metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊9Q8, C42.175D14, C14.832+ 1+4, C4⋊Q8⋊13D7, C4.19(Q8×D7), C7⋊8(D4⋊3Q8), C28.56(C2×Q8), C4⋊C4.220D14, (C4×D28).27C2, D14.12(C2×Q8), (C2×Q8).87D14, D14⋊3Q8⋊37C2, D14⋊2Q8⋊44C2, (C4×Dic14)⋊53C2, C28.3Q8⋊44C2, D28⋊C4.14C2, C28.137(C4○D4), C14.50(C22×Q8), (C2×C14).274C24, (C4×C28).215C22, (C2×C28).107C23, C4.40(Q8⋊2D7), C2.87(D4⋊6D14), D14⋊C4.153C22, (C2×D28).273C22, Dic7⋊C4.62C22, C4⋊Dic7.253C22, (Q8×C14).141C22, C22.295(C23×D7), (C2×Dic7).145C23, (C4×Dic7).163C22, (C22×D7).235C23, (C2×Dic14).303C22, (D7×C4⋊C4)⋊45C2, C2.33(C2×Q8×D7), (C7×C4⋊Q8)⋊16C2, C14.122(C2×C4○D4), C2.30(C2×Q8⋊2D7), (C2×C4×D7).147C22, (C7×C4⋊C4).217C22, (C2×C4).220(C22×D7), SmallGroup(448,1183)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊9Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=a-1, cac-1=a15, ad=da, cbc-1=dbd-1=a14b, dcd-1=c-1 >
Subgroups: 1004 in 228 conjugacy classes, 107 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, D4⋊3Q8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C4×Dic14, C4×D28, C28.3Q8, D7×C4⋊C4, D28⋊C4, D14⋊2Q8, D14⋊3Q8, C7×C4⋊Q8, D28⋊9Q8
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D7, D4⋊3Q8, Q8×D7, Q8⋊2D7, C23×D7, D4⋊6D14, C2×Q8×D7, C2×Q8⋊2D7, D28⋊9Q8
►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 92)(2 91)(3 90)(4 89)(5 88)(6 87)(7 86)(8 85)(9 112)(10 111)(11 110)(12 109)(13 108)(14 107)(15 106)(16 105)(17 104)(18 103)(19 102)(20 101)(21 100)(22 99)(23 98)(24 97)(25 96)(26 95)(27 94)(28 93)(29 197)(30 224)(31 223)(32 222)(33 221)(34 220)(35 219)(36 218)(37 217)(38 216)(39 215)(40 214)(41 213)(42 212)(43 211)(44 210)(45 209)(46 208)(47 207)(48 206)(49 205)(50 204)(51 203)(52 202)(53 201)(54 200)(55 199)(56 198)(57 120)(58 119)(59 118)(60 117)(61 116)(62 115)(63 114)(64 113)(65 140)(66 139)(67 138)(68 137)(69 136)(70 135)(71 134)(72 133)(73 132)(74 131)(75 130)(76 129)(77 128)(78 127)(79 126)(80 125)(81 124)(82 123)(83 122)(84 121)(141 172)(142 171)(143 170)(144 169)(145 196)(146 195)(147 194)(148 193)(149 192)(150 191)(151 190)(152 189)(153 188)(154 187)(155 186)(156 185)(157 184)(158 183)(159 182)(160 181)(161 180)(162 179)(163 178)(164 177)(165 176)(166 175)(167 174)(168 173)
(1 138 100 61)(2 125 101 76)(3 140 102 63)(4 127 103 78)(5 114 104 65)(6 129 105 80)(7 116 106 67)(8 131 107 82)(9 118 108 69)(10 133 109 84)(11 120 110 71)(12 135 111 58)(13 122 112 73)(14 137 85 60)(15 124 86 75)(16 139 87 62)(17 126 88 77)(18 113 89 64)(19 128 90 79)(20 115 91 66)(21 130 92 81)(22 117 93 68)(23 132 94 83)(24 119 95 70)(25 134 96 57)(26 121 97 72)(27 136 98 59)(28 123 99 74)(29 146 205 189)(30 161 206 176)(31 148 207 191)(32 163 208 178)(33 150 209 193)(34 165 210 180)(35 152 211 195)(36 167 212 182)(37 154 213 169)(38 141 214 184)(39 156 215 171)(40 143 216 186)(41 158 217 173)(42 145 218 188)(43 160 219 175)(44 147 220 190)(45 162 221 177)(46 149 222 192)(47 164 223 179)(48 151 224 194)(49 166 197 181)(50 153 198 196)(51 168 199 183)(52 155 200 170)(53 142 201 185)(54 157 202 172)(55 144 203 187)(56 159 204 174)
(1 198 100 50)(2 199 101 51)(3 200 102 52)(4 201 103 53)(5 202 104 54)(6 203 105 55)(7 204 106 56)(8 205 107 29)(9 206 108 30)(10 207 109 31)(11 208 110 32)(12 209 111 33)(13 210 112 34)(14 211 85 35)(15 212 86 36)(16 213 87 37)(17 214 88 38)(18 215 89 39)(19 216 90 40)(20 217 91 41)(21 218 92 42)(22 219 93 43)(23 220 94 44)(24 221 95 45)(25 222 96 46)(26 223 97 47)(27 224 98 48)(28 197 99 49)(57 192 134 149)(58 193 135 150)(59 194 136 151)(60 195 137 152)(61 196 138 153)(62 169 139 154)(63 170 140 155)(64 171 113 156)(65 172 114 157)(66 173 115 158)(67 174 116 159)(68 175 117 160)(69 176 118 161)(70 177 119 162)(71 178 120 163)(72 179 121 164)(73 180 122 165)(74 181 123 166)(75 182 124 167)(76 183 125 168)(77 184 126 141)(78 185 127 142)(79 186 128 143)(80 187 129 144)(81 188 130 145)(82 189 131 146)(83 190 132 147)(84 191 133 148)
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), (1,92)(2,91)(3,90)(4,89)(5,88)(6,87)(7,86)(8,85)(9,112)(10,111)(11,110)(12,109)(13,108)(14,107)(15,106)(16,105)(17,104)(18,103)(19,102)(20,101)(21,100)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,197)(30,224)(31,223)(32,222)(33,221)(34,220)(35,219)(36,218)(37,217)(38,216)(39,215)(40,214)(41,213)(42,212)(43,211)(44,210)(45,209)(46,208)(47,207)(48,206)(49,205)(50,204)(51,203)(52,202)(53,201)(54,200)(55,199)(56,198)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,140)(66,139)(67,138)(68,137)(69,136)(70,135)(71,134)(72,133)(73,132)(74,131)(75,130)(76,129)(77,128)(78,127)(79,126)(80,125)(81,124)(82,123)(83,122)(84,121)(141,172)(142,171)(143,170)(144,169)(145,196)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173), (1,138,100,61)(2,125,101,76)(3,140,102,63)(4,127,103,78)(5,114,104,65)(6,129,105,80)(7,116,106,67)(8,131,107,82)(9,118,108,69)(10,133,109,84)(11,120,110,71)(12,135,111,58)(13,122,112,73)(14,137,85,60)(15,124,86,75)(16,139,87,62)(17,126,88,77)(18,113,89,64)(19,128,90,79)(20,115,91,66)(21,130,92,81)(22,117,93,68)(23,132,94,83)(24,119,95,70)(25,134,96,57)(26,121,97,72)(27,136,98,59)(28,123,99,74)(29,146,205,189)(30,161,206,176)(31,148,207,191)(32,163,208,178)(33,150,209,193)(34,165,210,180)(35,152,211,195)(36,167,212,182)(37,154,213,169)(38,141,214,184)(39,156,215,171)(40,143,216,186)(41,158,217,173)(42,145,218,188)(43,160,219,175)(44,147,220,190)(45,162,221,177)(46,149,222,192)(47,164,223,179)(48,151,224,194)(49,166,197,181)(50,153,198,196)(51,168,199,183)(52,155,200,170)(53,142,201,185)(54,157,202,172)(55,144,203,187)(56,159,204,174), (1,198,100,50)(2,199,101,51)(3,200,102,52)(4,201,103,53)(5,202,104,54)(6,203,105,55)(7,204,106,56)(8,205,107,29)(9,206,108,30)(10,207,109,31)(11,208,110,32)(12,209,111,33)(13,210,112,34)(14,211,85,35)(15,212,86,36)(16,213,87,37)(17,214,88,38)(18,215,89,39)(19,216,90,40)(20,217,91,41)(21,218,92,42)(22,219,93,43)(23,220,94,44)(24,221,95,45)(25,222,96,46)(26,223,97,47)(27,224,98,48)(28,197,99,49)(57,192,134,149)(58,193,135,150)(59,194,136,151)(60,195,137,152)(61,196,138,153)(62,169,139,154)(63,170,140,155)(64,171,113,156)(65,172,114,157)(66,173,115,158)(67,174,116,159)(68,175,117,160)(69,176,118,161)(70,177,119,162)(71,178,120,163)(72,179,121,164)(73,180,122,165)(74,181,123,166)(75,182,124,167)(76,183,125,168)(77,184,126,141)(78,185,127,142)(79,186,128,143)(80,187,129,144)(81,188,130,145)(82,189,131,146)(83,190,132,147)(84,191,133,148)>;
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), (1,92)(2,91)(3,90)(4,89)(5,88)(6,87)(7,86)(8,85)(9,112)(10,111)(11,110)(12,109)(13,108)(14,107)(15,106)(16,105)(17,104)(18,103)(19,102)(20,101)(21,100)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,197)(30,224)(31,223)(32,222)(33,221)(34,220)(35,219)(36,218)(37,217)(38,216)(39,215)(40,214)(41,213)(42,212)(43,211)(44,210)(45,209)(46,208)(47,207)(48,206)(49,205)(50,204)(51,203)(52,202)(53,201)(54,200)(55,199)(56,198)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,140)(66,139)(67,138)(68,137)(69,136)(70,135)(71,134)(72,133)(73,132)(74,131)(75,130)(76,129)(77,128)(78,127)(79,126)(80,125)(81,124)(82,123)(83,122)(84,121)(141,172)(142,171)(143,170)(144,169)(145,196)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173), (1,138,100,61)(2,125,101,76)(3,140,102,63)(4,127,103,78)(5,114,104,65)(6,129,105,80)(7,116,106,67)(8,131,107,82)(9,118,108,69)(10,133,109,84)(11,120,110,71)(12,135,111,58)(13,122,112,73)(14,137,85,60)(15,124,86,75)(16,139,87,62)(17,126,88,77)(18,113,89,64)(19,128,90,79)(20,115,91,66)(21,130,92,81)(22,117,93,68)(23,132,94,83)(24,119,95,70)(25,134,96,57)(26,121,97,72)(27,136,98,59)(28,123,99,74)(29,146,205,189)(30,161,206,176)(31,148,207,191)(32,163,208,178)(33,150,209,193)(34,165,210,180)(35,152,211,195)(36,167,212,182)(37,154,213,169)(38,141,214,184)(39,156,215,171)(40,143,216,186)(41,158,217,173)(42,145,218,188)(43,160,219,175)(44,147,220,190)(45,162,221,177)(46,149,222,192)(47,164,223,179)(48,151,224,194)(49,166,197,181)(50,153,198,196)(51,168,199,183)(52,155,200,170)(53,142,201,185)(54,157,202,172)(55,144,203,187)(56,159,204,174), (1,198,100,50)(2,199,101,51)(3,200,102,52)(4,201,103,53)(5,202,104,54)(6,203,105,55)(7,204,106,56)(8,205,107,29)(9,206,108,30)(10,207,109,31)(11,208,110,32)(12,209,111,33)(13,210,112,34)(14,211,85,35)(15,212,86,36)(16,213,87,37)(17,214,88,38)(18,215,89,39)(19,216,90,40)(20,217,91,41)(21,218,92,42)(22,219,93,43)(23,220,94,44)(24,221,95,45)(25,222,96,46)(26,223,97,47)(27,224,98,48)(28,197,99,49)(57,192,134,149)(58,193,135,150)(59,194,136,151)(60,195,137,152)(61,196,138,153)(62,169,139,154)(63,170,140,155)(64,171,113,156)(65,172,114,157)(66,173,115,158)(67,174,116,159)(68,175,117,160)(69,176,118,161)(70,177,119,162)(71,178,120,163)(72,179,121,164)(73,180,122,165)(74,181,123,166)(75,182,124,167)(76,183,125,168)(77,184,126,141)(78,185,127,142)(79,186,128,143)(80,187,129,144)(81,188,130,145)(82,189,131,146)(83,190,132,147)(84,191,133,148) );
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)], [(1,92),(2,91),(3,90),(4,89),(5,88),(6,87),(7,86),(8,85),(9,112),(10,111),(11,110),(12,109),(13,108),(14,107),(15,106),(16,105),(17,104),(18,103),(19,102),(20,101),(21,100),(22,99),(23,98),(24,97),(25,96),(26,95),(27,94),(28,93),(29,197),(30,224),(31,223),(32,222),(33,221),(34,220),(35,219),(36,218),(37,217),(38,216),(39,215),(40,214),(41,213),(42,212),(43,211),(44,210),(45,209),(46,208),(47,207),(48,206),(49,205),(50,204),(51,203),(52,202),(53,201),(54,200),(55,199),(56,198),(57,120),(58,119),(59,118),(60,117),(61,116),(62,115),(63,114),(64,113),(65,140),(66,139),(67,138),(68,137),(69,136),(70,135),(71,134),(72,133),(73,132),(74,131),(75,130),(76,129),(77,128),(78,127),(79,126),(80,125),(81,124),(82,123),(83,122),(84,121),(141,172),(142,171),(143,170),(144,169),(145,196),(146,195),(147,194),(148,193),(149,192),(150,191),(151,190),(152,189),(153,188),(154,187),(155,186),(156,185),(157,184),(158,183),(159,182),(160,181),(161,180),(162,179),(163,178),(164,177),(165,176),(166,175),(167,174),(168,173)], [(1,138,100,61),(2,125,101,76),(3,140,102,63),(4,127,103,78),(5,114,104,65),(6,129,105,80),(7,116,106,67),(8,131,107,82),(9,118,108,69),(10,133,109,84),(11,120,110,71),(12,135,111,58),(13,122,112,73),(14,137,85,60),(15,124,86,75),(16,139,87,62),(17,126,88,77),(18,113,89,64),(19,128,90,79),(20,115,91,66),(21,130,92,81),(22,117,93,68),(23,132,94,83),(24,119,95,70),(25,134,96,57),(26,121,97,72),(27,136,98,59),(28,123,99,74),(29,146,205,189),(30,161,206,176),(31,148,207,191),(32,163,208,178),(33,150,209,193),(34,165,210,180),(35,152,211,195),(36,167,212,182),(37,154,213,169),(38,141,214,184),(39,156,215,171),(40,143,216,186),(41,158,217,173),(42,145,218,188),(43,160,219,175),(44,147,220,190),(45,162,221,177),(46,149,222,192),(47,164,223,179),(48,151,224,194),(49,166,197,181),(50,153,198,196),(51,168,199,183),(52,155,200,170),(53,142,201,185),(54,157,202,172),(55,144,203,187),(56,159,204,174)], [(1,198,100,50),(2,199,101,51),(3,200,102,52),(4,201,103,53),(5,202,104,54),(6,203,105,55),(7,204,106,56),(8,205,107,29),(9,206,108,30),(10,207,109,31),(11,208,110,32),(12,209,111,33),(13,210,112,34),(14,211,85,35),(15,212,86,36),(16,213,87,37),(17,214,88,38),(18,215,89,39),(19,216,90,40),(20,217,91,41),(21,218,92,42),(22,219,93,43),(23,220,94,44),(24,221,95,45),(25,222,96,46),(26,223,97,47),(27,224,98,48),(28,197,99,49),(57,192,134,149),(58,193,135,150),(59,194,136,151),(60,195,137,152),(61,196,138,153),(62,169,139,154),(63,170,140,155),(64,171,113,156),(65,172,114,157),(66,173,115,158),(67,174,116,159),(68,175,117,160),(69,176,118,161),(70,177,119,162),(71,178,120,163),(72,179,121,164),(73,180,122,165),(74,181,123,166),(75,182,124,167),(76,183,125,168),(77,184,126,141),(78,185,127,142),(79,186,128,143),(80,187,129,144),(81,188,130,145),(82,189,131,146),(83,190,132,147),(84,191,133,148)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | Q8×D7 | Q8⋊2D7 | D4⋊6D14 |
| kernel | D28⋊9Q8 | C4×Dic14 | C4×D28 | C28.3Q8 | D7×C4⋊C4 | D28⋊C4 | D14⋊2Q8 | D14⋊3Q8 | C7×C4⋊Q8 | D28 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 1 | 4 | 3 | 4 | 3 | 12 | 6 | 1 | 6 | 6 | 6 |
Matrix representation of D28⋊9Q8 ►in GL6(𝔽29)
| 25 | 18 | 0 | 0 | 0 | 0 |
| 11 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 11 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 4 | 11 | 0 | 0 | 0 | 0 |
| 25 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 18 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 13 | 0 | 0 |
| 0 | 0 | 11 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 0 | 27 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 11 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 9 |
| 0 | 0 | 0 | 0 | 7 | 9 |
G:=sub<GL(6,GF(29))| [25,11,0,0,0,0,18,1,0,0,0,0,0,0,12,0,0,0,0,0,11,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[4,25,0,0,0,0,11,25,0,0,0,0,0,0,28,18,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,11,0,0,0,0,13,28,0,0,0,0,0,0,1,27,0,0,0,0,1,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,11,17,0,0,0,0,0,0,20,7,0,0,0,0,9,9] >;
D28⋊9Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_9Q_8 % in TeX
G:=Group("D28:9Q8"); // GroupNames label
G:=SmallGroup(448,1183);
// by ID
G=gap.SmallGroup(448,1183);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,570,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=c^2,b*a*b=a^-1,c*a*c^-1=a^15,a*d=d*a,c*b*c^-1=d*b*d^-1=a^14*b,d*c*d^-1=c^-1>;
// generators/relations