direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C4⋊SD16, C28⋊15SD16, C4⋊C8⋊8C14, Q8⋊1(C7×D4), (C4×Q8)⋊3C14, (C7×Q8)⋊12D4, C4⋊3(C7×SD16), (Q8×C28)⋊23C2, C4.32(D4×C14), C28.393(C2×D4), C4⋊1D4.3C14, (C2×C28).322D4, D4⋊C4⋊10C14, C2.7(C14×SD16), (C14×SD16)⋊28C2, (C2×SD16)⋊11C14, C42.15(C2×C14), C14.87(C2×SD16), C22.84(D4×C14), C28.342(C4○D4), (C2×C56).299C22, (C2×C28).919C23, (C4×C28).257C22, C14.143(C4⋊D4), C14.135(C8⋊C22), (D4×C14).186C22, (Q8×C14).262C22, (C7×C4⋊C8)⋊27C2, C4.41(C7×C4○D4), C4⋊C4.52(C2×C14), (C2×C8).36(C2×C14), (C2×C4).128(C7×D4), C2.12(C7×C4⋊D4), C2.10(C7×C8⋊C22), (C7×D4⋊C4)⋊34C2, (C2×D4).10(C2×C14), (C7×C4⋊1D4).10C2, (C2×C14).640(C2×D4), (C2×Q8).47(C2×C14), (C7×C4⋊C4).373C22, (C2×C4).94(C22×C14), SmallGroup(448,868)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C4⋊SD16
G = < a,b,c,d | a7=b4=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c3 >
Subgroups: 266 in 128 conjugacy classes, 58 normal (34 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, C14, C14, C42, C42, C4⋊C4, C4⋊C4, C2×C8, SD16, C2×D4, C2×D4, C2×Q8, C28, C28, C28, C2×C14, C2×C14, D4⋊C4, C4⋊C8, C4×Q8, C4⋊1D4, C2×SD16, C56, C2×C28, C2×C28, C7×D4, C7×Q8, C7×Q8, C22×C14, C4⋊SD16, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C56, C7×SD16, D4×C14, D4×C14, Q8×C14, C7×D4⋊C4, C7×C4⋊C8, Q8×C28, C7×C4⋊1D4, C14×SD16, C7×C4⋊SD16
Quotients: C1, C2, C22, C7, D4, C23, C14, SD16, C2×D4, C4○D4, C2×C14, C4⋊D4, C2×SD16, C8⋊C22, C7×D4, C22×C14, C4⋊SD16, C7×SD16, D4×C14, C7×C4○D4, C7×C4⋊D4, C14×SD16, C7×C8⋊C22, C7×C4⋊SD16
►On 224 points
Generators in S224
(1 14 85 28 77 20 69)(2 15 86 29 78 21 70)(3 16 87 30 79 22 71)(4 9 88 31 80 23 72)(5 10 81 32 73 24 65)(6 11 82 25 74 17 66)(7 12 83 26 75 18 67)(8 13 84 27 76 19 68)(33 117 106 49 98 41 90)(34 118 107 50 99 42 91)(35 119 108 51 100 43 92)(36 120 109 52 101 44 93)(37 113 110 53 102 45 94)(38 114 111 54 103 46 95)(39 115 112 55 104 47 96)(40 116 105 56 97 48 89)(57 221 168 213 160 205 152)(58 222 161 214 153 206 145)(59 223 162 215 154 207 146)(60 224 163 216 155 208 147)(61 217 164 209 156 201 148)(62 218 165 210 157 202 149)(63 219 166 211 158 203 150)(64 220 167 212 159 204 151)(121 174 198 137 190 129 182)(122 175 199 138 191 130 183)(123 176 200 139 192 131 184)(124 169 193 140 185 132 177)(125 170 194 141 186 133 178)(126 171 195 142 187 134 179)(127 172 196 143 188 135 180)(128 173 197 144 189 136 181)
(1 170 38 146)(2 147 39 171)(3 172 40 148)(4 149 33 173)(5 174 34 150)(6 151 35 175)(7 176 36 152)(8 145 37 169)(9 62 117 197)(10 198 118 63)(11 64 119 199)(12 200 120 57)(13 58 113 193)(14 194 114 59)(15 60 115 195)(16 196 116 61)(17 159 43 183)(18 184 44 160)(19 153 45 177)(20 178 46 154)(21 155 47 179)(22 180 48 156)(23 157 41 181)(24 182 42 158)(25 167 51 191)(26 192 52 168)(27 161 53 185)(28 186 54 162)(29 163 55 187)(30 188 56 164)(31 165 49 189)(32 190 50 166)(65 121 91 203)(66 204 92 122)(67 123 93 205)(68 206 94 124)(69 125 95 207)(70 208 96 126)(71 127 89 201)(72 202 90 128)(73 129 99 211)(74 212 100 130)(75 131 101 213)(76 214 102 132)(77 133 103 215)(78 216 104 134)(79 135 97 209)(80 210 98 136)(81 137 107 219)(82 220 108 138)(83 139 109 221)(84 222 110 140)(85 141 111 223)(86 224 112 142)(87 143 105 217)(88 218 106 144)
(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)
(2 4)(3 7)(6 8)(9 15)(11 13)(12 16)(17 19)(18 22)(21 23)(25 27)(26 30)(29 31)(33 39)(35 37)(36 40)(41 47)(43 45)(44 48)(49 55)(51 53)(52 56)(57 196)(58 199)(59 194)(60 197)(61 200)(62 195)(63 198)(64 193)(66 68)(67 71)(70 72)(74 76)(75 79)(78 80)(82 84)(83 87)(86 88)(89 93)(90 96)(92 94)(97 101)(98 104)(100 102)(105 109)(106 112)(108 110)(113 119)(115 117)(116 120)(121 203)(122 206)(123 201)(124 204)(125 207)(126 202)(127 205)(128 208)(129 211)(130 214)(131 209)(132 212)(133 215)(134 210)(135 213)(136 216)(137 219)(138 222)(139 217)(140 220)(141 223)(142 218)(143 221)(144 224)(145 175)(146 170)(147 173)(148 176)(149 171)(150 174)(151 169)(152 172)(153 183)(154 178)(155 181)(156 184)(157 179)(158 182)(159 177)(160 180)(161 191)(162 186)(163 189)(164 192)(165 187)(166 190)(167 185)(168 188)
G:=sub<Sym(224)| (1,14,85,28,77,20,69)(2,15,86,29,78,21,70)(3,16,87,30,79,22,71)(4,9,88,31,80,23,72)(5,10,81,32,73,24,65)(6,11,82,25,74,17,66)(7,12,83,26,75,18,67)(8,13,84,27,76,19,68)(33,117,106,49,98,41,90)(34,118,107,50,99,42,91)(35,119,108,51,100,43,92)(36,120,109,52,101,44,93)(37,113,110,53,102,45,94)(38,114,111,54,103,46,95)(39,115,112,55,104,47,96)(40,116,105,56,97,48,89)(57,221,168,213,160,205,152)(58,222,161,214,153,206,145)(59,223,162,215,154,207,146)(60,224,163,216,155,208,147)(61,217,164,209,156,201,148)(62,218,165,210,157,202,149)(63,219,166,211,158,203,150)(64,220,167,212,159,204,151)(121,174,198,137,190,129,182)(122,175,199,138,191,130,183)(123,176,200,139,192,131,184)(124,169,193,140,185,132,177)(125,170,194,141,186,133,178)(126,171,195,142,187,134,179)(127,172,196,143,188,135,180)(128,173,197,144,189,136,181), (1,170,38,146)(2,147,39,171)(3,172,40,148)(4,149,33,173)(5,174,34,150)(6,151,35,175)(7,176,36,152)(8,145,37,169)(9,62,117,197)(10,198,118,63)(11,64,119,199)(12,200,120,57)(13,58,113,193)(14,194,114,59)(15,60,115,195)(16,196,116,61)(17,159,43,183)(18,184,44,160)(19,153,45,177)(20,178,46,154)(21,155,47,179)(22,180,48,156)(23,157,41,181)(24,182,42,158)(25,167,51,191)(26,192,52,168)(27,161,53,185)(28,186,54,162)(29,163,55,187)(30,188,56,164)(31,165,49,189)(32,190,50,166)(65,121,91,203)(66,204,92,122)(67,123,93,205)(68,206,94,124)(69,125,95,207)(70,208,96,126)(71,127,89,201)(72,202,90,128)(73,129,99,211)(74,212,100,130)(75,131,101,213)(76,214,102,132)(77,133,103,215)(78,216,104,134)(79,135,97,209)(80,210,98,136)(81,137,107,219)(82,220,108,138)(83,139,109,221)(84,222,110,140)(85,141,111,223)(86,224,112,142)(87,143,105,217)(88,218,106,144), (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), (2,4)(3,7)(6,8)(9,15)(11,13)(12,16)(17,19)(18,22)(21,23)(25,27)(26,30)(29,31)(33,39)(35,37)(36,40)(41,47)(43,45)(44,48)(49,55)(51,53)(52,56)(57,196)(58,199)(59,194)(60,197)(61,200)(62,195)(63,198)(64,193)(66,68)(67,71)(70,72)(74,76)(75,79)(78,80)(82,84)(83,87)(86,88)(89,93)(90,96)(92,94)(97,101)(98,104)(100,102)(105,109)(106,112)(108,110)(113,119)(115,117)(116,120)(121,203)(122,206)(123,201)(124,204)(125,207)(126,202)(127,205)(128,208)(129,211)(130,214)(131,209)(132,212)(133,215)(134,210)(135,213)(136,216)(137,219)(138,222)(139,217)(140,220)(141,223)(142,218)(143,221)(144,224)(145,175)(146,170)(147,173)(148,176)(149,171)(150,174)(151,169)(152,172)(153,183)(154,178)(155,181)(156,184)(157,179)(158,182)(159,177)(160,180)(161,191)(162,186)(163,189)(164,192)(165,187)(166,190)(167,185)(168,188)>;
G:=Group( (1,14,85,28,77,20,69)(2,15,86,29,78,21,70)(3,16,87,30,79,22,71)(4,9,88,31,80,23,72)(5,10,81,32,73,24,65)(6,11,82,25,74,17,66)(7,12,83,26,75,18,67)(8,13,84,27,76,19,68)(33,117,106,49,98,41,90)(34,118,107,50,99,42,91)(35,119,108,51,100,43,92)(36,120,109,52,101,44,93)(37,113,110,53,102,45,94)(38,114,111,54,103,46,95)(39,115,112,55,104,47,96)(40,116,105,56,97,48,89)(57,221,168,213,160,205,152)(58,222,161,214,153,206,145)(59,223,162,215,154,207,146)(60,224,163,216,155,208,147)(61,217,164,209,156,201,148)(62,218,165,210,157,202,149)(63,219,166,211,158,203,150)(64,220,167,212,159,204,151)(121,174,198,137,190,129,182)(122,175,199,138,191,130,183)(123,176,200,139,192,131,184)(124,169,193,140,185,132,177)(125,170,194,141,186,133,178)(126,171,195,142,187,134,179)(127,172,196,143,188,135,180)(128,173,197,144,189,136,181), (1,170,38,146)(2,147,39,171)(3,172,40,148)(4,149,33,173)(5,174,34,150)(6,151,35,175)(7,176,36,152)(8,145,37,169)(9,62,117,197)(10,198,118,63)(11,64,119,199)(12,200,120,57)(13,58,113,193)(14,194,114,59)(15,60,115,195)(16,196,116,61)(17,159,43,183)(18,184,44,160)(19,153,45,177)(20,178,46,154)(21,155,47,179)(22,180,48,156)(23,157,41,181)(24,182,42,158)(25,167,51,191)(26,192,52,168)(27,161,53,185)(28,186,54,162)(29,163,55,187)(30,188,56,164)(31,165,49,189)(32,190,50,166)(65,121,91,203)(66,204,92,122)(67,123,93,205)(68,206,94,124)(69,125,95,207)(70,208,96,126)(71,127,89,201)(72,202,90,128)(73,129,99,211)(74,212,100,130)(75,131,101,213)(76,214,102,132)(77,133,103,215)(78,216,104,134)(79,135,97,209)(80,210,98,136)(81,137,107,219)(82,220,108,138)(83,139,109,221)(84,222,110,140)(85,141,111,223)(86,224,112,142)(87,143,105,217)(88,218,106,144), (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), (2,4)(3,7)(6,8)(9,15)(11,13)(12,16)(17,19)(18,22)(21,23)(25,27)(26,30)(29,31)(33,39)(35,37)(36,40)(41,47)(43,45)(44,48)(49,55)(51,53)(52,56)(57,196)(58,199)(59,194)(60,197)(61,200)(62,195)(63,198)(64,193)(66,68)(67,71)(70,72)(74,76)(75,79)(78,80)(82,84)(83,87)(86,88)(89,93)(90,96)(92,94)(97,101)(98,104)(100,102)(105,109)(106,112)(108,110)(113,119)(115,117)(116,120)(121,203)(122,206)(123,201)(124,204)(125,207)(126,202)(127,205)(128,208)(129,211)(130,214)(131,209)(132,212)(133,215)(134,210)(135,213)(136,216)(137,219)(138,222)(139,217)(140,220)(141,223)(142,218)(143,221)(144,224)(145,175)(146,170)(147,173)(148,176)(149,171)(150,174)(151,169)(152,172)(153,183)(154,178)(155,181)(156,184)(157,179)(158,182)(159,177)(160,180)(161,191)(162,186)(163,189)(164,192)(165,187)(166,190)(167,185)(168,188) );
G=PermutationGroup([[(1,14,85,28,77,20,69),(2,15,86,29,78,21,70),(3,16,87,30,79,22,71),(4,9,88,31,80,23,72),(5,10,81,32,73,24,65),(6,11,82,25,74,17,66),(7,12,83,26,75,18,67),(8,13,84,27,76,19,68),(33,117,106,49,98,41,90),(34,118,107,50,99,42,91),(35,119,108,51,100,43,92),(36,120,109,52,101,44,93),(37,113,110,53,102,45,94),(38,114,111,54,103,46,95),(39,115,112,55,104,47,96),(40,116,105,56,97,48,89),(57,221,168,213,160,205,152),(58,222,161,214,153,206,145),(59,223,162,215,154,207,146),(60,224,163,216,155,208,147),(61,217,164,209,156,201,148),(62,218,165,210,157,202,149),(63,219,166,211,158,203,150),(64,220,167,212,159,204,151),(121,174,198,137,190,129,182),(122,175,199,138,191,130,183),(123,176,200,139,192,131,184),(124,169,193,140,185,132,177),(125,170,194,141,186,133,178),(126,171,195,142,187,134,179),(127,172,196,143,188,135,180),(128,173,197,144,189,136,181)], [(1,170,38,146),(2,147,39,171),(3,172,40,148),(4,149,33,173),(5,174,34,150),(6,151,35,175),(7,176,36,152),(8,145,37,169),(9,62,117,197),(10,198,118,63),(11,64,119,199),(12,200,120,57),(13,58,113,193),(14,194,114,59),(15,60,115,195),(16,196,116,61),(17,159,43,183),(18,184,44,160),(19,153,45,177),(20,178,46,154),(21,155,47,179),(22,180,48,156),(23,157,41,181),(24,182,42,158),(25,167,51,191),(26,192,52,168),(27,161,53,185),(28,186,54,162),(29,163,55,187),(30,188,56,164),(31,165,49,189),(32,190,50,166),(65,121,91,203),(66,204,92,122),(67,123,93,205),(68,206,94,124),(69,125,95,207),(70,208,96,126),(71,127,89,201),(72,202,90,128),(73,129,99,211),(74,212,100,130),(75,131,101,213),(76,214,102,132),(77,133,103,215),(78,216,104,134),(79,135,97,209),(80,210,98,136),(81,137,107,219),(82,220,108,138),(83,139,109,221),(84,222,110,140),(85,141,111,223),(86,224,112,142),(87,143,105,217),(88,218,106,144)], [(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)], [(2,4),(3,7),(6,8),(9,15),(11,13),(12,16),(17,19),(18,22),(21,23),(25,27),(26,30),(29,31),(33,39),(35,37),(36,40),(41,47),(43,45),(44,48),(49,55),(51,53),(52,56),(57,196),(58,199),(59,194),(60,197),(61,200),(62,195),(63,198),(64,193),(66,68),(67,71),(70,72),(74,76),(75,79),(78,80),(82,84),(83,87),(86,88),(89,93),(90,96),(92,94),(97,101),(98,104),(100,102),(105,109),(106,112),(108,110),(113,119),(115,117),(116,120),(121,203),(122,206),(123,201),(124,204),(125,207),(126,202),(127,205),(128,208),(129,211),(130,214),(131,209),(132,212),(133,215),(134,210),(135,213),(136,216),(137,219),(138,222),(139,217),(140,220),(141,223),(142,218),(143,221),(144,224),(145,175),(146,170),(147,173),(148,176),(149,171),(150,174),(151,169),(152,172),(153,183),(154,178),(155,181),(156,184),(157,179),(158,182),(159,177),(160,180),(161,191),(162,186),(163,189),(164,192),(165,187),(166,190),(167,185),(168,188)]])
133 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14AD | 28A | ··· | 28X | 28Y | ··· | 28BB | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 8 | ··· | 8 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | |||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | SD16 | C4○D4 | C7×D4 | C7×D4 | C7×SD16 | C7×C4○D4 | C8⋊C22 | C7×C8⋊C22 |
| kernel | C7×C4⋊SD16 | C7×D4⋊C4 | C7×C4⋊C8 | Q8×C28 | C7×C4⋊1D4 | C14×SD16 | C4⋊SD16 | D4⋊C4 | C4⋊C8 | C4×Q8 | C4⋊1D4 | C2×SD16 | C2×C28 | C7×Q8 | C28 | C28 | C2×C4 | Q8 | C4 | C4 | C14 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 6 | 12 | 6 | 6 | 6 | 12 | 2 | 2 | 4 | 2 | 12 | 12 | 24 | 12 | 1 | 6 |
Matrix representation of C7×C4⋊SD16 ►in GL4(𝔽113) generated by
| 109 | 0 | 0 | 0 |
| 0 | 109 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 96 | 109 | 0 | 0 |
| 16 | 17 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 |
| 48 | 112 | 0 | 0 |
| 0 | 0 | 100 | 13 |
| 0 | 0 | 100 | 100 |
| 1 | 0 | 0 | 0 |
| 48 | 112 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
G:=sub<GL(4,GF(113))| [109,0,0,0,0,109,0,0,0,0,28,0,0,0,0,28],[96,16,0,0,109,17,0,0,0,0,112,0,0,0,0,112],[1,48,0,0,0,112,0,0,0,0,100,100,0,0,13,100],[1,48,0,0,0,112,0,0,0,0,0,1,0,0,1,0] >;
C7×C4⋊SD16 in GAP, Magma, Sage, TeX
C_7\times C_4\rtimes {\rm SD}_{16} % in TeX
G:=Group("C7xC4:SD16"); // GroupNames label
G:=SmallGroup(448,868);
// by ID
G=gap.SmallGroup(448,868);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,813,400,2438,1192,14117,3547,124]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^4=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^3>;
// generators/relations