metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.4Q8, C42.69D14, C7⋊7(D4.Q8), C4.10(Q8×D7), C4⋊C4.75D14, C28⋊C8⋊30C2, C28.34(C2×Q8), C42.C2⋊1D7, (C4×D28).16C2, (C2×C28).275D4, C28.70(C4○D4), C28.Q8⋊42C2, C4.Dic14⋊41C2, C14.D8.12C2, C14.109(C4○D8), (C4×C28).114C22, (C2×C28).384C23, C4.33(Q8⋊2D7), C14.74(C22⋊Q8), C2.21(D4⋊D14), C14.122(C8⋊C22), C2.11(D14⋊3Q8), (C2×D28).245C22, C4⋊Dic7.343C22, C2.28(D4.8D14), (C7×C42.C2)⋊1C2, (C2×C14).515(C2×D4), (C2×C4).66(C7⋊D4), (C2×C7⋊C8).126C22, (C7×C4⋊C4).122C22, (C2×C4).482(C22×D7), C22.188(C2×C7⋊D4), SmallGroup(448,600)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.4Q8
G = < a,b,c,d | a28=b2=c4=1, d2=a14c2, bab=a-1, cac-1=a15, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 540 in 102 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C4×D4, C42.C2, C7⋊C8, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, D4.Q8, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C28⋊C8, C28.Q8, C4.Dic14, C14.D8, C4×D28, C7×C42.C2, D28.4Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C4○D8, C8⋊C22, C7⋊D4, C22×D7, D4.Q8, Q8×D7, Q8⋊2D7, C2×C7⋊D4, D14⋊3Q8, D4⋊D14, D4.8D14, D28.4Q8
►On 224 points
Generators in S224
(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)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 28)(16 27)(17 26)(18 25)(19 24)(20 23)(21 22)(29 56)(30 55)(31 54)(32 53)(33 52)(34 51)(35 50)(36 49)(37 48)(38 47)(39 46)(40 45)(41 44)(42 43)(57 65)(58 64)(59 63)(60 62)(66 84)(67 83)(68 82)(69 81)(70 80)(71 79)(72 78)(73 77)(74 76)(85 105)(86 104)(87 103)(88 102)(89 101)(90 100)(91 99)(92 98)(93 97)(94 96)(106 112)(107 111)(108 110)(113 122)(114 121)(115 120)(116 119)(117 118)(123 140)(124 139)(125 138)(126 137)(127 136)(128 135)(129 134)(130 133)(131 132)(141 145)(142 144)(146 168)(147 167)(148 166)(149 165)(150 164)(151 163)(152 162)(153 161)(154 160)(155 159)(156 158)(169 179)(170 178)(171 177)(172 176)(173 175)(180 196)(181 195)(182 194)(183 193)(184 192)(185 191)(186 190)(187 189)(197 222)(198 221)(199 220)(200 219)(201 218)(202 217)(203 216)(204 215)(205 214)(206 213)(207 212)(208 211)(209 210)(223 224)
(1 154 50 92)(2 141 51 107)(3 156 52 94)(4 143 53 109)(5 158 54 96)(6 145 55 111)(7 160 56 98)(8 147 29 85)(9 162 30 100)(10 149 31 87)(11 164 32 102)(12 151 33 89)(13 166 34 104)(14 153 35 91)(15 168 36 106)(16 155 37 93)(17 142 38 108)(18 157 39 95)(19 144 40 110)(20 159 41 97)(21 146 42 112)(22 161 43 99)(23 148 44 86)(24 163 45 101)(25 150 46 88)(26 165 47 103)(27 152 48 90)(28 167 49 105)(57 202 184 124)(58 217 185 139)(59 204 186 126)(60 219 187 113)(61 206 188 128)(62 221 189 115)(63 208 190 130)(64 223 191 117)(65 210 192 132)(66 197 193 119)(67 212 194 134)(68 199 195 121)(69 214 196 136)(70 201 169 123)(71 216 170 138)(72 203 171 125)(73 218 172 140)(74 205 173 127)(75 220 174 114)(76 207 175 129)(77 222 176 116)(78 209 177 131)(79 224 178 118)(80 211 179 133)(81 198 180 120)(82 213 181 135)(83 200 182 122)(84 215 183 137)
(1 203 36 139)(2 204 37 140)(3 205 38 113)(4 206 39 114)(5 207 40 115)(6 208 41 116)(7 209 42 117)(8 210 43 118)(9 211 44 119)(10 212 45 120)(11 213 46 121)(12 214 47 122)(13 215 48 123)(14 216 49 124)(15 217 50 125)(16 218 51 126)(17 219 52 127)(18 220 53 128)(19 221 54 129)(20 222 55 130)(21 223 56 131)(22 224 29 132)(23 197 30 133)(24 198 31 134)(25 199 32 135)(26 200 33 136)(27 201 34 137)(28 202 35 138)(57 91 170 167)(58 92 171 168)(59 93 172 141)(60 94 173 142)(61 95 174 143)(62 96 175 144)(63 97 176 145)(64 98 177 146)(65 99 178 147)(66 100 179 148)(67 101 180 149)(68 102 181 150)(69 103 182 151)(70 104 183 152)(71 105 184 153)(72 106 185 154)(73 107 186 155)(74 108 187 156)(75 109 188 157)(76 110 189 158)(77 111 190 159)(78 112 191 160)(79 85 192 161)(80 86 193 162)(81 87 194 163)(82 88 195 164)(83 89 196 165)(84 90 169 166)
G:=sub<Sym(224)| (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)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)(57,65)(58,64)(59,63)(60,62)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(85,105)(86,104)(87,103)(88,102)(89,101)(90,100)(91,99)(92,98)(93,97)(94,96)(106,112)(107,111)(108,110)(113,122)(114,121)(115,120)(116,119)(117,118)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(141,145)(142,144)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,179)(170,178)(171,177)(172,176)(173,175)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,210)(223,224), (1,154,50,92)(2,141,51,107)(3,156,52,94)(4,143,53,109)(5,158,54,96)(6,145,55,111)(7,160,56,98)(8,147,29,85)(9,162,30,100)(10,149,31,87)(11,164,32,102)(12,151,33,89)(13,166,34,104)(14,153,35,91)(15,168,36,106)(16,155,37,93)(17,142,38,108)(18,157,39,95)(19,144,40,110)(20,159,41,97)(21,146,42,112)(22,161,43,99)(23,148,44,86)(24,163,45,101)(25,150,46,88)(26,165,47,103)(27,152,48,90)(28,167,49,105)(57,202,184,124)(58,217,185,139)(59,204,186,126)(60,219,187,113)(61,206,188,128)(62,221,189,115)(63,208,190,130)(64,223,191,117)(65,210,192,132)(66,197,193,119)(67,212,194,134)(68,199,195,121)(69,214,196,136)(70,201,169,123)(71,216,170,138)(72,203,171,125)(73,218,172,140)(74,205,173,127)(75,220,174,114)(76,207,175,129)(77,222,176,116)(78,209,177,131)(79,224,178,118)(80,211,179,133)(81,198,180,120)(82,213,181,135)(83,200,182,122)(84,215,183,137), (1,203,36,139)(2,204,37,140)(3,205,38,113)(4,206,39,114)(5,207,40,115)(6,208,41,116)(7,209,42,117)(8,210,43,118)(9,211,44,119)(10,212,45,120)(11,213,46,121)(12,214,47,122)(13,215,48,123)(14,216,49,124)(15,217,50,125)(16,218,51,126)(17,219,52,127)(18,220,53,128)(19,221,54,129)(20,222,55,130)(21,223,56,131)(22,224,29,132)(23,197,30,133)(24,198,31,134)(25,199,32,135)(26,200,33,136)(27,201,34,137)(28,202,35,138)(57,91,170,167)(58,92,171,168)(59,93,172,141)(60,94,173,142)(61,95,174,143)(62,96,175,144)(63,97,176,145)(64,98,177,146)(65,99,178,147)(66,100,179,148)(67,101,180,149)(68,102,181,150)(69,103,182,151)(70,104,183,152)(71,105,184,153)(72,106,185,154)(73,107,186,155)(74,108,187,156)(75,109,188,157)(76,110,189,158)(77,111,190,159)(78,112,191,160)(79,85,192,161)(80,86,193,162)(81,87,194,163)(82,88,195,164)(83,89,196,165)(84,90,169,166)>;
G:=Group( (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)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)(57,65)(58,64)(59,63)(60,62)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(85,105)(86,104)(87,103)(88,102)(89,101)(90,100)(91,99)(92,98)(93,97)(94,96)(106,112)(107,111)(108,110)(113,122)(114,121)(115,120)(116,119)(117,118)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(141,145)(142,144)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,179)(170,178)(171,177)(172,176)(173,175)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,210)(223,224), (1,154,50,92)(2,141,51,107)(3,156,52,94)(4,143,53,109)(5,158,54,96)(6,145,55,111)(7,160,56,98)(8,147,29,85)(9,162,30,100)(10,149,31,87)(11,164,32,102)(12,151,33,89)(13,166,34,104)(14,153,35,91)(15,168,36,106)(16,155,37,93)(17,142,38,108)(18,157,39,95)(19,144,40,110)(20,159,41,97)(21,146,42,112)(22,161,43,99)(23,148,44,86)(24,163,45,101)(25,150,46,88)(26,165,47,103)(27,152,48,90)(28,167,49,105)(57,202,184,124)(58,217,185,139)(59,204,186,126)(60,219,187,113)(61,206,188,128)(62,221,189,115)(63,208,190,130)(64,223,191,117)(65,210,192,132)(66,197,193,119)(67,212,194,134)(68,199,195,121)(69,214,196,136)(70,201,169,123)(71,216,170,138)(72,203,171,125)(73,218,172,140)(74,205,173,127)(75,220,174,114)(76,207,175,129)(77,222,176,116)(78,209,177,131)(79,224,178,118)(80,211,179,133)(81,198,180,120)(82,213,181,135)(83,200,182,122)(84,215,183,137), (1,203,36,139)(2,204,37,140)(3,205,38,113)(4,206,39,114)(5,207,40,115)(6,208,41,116)(7,209,42,117)(8,210,43,118)(9,211,44,119)(10,212,45,120)(11,213,46,121)(12,214,47,122)(13,215,48,123)(14,216,49,124)(15,217,50,125)(16,218,51,126)(17,219,52,127)(18,220,53,128)(19,221,54,129)(20,222,55,130)(21,223,56,131)(22,224,29,132)(23,197,30,133)(24,198,31,134)(25,199,32,135)(26,200,33,136)(27,201,34,137)(28,202,35,138)(57,91,170,167)(58,92,171,168)(59,93,172,141)(60,94,173,142)(61,95,174,143)(62,96,175,144)(63,97,176,145)(64,98,177,146)(65,99,178,147)(66,100,179,148)(67,101,180,149)(68,102,181,150)(69,103,182,151)(70,104,183,152)(71,105,184,153)(72,106,185,154)(73,107,186,155)(74,108,187,156)(75,109,188,157)(76,110,189,158)(77,111,190,159)(78,112,191,160)(79,85,192,161)(80,86,193,162)(81,87,194,163)(82,88,195,164)(83,89,196,165)(84,90,169,166) );
G=PermutationGroup([[(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),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,28),(16,27),(17,26),(18,25),(19,24),(20,23),(21,22),(29,56),(30,55),(31,54),(32,53),(33,52),(34,51),(35,50),(36,49),(37,48),(38,47),(39,46),(40,45),(41,44),(42,43),(57,65),(58,64),(59,63),(60,62),(66,84),(67,83),(68,82),(69,81),(70,80),(71,79),(72,78),(73,77),(74,76),(85,105),(86,104),(87,103),(88,102),(89,101),(90,100),(91,99),(92,98),(93,97),(94,96),(106,112),(107,111),(108,110),(113,122),(114,121),(115,120),(116,119),(117,118),(123,140),(124,139),(125,138),(126,137),(127,136),(128,135),(129,134),(130,133),(131,132),(141,145),(142,144),(146,168),(147,167),(148,166),(149,165),(150,164),(151,163),(152,162),(153,161),(154,160),(155,159),(156,158),(169,179),(170,178),(171,177),(172,176),(173,175),(180,196),(181,195),(182,194),(183,193),(184,192),(185,191),(186,190),(187,189),(197,222),(198,221),(199,220),(200,219),(201,218),(202,217),(203,216),(204,215),(205,214),(206,213),(207,212),(208,211),(209,210),(223,224)], [(1,154,50,92),(2,141,51,107),(3,156,52,94),(4,143,53,109),(5,158,54,96),(6,145,55,111),(7,160,56,98),(8,147,29,85),(9,162,30,100),(10,149,31,87),(11,164,32,102),(12,151,33,89),(13,166,34,104),(14,153,35,91),(15,168,36,106),(16,155,37,93),(17,142,38,108),(18,157,39,95),(19,144,40,110),(20,159,41,97),(21,146,42,112),(22,161,43,99),(23,148,44,86),(24,163,45,101),(25,150,46,88),(26,165,47,103),(27,152,48,90),(28,167,49,105),(57,202,184,124),(58,217,185,139),(59,204,186,126),(60,219,187,113),(61,206,188,128),(62,221,189,115),(63,208,190,130),(64,223,191,117),(65,210,192,132),(66,197,193,119),(67,212,194,134),(68,199,195,121),(69,214,196,136),(70,201,169,123),(71,216,170,138),(72,203,171,125),(73,218,172,140),(74,205,173,127),(75,220,174,114),(76,207,175,129),(77,222,176,116),(78,209,177,131),(79,224,178,118),(80,211,179,133),(81,198,180,120),(82,213,181,135),(83,200,182,122),(84,215,183,137)], [(1,203,36,139),(2,204,37,140),(3,205,38,113),(4,206,39,114),(5,207,40,115),(6,208,41,116),(7,209,42,117),(8,210,43,118),(9,211,44,119),(10,212,45,120),(11,213,46,121),(12,214,47,122),(13,215,48,123),(14,216,49,124),(15,217,50,125),(16,218,51,126),(17,219,52,127),(18,220,53,128),(19,221,54,129),(20,222,55,130),(21,223,56,131),(22,224,29,132),(23,197,30,133),(24,198,31,134),(25,199,32,135),(26,200,33,136),(27,201,34,137),(28,202,35,138),(57,91,170,167),(58,92,171,168),(59,93,172,141),(60,94,173,142),(61,95,174,143),(62,96,175,144),(63,97,176,145),(64,98,177,146),(65,99,178,147),(66,100,179,148),(67,101,180,149),(68,102,181,150),(69,103,182,151),(70,104,183,152),(71,105,184,153),(72,106,185,154),(73,107,186,155),(74,108,187,156),(75,109,188,157),(76,110,189,158),(77,111,190,159),(78,112,191,160),(79,85,192,161),(80,86,193,162),(81,87,194,163),(82,88,195,164),(83,89,196,165),(84,90,169,166)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | C7⋊D4 | C8⋊C22 | Q8×D7 | Q8⋊2D7 | D4⋊D14 | D4.8D14 |
| kernel | D28.4Q8 | C28⋊C8 | C28.Q8 | C4.Dic14 | C14.D8 | C4×D28 | C7×C42.C2 | D28 | C2×C28 | C42.C2 | C28 | C42 | C4⋊C4 | C14 | C2×C4 | C14 | C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 6 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28.4Q8 ►in GL6(𝔽113)
| 3 | 111 | 0 | 0 | 0 | 0 |
| 5 | 110 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 89 | 0 | 0 |
| 0 | 0 | 24 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 110 | 2 | 0 | 0 | 0 | 0 |
| 109 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 89 | 0 | 0 |
| 0 | 0 | 103 | 103 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 102 | 62 | 0 | 0 | 0 | 0 |
| 9 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 72 |
| 0 | 0 | 0 | 0 | 91 | 1 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 81 |
| 0 | 0 | 0 | 0 | 53 | 0 |
G:=sub<GL(6,GF(113))| [3,5,0,0,0,0,111,110,0,0,0,0,0,0,10,24,0,0,0,0,89,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[110,109,0,0,0,0,2,3,0,0,0,0,0,0,10,103,0,0,0,0,89,103,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[102,9,0,0,0,0,62,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,91,0,0,0,0,72,1],[98,0,0,0,0,0,0,98,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,53,0,0,0,0,81,0] >;
D28.4Q8 in GAP, Magma, Sage, TeX
D_{28}._4Q_8 % in TeX
G:=Group("D28.4Q8"); // GroupNames label
G:=SmallGroup(448,600);
// by ID
G=gap.SmallGroup(448,600);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,344,254,219,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^14*c^2,b*a*b=a^-1,c*a*c^-1=a^15,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations