metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic7⋊7SD16, Q8⋊D7⋊1C4, Q8⋊1(C4×D7), C7⋊3(C4×SD16), (Q8×Dic7)⋊1C2, D28.2(C2×C4), C14.34(C4×D4), C2.3(D7×SD16), C4⋊C4.142D14, Q8⋊C4⋊21D7, (C8×Dic7)⋊21C2, (C2×C8).204D14, C28.9(C22×C4), (C2×Q8).96D14, C4.Dic14⋊9C2, C22.73(D4×D7), C2.D56.6C2, D28⋊C4.1C2, C14.66(C4○D8), C14.26(C2×SD16), C28.154(C4○D4), C4.51(D4⋊2D7), C2.1(Q8.D14), (C2×C28).228C23, (C2×C56).189C22, (C2×Dic7).202D4, (C2×D28).56C22, C4⋊Dic7.78C22, (Q8×C14).11C22, C2.18(Dic7⋊4D4), (C4×Dic7).224C22, C4.9(C2×C4×D7), C7⋊C8⋊13(C2×C4), (C7×Q8)⋊1(C2×C4), (C2×Q8⋊D7).1C2, (C7×Q8⋊C4)⋊15C2, (C2×C14).241(C2×D4), (C7×C4⋊C4).29C22, (C2×C7⋊C8).214C22, (C2×C4).335(C22×D7), SmallGroup(448,322)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic7⋊7SD16
G = < a,b,c,d | a14=c8=d2=1, b2=a7, bab-1=cac-1=dad=a-1, bc=cb, bd=db, dcd=c3 >
Subgroups: 628 in 122 conjugacy classes, 51 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C4×C8, D4⋊C4, Q8⋊C4, C4.Q8, C4×D4, C4×Q8, C2×SD16, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, C4×SD16, C2×C7⋊C8, C4×Dic7, C4×Dic7, C4⋊Dic7, C4⋊Dic7, D14⋊C4, Q8⋊D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, Q8×C14, C4.Dic14, C8×Dic7, C2.D56, C7×Q8⋊C4, D28⋊C4, C2×Q8⋊D7, Q8×Dic7, Dic7⋊7SD16
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, SD16, C22×C4, C2×D4, C4○D4, D14, C4×D4, C2×SD16, C4○D8, C4×D7, C22×D7, C4×SD16, C2×C4×D7, D4×D7, D4⋊2D7, Dic7⋊4D4, D7×SD16, Q8.D14, Dic7⋊7SD16
►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)
(1 100 8 107)(2 99 9 106)(3 112 10 105)(4 111 11 104)(5 110 12 103)(6 109 13 102)(7 108 14 101)(15 114 22 121)(16 113 23 120)(17 126 24 119)(18 125 25 118)(19 124 26 117)(20 123 27 116)(21 122 28 115)(29 62 36 69)(30 61 37 68)(31 60 38 67)(32 59 39 66)(33 58 40 65)(34 57 41 64)(35 70 42 63)(43 223 50 216)(44 222 51 215)(45 221 52 214)(46 220 53 213)(47 219 54 212)(48 218 55 211)(49 217 56 224)(71 181 78 174)(72 180 79 173)(73 179 80 172)(74 178 81 171)(75 177 82 170)(76 176 83 169)(77 175 84 182)(85 138 92 131)(86 137 93 130)(87 136 94 129)(88 135 95 128)(89 134 96 127)(90 133 97 140)(91 132 98 139)(141 203 148 210)(142 202 149 209)(143 201 150 208)(144 200 151 207)(145 199 152 206)(146 198 153 205)(147 197 154 204)(155 183 162 190)(156 196 163 189)(157 195 164 188)(158 194 165 187)(159 193 166 186)(160 192 167 185)(161 191 168 184)
(1 79 88 34 199 218 27 161)(2 78 89 33 200 217 28 160)(3 77 90 32 201 216 15 159)(4 76 91 31 202 215 16 158)(5 75 92 30 203 214 17 157)(6 74 93 29 204 213 18 156)(7 73 94 42 205 212 19 155)(8 72 95 41 206 211 20 168)(9 71 96 40 207 224 21 167)(10 84 97 39 208 223 22 166)(11 83 98 38 209 222 23 165)(12 82 85 37 210 221 24 164)(13 81 86 36 197 220 25 163)(14 80 87 35 198 219 26 162)(43 114 193 112 175 133 59 150)(44 113 194 111 176 132 60 149)(45 126 195 110 177 131 61 148)(46 125 196 109 178 130 62 147)(47 124 183 108 179 129 63 146)(48 123 184 107 180 128 64 145)(49 122 185 106 181 127 65 144)(50 121 186 105 182 140 66 143)(51 120 187 104 169 139 67 142)(52 119 188 103 170 138 68 141)(53 118 189 102 171 137 69 154)(54 117 190 101 172 136 70 153)(55 116 191 100 173 135 57 152)(56 115 192 99 174 134 58 151)
(1 206)(2 205)(3 204)(4 203)(5 202)(6 201)(7 200)(8 199)(9 198)(10 197)(11 210)(12 209)(13 208)(14 207)(15 18)(16 17)(19 28)(20 27)(21 26)(22 25)(23 24)(29 216)(30 215)(31 214)(32 213)(33 212)(34 211)(35 224)(36 223)(37 222)(38 221)(39 220)(40 219)(41 218)(42 217)(43 62)(44 61)(45 60)(46 59)(47 58)(48 57)(49 70)(50 69)(51 68)(52 67)(53 66)(54 65)(55 64)(56 63)(71 162)(72 161)(73 160)(74 159)(75 158)(76 157)(77 156)(78 155)(79 168)(80 167)(81 166)(82 165)(83 164)(84 163)(85 98)(86 97)(87 96)(88 95)(89 94)(90 93)(91 92)(99 146)(100 145)(101 144)(102 143)(103 142)(104 141)(105 154)(106 153)(107 152)(108 151)(109 150)(110 149)(111 148)(112 147)(113 126)(114 125)(115 124)(116 123)(117 122)(118 121)(119 120)(127 136)(128 135)(129 134)(130 133)(131 132)(137 140)(138 139)(169 188)(170 187)(171 186)(172 185)(173 184)(174 183)(175 196)(176 195)(177 194)(178 193)(179 192)(180 191)(181 190)(182 189)
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), (1,100,8,107)(2,99,9,106)(3,112,10,105)(4,111,11,104)(5,110,12,103)(6,109,13,102)(7,108,14,101)(15,114,22,121)(16,113,23,120)(17,126,24,119)(18,125,25,118)(19,124,26,117)(20,123,27,116)(21,122,28,115)(29,62,36,69)(30,61,37,68)(31,60,38,67)(32,59,39,66)(33,58,40,65)(34,57,41,64)(35,70,42,63)(43,223,50,216)(44,222,51,215)(45,221,52,214)(46,220,53,213)(47,219,54,212)(48,218,55,211)(49,217,56,224)(71,181,78,174)(72,180,79,173)(73,179,80,172)(74,178,81,171)(75,177,82,170)(76,176,83,169)(77,175,84,182)(85,138,92,131)(86,137,93,130)(87,136,94,129)(88,135,95,128)(89,134,96,127)(90,133,97,140)(91,132,98,139)(141,203,148,210)(142,202,149,209)(143,201,150,208)(144,200,151,207)(145,199,152,206)(146,198,153,205)(147,197,154,204)(155,183,162,190)(156,196,163,189)(157,195,164,188)(158,194,165,187)(159,193,166,186)(160,192,167,185)(161,191,168,184), (1,79,88,34,199,218,27,161)(2,78,89,33,200,217,28,160)(3,77,90,32,201,216,15,159)(4,76,91,31,202,215,16,158)(5,75,92,30,203,214,17,157)(6,74,93,29,204,213,18,156)(7,73,94,42,205,212,19,155)(8,72,95,41,206,211,20,168)(9,71,96,40,207,224,21,167)(10,84,97,39,208,223,22,166)(11,83,98,38,209,222,23,165)(12,82,85,37,210,221,24,164)(13,81,86,36,197,220,25,163)(14,80,87,35,198,219,26,162)(43,114,193,112,175,133,59,150)(44,113,194,111,176,132,60,149)(45,126,195,110,177,131,61,148)(46,125,196,109,178,130,62,147)(47,124,183,108,179,129,63,146)(48,123,184,107,180,128,64,145)(49,122,185,106,181,127,65,144)(50,121,186,105,182,140,66,143)(51,120,187,104,169,139,67,142)(52,119,188,103,170,138,68,141)(53,118,189,102,171,137,69,154)(54,117,190,101,172,136,70,153)(55,116,191,100,173,135,57,152)(56,115,192,99,174,134,58,151), (1,206)(2,205)(3,204)(4,203)(5,202)(6,201)(7,200)(8,199)(9,198)(10,197)(11,210)(12,209)(13,208)(14,207)(15,18)(16,17)(19,28)(20,27)(21,26)(22,25)(23,24)(29,216)(30,215)(31,214)(32,213)(33,212)(34,211)(35,224)(36,223)(37,222)(38,221)(39,220)(40,219)(41,218)(42,217)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(71,162)(72,161)(73,160)(74,159)(75,158)(76,157)(77,156)(78,155)(79,168)(80,167)(81,166)(82,165)(83,164)(84,163)(85,98)(86,97)(87,96)(88,95)(89,94)(90,93)(91,92)(99,146)(100,145)(101,144)(102,143)(103,142)(104,141)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,136)(128,135)(129,134)(130,133)(131,132)(137,140)(138,139)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)>;
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), (1,100,8,107)(2,99,9,106)(3,112,10,105)(4,111,11,104)(5,110,12,103)(6,109,13,102)(7,108,14,101)(15,114,22,121)(16,113,23,120)(17,126,24,119)(18,125,25,118)(19,124,26,117)(20,123,27,116)(21,122,28,115)(29,62,36,69)(30,61,37,68)(31,60,38,67)(32,59,39,66)(33,58,40,65)(34,57,41,64)(35,70,42,63)(43,223,50,216)(44,222,51,215)(45,221,52,214)(46,220,53,213)(47,219,54,212)(48,218,55,211)(49,217,56,224)(71,181,78,174)(72,180,79,173)(73,179,80,172)(74,178,81,171)(75,177,82,170)(76,176,83,169)(77,175,84,182)(85,138,92,131)(86,137,93,130)(87,136,94,129)(88,135,95,128)(89,134,96,127)(90,133,97,140)(91,132,98,139)(141,203,148,210)(142,202,149,209)(143,201,150,208)(144,200,151,207)(145,199,152,206)(146,198,153,205)(147,197,154,204)(155,183,162,190)(156,196,163,189)(157,195,164,188)(158,194,165,187)(159,193,166,186)(160,192,167,185)(161,191,168,184), (1,79,88,34,199,218,27,161)(2,78,89,33,200,217,28,160)(3,77,90,32,201,216,15,159)(4,76,91,31,202,215,16,158)(5,75,92,30,203,214,17,157)(6,74,93,29,204,213,18,156)(7,73,94,42,205,212,19,155)(8,72,95,41,206,211,20,168)(9,71,96,40,207,224,21,167)(10,84,97,39,208,223,22,166)(11,83,98,38,209,222,23,165)(12,82,85,37,210,221,24,164)(13,81,86,36,197,220,25,163)(14,80,87,35,198,219,26,162)(43,114,193,112,175,133,59,150)(44,113,194,111,176,132,60,149)(45,126,195,110,177,131,61,148)(46,125,196,109,178,130,62,147)(47,124,183,108,179,129,63,146)(48,123,184,107,180,128,64,145)(49,122,185,106,181,127,65,144)(50,121,186,105,182,140,66,143)(51,120,187,104,169,139,67,142)(52,119,188,103,170,138,68,141)(53,118,189,102,171,137,69,154)(54,117,190,101,172,136,70,153)(55,116,191,100,173,135,57,152)(56,115,192,99,174,134,58,151), (1,206)(2,205)(3,204)(4,203)(5,202)(6,201)(7,200)(8,199)(9,198)(10,197)(11,210)(12,209)(13,208)(14,207)(15,18)(16,17)(19,28)(20,27)(21,26)(22,25)(23,24)(29,216)(30,215)(31,214)(32,213)(33,212)(34,211)(35,224)(36,223)(37,222)(38,221)(39,220)(40,219)(41,218)(42,217)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(71,162)(72,161)(73,160)(74,159)(75,158)(76,157)(77,156)(78,155)(79,168)(80,167)(81,166)(82,165)(83,164)(84,163)(85,98)(86,97)(87,96)(88,95)(89,94)(90,93)(91,92)(99,146)(100,145)(101,144)(102,143)(103,142)(104,141)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,136)(128,135)(129,134)(130,133)(131,132)(137,140)(138,139)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189) );
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)], [(1,100,8,107),(2,99,9,106),(3,112,10,105),(4,111,11,104),(5,110,12,103),(6,109,13,102),(7,108,14,101),(15,114,22,121),(16,113,23,120),(17,126,24,119),(18,125,25,118),(19,124,26,117),(20,123,27,116),(21,122,28,115),(29,62,36,69),(30,61,37,68),(31,60,38,67),(32,59,39,66),(33,58,40,65),(34,57,41,64),(35,70,42,63),(43,223,50,216),(44,222,51,215),(45,221,52,214),(46,220,53,213),(47,219,54,212),(48,218,55,211),(49,217,56,224),(71,181,78,174),(72,180,79,173),(73,179,80,172),(74,178,81,171),(75,177,82,170),(76,176,83,169),(77,175,84,182),(85,138,92,131),(86,137,93,130),(87,136,94,129),(88,135,95,128),(89,134,96,127),(90,133,97,140),(91,132,98,139),(141,203,148,210),(142,202,149,209),(143,201,150,208),(144,200,151,207),(145,199,152,206),(146,198,153,205),(147,197,154,204),(155,183,162,190),(156,196,163,189),(157,195,164,188),(158,194,165,187),(159,193,166,186),(160,192,167,185),(161,191,168,184)], [(1,79,88,34,199,218,27,161),(2,78,89,33,200,217,28,160),(3,77,90,32,201,216,15,159),(4,76,91,31,202,215,16,158),(5,75,92,30,203,214,17,157),(6,74,93,29,204,213,18,156),(7,73,94,42,205,212,19,155),(8,72,95,41,206,211,20,168),(9,71,96,40,207,224,21,167),(10,84,97,39,208,223,22,166),(11,83,98,38,209,222,23,165),(12,82,85,37,210,221,24,164),(13,81,86,36,197,220,25,163),(14,80,87,35,198,219,26,162),(43,114,193,112,175,133,59,150),(44,113,194,111,176,132,60,149),(45,126,195,110,177,131,61,148),(46,125,196,109,178,130,62,147),(47,124,183,108,179,129,63,146),(48,123,184,107,180,128,64,145),(49,122,185,106,181,127,65,144),(50,121,186,105,182,140,66,143),(51,120,187,104,169,139,67,142),(52,119,188,103,170,138,68,141),(53,118,189,102,171,137,69,154),(54,117,190,101,172,136,70,153),(55,116,191,100,173,135,57,152),(56,115,192,99,174,134,58,151)], [(1,206),(2,205),(3,204),(4,203),(5,202),(6,201),(7,200),(8,199),(9,198),(10,197),(11,210),(12,209),(13,208),(14,207),(15,18),(16,17),(19,28),(20,27),(21,26),(22,25),(23,24),(29,216),(30,215),(31,214),(32,213),(33,212),(34,211),(35,224),(36,223),(37,222),(38,221),(39,220),(40,219),(41,218),(42,217),(43,62),(44,61),(45,60),(46,59),(47,58),(48,57),(49,70),(50,69),(51,68),(52,67),(53,66),(54,65),(55,64),(56,63),(71,162),(72,161),(73,160),(74,159),(75,158),(76,157),(77,156),(78,155),(79,168),(80,167),(81,166),(82,165),(83,164),(84,163),(85,98),(86,97),(87,96),(88,95),(89,94),(90,93),(91,92),(99,146),(100,145),(101,144),(102,143),(103,142),(104,141),(105,154),(106,153),(107,152),(108,151),(109,150),(110,149),(111,148),(112,147),(113,126),(114,125),(115,124),(116,123),(117,122),(118,121),(119,120),(127,136),(128,135),(129,134),(130,133),(131,132),(137,140),(138,139),(169,188),(170,187),(171,186),(172,185),(173,184),(174,183),(175,196),(176,195),(177,194),(178,193),(179,192),(180,191),(181,190),(182,189)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
70 irreducible representations
| dim | 1 | 1 | 1 | 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 | C2 | C2 | C4 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4×D7 | D4⋊2D7 | D4×D7 | D7×SD16 | Q8.D14 |
| kernel | Dic7⋊7SD16 | C4.Dic14 | C8×Dic7 | C2.D56 | C7×Q8⋊C4 | D28⋊C4 | C2×Q8⋊D7 | Q8×Dic7 | Q8⋊D7 | C2×Dic7 | Q8⋊C4 | Dic7 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | Q8 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 4 | 2 | 3 | 3 | 3 | 4 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of Dic7⋊7SD16 ►in GL4(𝔽113) generated by
| 24 | 112 | 0 | 0 |
| 100 | 10 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 55 | 0 | 0 |
| 76 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 0 | 79 | 0 | 0 |
| 103 | 0 | 0 | 0 |
| 0 | 0 | 100 | 100 |
| 0 | 0 | 13 | 100 |
| 0 | 79 | 0 | 0 |
| 103 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 112 |
G:=sub<GL(4,GF(113))| [24,100,0,0,112,10,0,0,0,0,112,0,0,0,0,112],[0,76,0,0,55,0,0,0,0,0,15,0,0,0,0,15],[0,103,0,0,79,0,0,0,0,0,100,13,0,0,100,100],[0,103,0,0,79,0,0,0,0,0,1,0,0,0,0,112] >;
Dic7⋊7SD16 in GAP, Magma, Sage, TeX
{\rm Dic}_7\rtimes_7{\rm SD}_{16} % in TeX
G:=Group("Dic7:7SD16"); // GroupNames label
G:=SmallGroup(448,322);
// by ID
G=gap.SmallGroup(448,322);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,120,135,184,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=c^8=d^2=1,b^2=a^7,b*a*b^-1=c*a*c^-1=d*a*d=a^-1,b*c=c*b,b*d=d*b,d*c*d=c^3>;
// generators/relations