116,194,142,129),(117,195,143,130),(118,196,144,131),(119,183,145,132),(120,184,146,133),(121,185,147,134),(122,186,148,135),(123,187,149,136),(124,188,150,137),(125,189,151,138),(126,190,152,139)], [(1,78,43,111),(2,72,44,105),(3,80,45,99),(4,74,46,107),(5,82,47,101),(6,76,48,109),(7,84,49,103),(8,86,42,165),(9,94,36,159),(10,88,37,167),(11,96,38,161),(12,90,39,155),(13,98,40,163),(14,92,41,157),(15,158,33,93),(16,166,34,87),(17,160,35,95),(18,168,29,89),(19,162,30,97),(20,156,31,91),(21,164,32,85),(22,79,54,112),(23,73,55,106),(24,81,56,100),(25,75,50,108),(26,83,51,102),(27,77,52,110),(28,71,53,104),(57,145,206,152),(58,120,207,113),(59,147,208,154),(60,122,209,115),(61,149,210,142),(62,124,197,117),(63,151,198,144),(64,126,199,119),(65,153,200,146),(66,114,201,121),(67,141,202,148),(68,116,203,123),(69,143,204,150),(70,118,205,125),(127,218,134,177),(128,171,135,212),(129,220,136,179),(130,173,137,214),(131,222,138,181),(132,175,139,216),(133,224,140,169),(170,185,211,192),(172,187,213,194),(174,189,215,196),(176,191,217,184),(178,193,219,186),(180,195,221,188),(182,183,223,190)], [(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)], [(1,136,43,129),(2,128,44,135),(3,134,45,127),(4,140,46,133),(5,132,47,139),(6,138,48,131),(7,130,49,137),(8,141,42,148),(9,147,36,154),(10,153,37,146),(11,145,38,152),(12,151,39,144),(13,143,40,150),(14,149,41,142),(15,122,33,115),(16,114,34,121),(17,120,35,113),(18,126,29,119),(19,118,30,125),(20,124,31,117),(21,116,32,123),(22,193,54,186),(23,185,55,192),(24,191,56,184),(25,183,50,190),(26,189,51,196),(27,195,52,188),(28,187,53,194),(57,89,206,168),(58,167,207,88),(59,87,208,166),(60,165,209,86),(61,85,210,164),(62,163,197,98),(63,97,198,162),(64,161,199,96),(65,95,200,160),(66,159,201,94),(67,93,202,158),(68,157,203,92),(69,91,204,156),(70,155,205,90),(71,179,104,220),(72,219,105,178),(73,177,106,218),(74,217,107,176),(75,175,108,216),(76,215,109,174),(77,173,110,214),(78,213,111,172),(79,171,112,212),(80,211,99,170),(81,169,100,224),(82,223,101,182),(83,181,102,222),(84,221,103,180)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | 4J | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 28 | 2 | ··· | 2 | 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 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | 2- 1+4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.99D14 | C4×Dic14 | C28⋊2Q8 | C4×D28 | C4.D28 | D14.D4 | Dic7.D4 | D14⋊Q8 | C4⋊C4⋊D7 | C28.48D4 | C28⋊7D4 | C7×C42⋊C2 | C42⋊C2 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 6 | 6 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.99D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 14 | 17 | 0 | 0 |
| 0 | 0 | 19 | 22 | 8 | 6 |
| 0 | 0 | 11 | 5 | 23 | 21 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 1 | 22 | 24 |
| 0 | 0 | 0 | 28 | 27 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 17 | 9 | 15 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 |
| 0 | 0 | 4 | 25 | 0 | 0 |
| 0 | 0 | 3 | 6 | 19 | 19 |
| 0 | 0 | 21 | 27 | 10 | 7 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 4 | 0 | 0 |
| 0 | 0 | 15 | 12 | 0 | 0 |
| 0 | 0 | 4 | 10 | 8 | 6 |
| 0 | 0 | 26 | 22 | 4 | 21 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,14,19,11,0,0,0,17,22,5,0,0,0,0,8,23,0,0,0,0,6,21],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,17,0,0,1,28,0,9,0,0,22,27,1,15,0,0,24,0,0,12],[1,24,0,0,0,0,0,28,0,0,0,0,0,0,7,4,3,21,0,0,0,25,6,27,0,0,0,0,19,10,0,0,0,0,19,7],[12,0,0,0,0,0,28,17,0,0,0,0,0,0,17,15,4,26,0,0,4,12,10,22,0,0,0,0,8,4,0,0,0,0,6,21] >;
C42.99D14 in GAP, Magma, Sage, TeX
C_4^2._{99}D_{14} % in TeX
G:=Group("C4^2.99D14"); // GroupNames label
G:=SmallGroup(448,987);
// by ID
G=gap.SmallGroup(448,987);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^-1>;
// generators/relations