metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊3Q8, C28.13SD16, C42.33D14, C4⋊C8⋊9D7, C4.43(Q8×D7), C7⋊2(D4⋊2Q8), C8⋊Dic7⋊16C2, C28⋊2Q8⋊12C2, (C4×D28).11C2, (C2×C28).121D4, (C2×C4).132D28, (C2×C8).129D14, C28.102(C2×Q8), C2.D56.5C2, C4.13(C56⋊C2), (C4×C28).68C22, C14.11(C2×SD16), C28.286(C4○D4), C2.16(C8⋊D14), C14.13(C8⋊C22), (C2×C28).752C23, (C2×C56).139C22, C22.115(C2×D28), C14.30(C22⋊Q8), C4⋊Dic7.18C22, C4.110(D4⋊2D7), C2.11(D14⋊2Q8), (C2×D28).195C22, (C7×C4⋊C8)⋊11C2, C2.14(C2×C56⋊C2), (C2×C14).135(C2×D4), (C2×C4).697(C22×D7), SmallGroup(448,376)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊3Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=cac-1=a-1, ad=da, cbc-1=a19b, dbd-1=a14b, dcd-1=c-1 >
Subgroups: 676 in 108 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4.Q8, C4×D4, C4⋊Q8, C56, Dic14, C4×D7, D28, D28, C2×Dic7, C2×C28, C22×D7, D4⋊2Q8, C4⋊Dic7, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C8⋊Dic7, C2.D56, C7×C4⋊C8, C28⋊2Q8, C4×D28, D28⋊3Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, SD16, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C2×SD16, C8⋊C22, D28, C22×D7, D4⋊2Q8, C56⋊C2, C2×D28, D4⋊2D7, Q8×D7, D14⋊2Q8, C2×C56⋊C2, C8⋊D14, D28⋊3Q8
►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 28)(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(29 45)(30 44)(31 43)(32 42)(33 41)(34 40)(35 39)(36 38)(46 56)(47 55)(48 54)(49 53)(50 52)(57 63)(58 62)(59 61)(64 84)(65 83)(66 82)(67 81)(68 80)(69 79)(70 78)(71 77)(72 76)(73 75)(85 106)(86 105)(87 104)(88 103)(89 102)(90 101)(91 100)(92 99)(93 98)(94 97)(95 96)(107 112)(108 111)(109 110)(113 126)(114 125)(115 124)(116 123)(117 122)(118 121)(119 120)(127 140)(128 139)(129 138)(130 137)(131 136)(132 135)(133 134)(141 159)(142 158)(143 157)(144 156)(145 155)(146 154)(147 153)(148 152)(149 151)(160 168)(161 167)(162 166)(163 165)(169 189)(170 188)(171 187)(172 186)(173 185)(174 184)(175 183)(176 182)(177 181)(178 180)(190 196)(191 195)(192 194)(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)
(1 154 110 55)(2 153 111 54)(3 152 112 53)(4 151 85 52)(5 150 86 51)(6 149 87 50)(7 148 88 49)(8 147 89 48)(9 146 90 47)(10 145 91 46)(11 144 92 45)(12 143 93 44)(13 142 94 43)(14 141 95 42)(15 168 96 41)(16 167 97 40)(17 166 98 39)(18 165 99 38)(19 164 100 37)(20 163 101 36)(21 162 102 35)(22 161 103 34)(23 160 104 33)(24 159 105 32)(25 158 106 31)(26 157 107 30)(27 156 108 29)(28 155 109 56)(57 113 176 203)(58 140 177 202)(59 139 178 201)(60 138 179 200)(61 137 180 199)(62 136 181 198)(63 135 182 197)(64 134 183 224)(65 133 184 223)(66 132 185 222)(67 131 186 221)(68 130 187 220)(69 129 188 219)(70 128 189 218)(71 127 190 217)(72 126 191 216)(73 125 192 215)(74 124 193 214)(75 123 194 213)(76 122 195 212)(77 121 196 211)(78 120 169 210)(79 119 170 209)(80 118 171 208)(81 117 172 207)(82 116 173 206)(83 115 174 205)(84 114 175 204)
(1 217 110 127)(2 218 111 128)(3 219 112 129)(4 220 85 130)(5 221 86 131)(6 222 87 132)(7 223 88 133)(8 224 89 134)(9 197 90 135)(10 198 91 136)(11 199 92 137)(12 200 93 138)(13 201 94 139)(14 202 95 140)(15 203 96 113)(16 204 97 114)(17 205 98 115)(18 206 99 116)(19 207 100 117)(20 208 101 118)(21 209 102 119)(22 210 103 120)(23 211 104 121)(24 212 105 122)(25 213 106 123)(26 214 107 124)(27 215 108 125)(28 216 109 126)(29 73 156 192)(30 74 157 193)(31 75 158 194)(32 76 159 195)(33 77 160 196)(34 78 161 169)(35 79 162 170)(36 80 163 171)(37 81 164 172)(38 82 165 173)(39 83 166 174)(40 84 167 175)(41 57 168 176)(42 58 141 177)(43 59 142 178)(44 60 143 179)(45 61 144 180)(46 62 145 181)(47 63 146 182)(48 64 147 183)(49 65 148 184)(50 66 149 185)(51 67 150 186)(52 68 151 187)(53 69 152 188)(54 70 153 189)(55 71 154 190)(56 72 155 191)
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,45)(30,44)(31,43)(32,42)(33,41)(34,40)(35,39)(36,38)(46,56)(47,55)(48,54)(49,53)(50,52)(57,63)(58,62)(59,61)(64,84)(65,83)(66,82)(67,81)(68,80)(69,79)(70,78)(71,77)(72,76)(73,75)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)(107,112)(108,111)(109,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,159)(142,158)(143,157)(144,156)(145,155)(146,154)(147,153)(148,152)(149,151)(160,168)(161,167)(162,166)(163,165)(169,189)(170,188)(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)(178,180)(190,196)(191,195)(192,194)(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), (1,154,110,55)(2,153,111,54)(3,152,112,53)(4,151,85,52)(5,150,86,51)(6,149,87,50)(7,148,88,49)(8,147,89,48)(9,146,90,47)(10,145,91,46)(11,144,92,45)(12,143,93,44)(13,142,94,43)(14,141,95,42)(15,168,96,41)(16,167,97,40)(17,166,98,39)(18,165,99,38)(19,164,100,37)(20,163,101,36)(21,162,102,35)(22,161,103,34)(23,160,104,33)(24,159,105,32)(25,158,106,31)(26,157,107,30)(27,156,108,29)(28,155,109,56)(57,113,176,203)(58,140,177,202)(59,139,178,201)(60,138,179,200)(61,137,180,199)(62,136,181,198)(63,135,182,197)(64,134,183,224)(65,133,184,223)(66,132,185,222)(67,131,186,221)(68,130,187,220)(69,129,188,219)(70,128,189,218)(71,127,190,217)(72,126,191,216)(73,125,192,215)(74,124,193,214)(75,123,194,213)(76,122,195,212)(77,121,196,211)(78,120,169,210)(79,119,170,209)(80,118,171,208)(81,117,172,207)(82,116,173,206)(83,115,174,205)(84,114,175,204), (1,217,110,127)(2,218,111,128)(3,219,112,129)(4,220,85,130)(5,221,86,131)(6,222,87,132)(7,223,88,133)(8,224,89,134)(9,197,90,135)(10,198,91,136)(11,199,92,137)(12,200,93,138)(13,201,94,139)(14,202,95,140)(15,203,96,113)(16,204,97,114)(17,205,98,115)(18,206,99,116)(19,207,100,117)(20,208,101,118)(21,209,102,119)(22,210,103,120)(23,211,104,121)(24,212,105,122)(25,213,106,123)(26,214,107,124)(27,215,108,125)(28,216,109,126)(29,73,156,192)(30,74,157,193)(31,75,158,194)(32,76,159,195)(33,77,160,196)(34,78,161,169)(35,79,162,170)(36,80,163,171)(37,81,164,172)(38,82,165,173)(39,83,166,174)(40,84,167,175)(41,57,168,176)(42,58,141,177)(43,59,142,178)(44,60,143,179)(45,61,144,180)(46,62,145,181)(47,63,146,182)(48,64,147,183)(49,65,148,184)(50,66,149,185)(51,67,150,186)(52,68,151,187)(53,69,152,188)(54,70,153,189)(55,71,154,190)(56,72,155,191)>;
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,45)(30,44)(31,43)(32,42)(33,41)(34,40)(35,39)(36,38)(46,56)(47,55)(48,54)(49,53)(50,52)(57,63)(58,62)(59,61)(64,84)(65,83)(66,82)(67,81)(68,80)(69,79)(70,78)(71,77)(72,76)(73,75)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)(107,112)(108,111)(109,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,159)(142,158)(143,157)(144,156)(145,155)(146,154)(147,153)(148,152)(149,151)(160,168)(161,167)(162,166)(163,165)(169,189)(170,188)(171,187)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)(178,180)(190,196)(191,195)(192,194)(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), (1,154,110,55)(2,153,111,54)(3,152,112,53)(4,151,85,52)(5,150,86,51)(6,149,87,50)(7,148,88,49)(8,147,89,48)(9,146,90,47)(10,145,91,46)(11,144,92,45)(12,143,93,44)(13,142,94,43)(14,141,95,42)(15,168,96,41)(16,167,97,40)(17,166,98,39)(18,165,99,38)(19,164,100,37)(20,163,101,36)(21,162,102,35)(22,161,103,34)(23,160,104,33)(24,159,105,32)(25,158,106,31)(26,157,107,30)(27,156,108,29)(28,155,109,56)(57,113,176,203)(58,140,177,202)(59,139,178,201)(60,138,179,200)(61,137,180,199)(62,136,181,198)(63,135,182,197)(64,134,183,224)(65,133,184,223)(66,132,185,222)(67,131,186,221)(68,130,187,220)(69,129,188,219)(70,128,189,218)(71,127,190,217)(72,126,191,216)(73,125,192,215)(74,124,193,214)(75,123,194,213)(76,122,195,212)(77,121,196,211)(78,120,169,210)(79,119,170,209)(80,118,171,208)(81,117,172,207)(82,116,173,206)(83,115,174,205)(84,114,175,204), (1,217,110,127)(2,218,111,128)(3,219,112,129)(4,220,85,130)(5,221,86,131)(6,222,87,132)(7,223,88,133)(8,224,89,134)(9,197,90,135)(10,198,91,136)(11,199,92,137)(12,200,93,138)(13,201,94,139)(14,202,95,140)(15,203,96,113)(16,204,97,114)(17,205,98,115)(18,206,99,116)(19,207,100,117)(20,208,101,118)(21,209,102,119)(22,210,103,120)(23,211,104,121)(24,212,105,122)(25,213,106,123)(26,214,107,124)(27,215,108,125)(28,216,109,126)(29,73,156,192)(30,74,157,193)(31,75,158,194)(32,76,159,195)(33,77,160,196)(34,78,161,169)(35,79,162,170)(36,80,163,171)(37,81,164,172)(38,82,165,173)(39,83,166,174)(40,84,167,175)(41,57,168,176)(42,58,141,177)(43,59,142,178)(44,60,143,179)(45,61,144,180)(46,62,145,181)(47,63,146,182)(48,64,147,183)(49,65,148,184)(50,66,149,185)(51,67,150,186)(52,68,151,187)(53,69,152,188)(54,70,153,189)(55,71,154,190)(56,72,155,191) );
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)], [(1,28),(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(29,45),(30,44),(31,43),(32,42),(33,41),(34,40),(35,39),(36,38),(46,56),(47,55),(48,54),(49,53),(50,52),(57,63),(58,62),(59,61),(64,84),(65,83),(66,82),(67,81),(68,80),(69,79),(70,78),(71,77),(72,76),(73,75),(85,106),(86,105),(87,104),(88,103),(89,102),(90,101),(91,100),(92,99),(93,98),(94,97),(95,96),(107,112),(108,111),(109,110),(113,126),(114,125),(115,124),(116,123),(117,122),(118,121),(119,120),(127,140),(128,139),(129,138),(130,137),(131,136),(132,135),(133,134),(141,159),(142,158),(143,157),(144,156),(145,155),(146,154),(147,153),(148,152),(149,151),(160,168),(161,167),(162,166),(163,165),(169,189),(170,188),(171,187),(172,186),(173,185),(174,184),(175,183),(176,182),(177,181),(178,180),(190,196),(191,195),(192,194),(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)], [(1,154,110,55),(2,153,111,54),(3,152,112,53),(4,151,85,52),(5,150,86,51),(6,149,87,50),(7,148,88,49),(8,147,89,48),(9,146,90,47),(10,145,91,46),(11,144,92,45),(12,143,93,44),(13,142,94,43),(14,141,95,42),(15,168,96,41),(16,167,97,40),(17,166,98,39),(18,165,99,38),(19,164,100,37),(20,163,101,36),(21,162,102,35),(22,161,103,34),(23,160,104,33),(24,159,105,32),(25,158,106,31),(26,157,107,30),(27,156,108,29),(28,155,109,56),(57,113,176,203),(58,140,177,202),(59,139,178,201),(60,138,179,200),(61,137,180,199),(62,136,181,198),(63,135,182,197),(64,134,183,224),(65,133,184,223),(66,132,185,222),(67,131,186,221),(68,130,187,220),(69,129,188,219),(70,128,189,218),(71,127,190,217),(72,126,191,216),(73,125,192,215),(74,124,193,214),(75,123,194,213),(76,122,195,212),(77,121,196,211),(78,120,169,210),(79,119,170,209),(80,118,171,208),(81,117,172,207),(82,116,173,206),(83,115,174,205),(84,114,175,204)], [(1,217,110,127),(2,218,111,128),(3,219,112,129),(4,220,85,130),(5,221,86,131),(6,222,87,132),(7,223,88,133),(8,224,89,134),(9,197,90,135),(10,198,91,136),(11,199,92,137),(12,200,93,138),(13,201,94,139),(14,202,95,140),(15,203,96,113),(16,204,97,114),(17,205,98,115),(18,206,99,116),(19,207,100,117),(20,208,101,118),(21,209,102,119),(22,210,103,120),(23,211,104,121),(24,212,105,122),(25,213,106,123),(26,214,107,124),(27,215,108,125),(28,216,109,126),(29,73,156,192),(30,74,157,193),(31,75,158,194),(32,76,159,195),(33,77,160,196),(34,78,161,169),(35,79,162,170),(36,80,163,171),(37,81,164,172),(38,82,165,173),(39,83,166,174),(40,84,167,175),(41,57,168,176),(42,58,141,177),(43,59,142,178),(44,60,143,179),(45,61,144,180),(46,62,145,181),(47,63,146,182),(48,64,147,183),(49,65,148,184),(50,66,149,185),(51,67,150,186),(52,68,151,187),(53,69,152,188),(54,70,153,189),(55,71,154,190),(56,72,155,191)]])
79 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 | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| 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 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 28 | 28 | 56 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | + | - | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | D28 | C56⋊C2 | C8⋊C22 | D4⋊2D7 | Q8×D7 | C8⋊D14 |
| kernel | D28⋊3Q8 | C8⋊Dic7 | C2.D56 | C7×C4⋊C8 | C28⋊2Q8 | C4×D28 | D28 | C2×C28 | C4⋊C8 | C28 | C28 | C42 | C2×C8 | C2×C4 | C4 | C14 | C4 | C4 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 6 | 12 | 24 | 1 | 3 | 3 | 6 |
Matrix representation of D28⋊3Q8 ►in GL4(𝔽113) generated by
| 23 | 100 | 0 | 0 |
| 26 | 5 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 71 | 94 | 0 | 0 |
| 69 | 42 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 65 | 1 |
| 77 | 66 | 0 | 0 |
| 30 | 36 | 0 | 0 |
| 0 | 0 | 54 | 26 |
| 0 | 0 | 66 | 59 |
| 29 | 46 | 0 | 0 |
| 21 | 84 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 42 | 98 |
G:=sub<GL(4,GF(113))| [23,26,0,0,100,5,0,0,0,0,112,0,0,0,0,112],[71,69,0,0,94,42,0,0,0,0,112,65,0,0,0,1],[77,30,0,0,66,36,0,0,0,0,54,66,0,0,26,59],[29,21,0,0,46,84,0,0,0,0,15,42,0,0,0,98] >;
D28⋊3Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_3Q_8 % in TeX
G:=Group("D28:3Q8"); // GroupNames label
G:=SmallGroup(448,376);
// by ID
G=gap.SmallGroup(448,376);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,254,219,142,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=c^2,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^19*b,d*b*d^-1=a^14*b,d*c*d^-1=c^-1>;
// generators/relations