metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic7.5M4(2), (C2×Dic7)⋊3C8, C22⋊C8.9D7, C22.6(C8×D7), Dic7⋊C8⋊15C2, (C8×Dic7)⋊13C2, (C2×C8).192D14, C14.5(C22×C8), Dic7.8(C2×C8), C23.44(C4×D7), C2.3(D7×M4(2)), (C4×Dic7).17C4, C28.294(C4○D4), (C2×C56).167C22, (C2×C28).816C23, C7⋊2(C42.12C4), (C22×C4).300D14, C14.19(C2×M4(2)), C4.120(D4⋊2D7), (C22×Dic7).7C4, C28.55D4.13C2, C14.20(C42⋊C2), (C22×C28).334C22, (C4×Dic7).300C22, C2.3(C23.11D14), C2.7(D7×C2×C8), (C2×C14).4(C2×C8), C22.42(C2×C4×D7), (C2×C4).129(C4×D7), (C7×C22⋊C8).9C2, (C2×C4×Dic7).29C2, (C2×C28).150(C2×C4), (C2×C7⋊C8).298C22, (C22×C14).34(C2×C4), (C2×C14).71(C22×C4), (C2×C4).758(C22×D7), (C2×Dic7).108(C2×C4), SmallGroup(448,252)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic7.5M4(2)
G = < a,b,c,d | a14=c8=d2=1, b2=a7, bab-1=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd=a7c5 >
Subgroups: 380 in 118 conjugacy classes, 61 normal (33 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C23, C14, C14, C42, C2×C8, C2×C8, C22×C4, C22×C4, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C4×C8, C22⋊C8, C22⋊C8, C4⋊C8, C2×C42, C7⋊C8, C56, C2×Dic7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C42.12C4, C2×C7⋊C8, C4×Dic7, C2×C56, C22×Dic7, C22×C28, C8×Dic7, Dic7⋊C8, C28.55D4, C7×C22⋊C8, C2×C4×Dic7, Dic7.5M4(2)
Quotients: C1, C2, C4, C22, C8, C2×C4, C23, D7, C2×C8, M4(2), C22×C4, C4○D4, D14, C42⋊C2, C22×C8, C2×M4(2), C4×D7, C22×D7, C42.12C4, C8×D7, C2×C4×D7, D4⋊2D7, C23.11D14, D7×C2×C8, D7×M4(2), Dic7.5M4(2)
►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 24 8 17)(2 23 9 16)(3 22 10 15)(4 21 11 28)(5 20 12 27)(6 19 13 26)(7 18 14 25)(29 160 36 167)(30 159 37 166)(31 158 38 165)(32 157 39 164)(33 156 40 163)(34 155 41 162)(35 168 42 161)(43 62 50 69)(44 61 51 68)(45 60 52 67)(46 59 53 66)(47 58 54 65)(48 57 55 64)(49 70 56 63)(71 205 78 198)(72 204 79 197)(73 203 80 210)(74 202 81 209)(75 201 82 208)(76 200 83 207)(77 199 84 206)(85 127 92 134)(86 140 93 133)(87 139 94 132)(88 138 95 131)(89 137 96 130)(90 136 97 129)(91 135 98 128)(99 153 106 146)(100 152 107 145)(101 151 108 144)(102 150 109 143)(103 149 110 142)(104 148 111 141)(105 147 112 154)(113 189 120 196)(114 188 121 195)(115 187 122 194)(116 186 123 193)(117 185 124 192)(118 184 125 191)(119 183 126 190)(169 220 176 213)(170 219 177 212)(171 218 178 211)(172 217 179 224)(173 216 180 223)(174 215 181 222)(175 214 182 221)
(1 156 204 102 184 180 127 55)(2 157 205 103 185 181 128 56)(3 158 206 104 186 182 129 43)(4 159 207 105 187 169 130 44)(5 160 208 106 188 170 131 45)(6 161 209 107 189 171 132 46)(7 162 210 108 190 172 133 47)(8 163 197 109 191 173 134 48)(9 164 198 110 192 174 135 49)(10 165 199 111 193 175 136 50)(11 166 200 112 194 176 137 51)(12 167 201 99 195 177 138 52)(13 168 202 100 196 178 139 53)(14 155 203 101 183 179 140 54)(15 31 84 141 116 214 97 69)(16 32 71 142 117 215 98 70)(17 33 72 143 118 216 85 57)(18 34 73 144 119 217 86 58)(19 35 74 145 120 218 87 59)(20 36 75 146 121 219 88 60)(21 37 76 147 122 220 89 61)(22 38 77 148 123 221 90 62)(23 39 78 149 124 222 91 63)(24 40 79 150 125 223 92 64)(25 41 80 151 126 224 93 65)(26 42 81 152 113 211 94 66)(27 29 82 153 114 212 95 67)(28 30 83 154 115 213 96 68)
(1 184)(2 185)(3 186)(4 187)(5 188)(6 189)(7 190)(8 191)(9 192)(10 193)(11 194)(12 195)(13 196)(14 183)(15 116)(16 117)(17 118)(18 119)(19 120)(20 121)(21 122)(22 123)(23 124)(24 125)(25 126)(26 113)(27 114)(28 115)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(71 98)(72 85)(73 86)(74 87)(75 88)(76 89)(77 90)(78 91)(79 92)(80 93)(81 94)(82 95)(83 96)(84 97)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)(127 204)(128 205)(129 206)(130 207)(131 208)(132 209)(133 210)(134 197)(135 198)(136 199)(137 200)(138 201)(139 202)(140 203)(141 148)(142 149)(143 150)(144 151)(145 152)(146 153)(147 154)(155 162)(156 163)(157 164)(158 165)(159 166)(160 167)(161 168)(169 176)(170 177)(171 178)(172 179)(173 180)(174 181)(175 182)(211 218)(212 219)(213 220)(214 221)(215 222)(216 223)(217 224)
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), (1,24,8,17)(2,23,9,16)(3,22,10,15)(4,21,11,28)(5,20,12,27)(6,19,13,26)(7,18,14,25)(29,160,36,167)(30,159,37,166)(31,158,38,165)(32,157,39,164)(33,156,40,163)(34,155,41,162)(35,168,42,161)(43,62,50,69)(44,61,51,68)(45,60,52,67)(46,59,53,66)(47,58,54,65)(48,57,55,64)(49,70,56,63)(71,205,78,198)(72,204,79,197)(73,203,80,210)(74,202,81,209)(75,201,82,208)(76,200,83,207)(77,199,84,206)(85,127,92,134)(86,140,93,133)(87,139,94,132)(88,138,95,131)(89,137,96,130)(90,136,97,129)(91,135,98,128)(99,153,106,146)(100,152,107,145)(101,151,108,144)(102,150,109,143)(103,149,110,142)(104,148,111,141)(105,147,112,154)(113,189,120,196)(114,188,121,195)(115,187,122,194)(116,186,123,193)(117,185,124,192)(118,184,125,191)(119,183,126,190)(169,220,176,213)(170,219,177,212)(171,218,178,211)(172,217,179,224)(173,216,180,223)(174,215,181,222)(175,214,182,221), (1,156,204,102,184,180,127,55)(2,157,205,103,185,181,128,56)(3,158,206,104,186,182,129,43)(4,159,207,105,187,169,130,44)(5,160,208,106,188,170,131,45)(6,161,209,107,189,171,132,46)(7,162,210,108,190,172,133,47)(8,163,197,109,191,173,134,48)(9,164,198,110,192,174,135,49)(10,165,199,111,193,175,136,50)(11,166,200,112,194,176,137,51)(12,167,201,99,195,177,138,52)(13,168,202,100,196,178,139,53)(14,155,203,101,183,179,140,54)(15,31,84,141,116,214,97,69)(16,32,71,142,117,215,98,70)(17,33,72,143,118,216,85,57)(18,34,73,144,119,217,86,58)(19,35,74,145,120,218,87,59)(20,36,75,146,121,219,88,60)(21,37,76,147,122,220,89,61)(22,38,77,148,123,221,90,62)(23,39,78,149,124,222,91,63)(24,40,79,150,125,223,92,64)(25,41,80,151,126,224,93,65)(26,42,81,152,113,211,94,66)(27,29,82,153,114,212,95,67)(28,30,83,154,115,213,96,68), (1,184)(2,185)(3,186)(4,187)(5,188)(6,189)(7,190)(8,191)(9,192)(10,193)(11,194)(12,195)(13,196)(14,183)(15,116)(16,117)(17,118)(18,119)(19,120)(20,121)(21,122)(22,123)(23,124)(24,125)(25,126)(26,113)(27,114)(28,115)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,98)(72,85)(73,86)(74,87)(75,88)(76,89)(77,90)(78,91)(79,92)(80,93)(81,94)(82,95)(83,96)(84,97)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)(147,154)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224)>;
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), (1,24,8,17)(2,23,9,16)(3,22,10,15)(4,21,11,28)(5,20,12,27)(6,19,13,26)(7,18,14,25)(29,160,36,167)(30,159,37,166)(31,158,38,165)(32,157,39,164)(33,156,40,163)(34,155,41,162)(35,168,42,161)(43,62,50,69)(44,61,51,68)(45,60,52,67)(46,59,53,66)(47,58,54,65)(48,57,55,64)(49,70,56,63)(71,205,78,198)(72,204,79,197)(73,203,80,210)(74,202,81,209)(75,201,82,208)(76,200,83,207)(77,199,84,206)(85,127,92,134)(86,140,93,133)(87,139,94,132)(88,138,95,131)(89,137,96,130)(90,136,97,129)(91,135,98,128)(99,153,106,146)(100,152,107,145)(101,151,108,144)(102,150,109,143)(103,149,110,142)(104,148,111,141)(105,147,112,154)(113,189,120,196)(114,188,121,195)(115,187,122,194)(116,186,123,193)(117,185,124,192)(118,184,125,191)(119,183,126,190)(169,220,176,213)(170,219,177,212)(171,218,178,211)(172,217,179,224)(173,216,180,223)(174,215,181,222)(175,214,182,221), (1,156,204,102,184,180,127,55)(2,157,205,103,185,181,128,56)(3,158,206,104,186,182,129,43)(4,159,207,105,187,169,130,44)(5,160,208,106,188,170,131,45)(6,161,209,107,189,171,132,46)(7,162,210,108,190,172,133,47)(8,163,197,109,191,173,134,48)(9,164,198,110,192,174,135,49)(10,165,199,111,193,175,136,50)(11,166,200,112,194,176,137,51)(12,167,201,99,195,177,138,52)(13,168,202,100,196,178,139,53)(14,155,203,101,183,179,140,54)(15,31,84,141,116,214,97,69)(16,32,71,142,117,215,98,70)(17,33,72,143,118,216,85,57)(18,34,73,144,119,217,86,58)(19,35,74,145,120,218,87,59)(20,36,75,146,121,219,88,60)(21,37,76,147,122,220,89,61)(22,38,77,148,123,221,90,62)(23,39,78,149,124,222,91,63)(24,40,79,150,125,223,92,64)(25,41,80,151,126,224,93,65)(26,42,81,152,113,211,94,66)(27,29,82,153,114,212,95,67)(28,30,83,154,115,213,96,68), (1,184)(2,185)(3,186)(4,187)(5,188)(6,189)(7,190)(8,191)(9,192)(10,193)(11,194)(12,195)(13,196)(14,183)(15,116)(16,117)(17,118)(18,119)(19,120)(20,121)(21,122)(22,123)(23,124)(24,125)(25,126)(26,113)(27,114)(28,115)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,98)(72,85)(73,86)(74,87)(75,88)(76,89)(77,90)(78,91)(79,92)(80,93)(81,94)(82,95)(83,96)(84,97)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)(147,154)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224) );
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)], [(1,24,8,17),(2,23,9,16),(3,22,10,15),(4,21,11,28),(5,20,12,27),(6,19,13,26),(7,18,14,25),(29,160,36,167),(30,159,37,166),(31,158,38,165),(32,157,39,164),(33,156,40,163),(34,155,41,162),(35,168,42,161),(43,62,50,69),(44,61,51,68),(45,60,52,67),(46,59,53,66),(47,58,54,65),(48,57,55,64),(49,70,56,63),(71,205,78,198),(72,204,79,197),(73,203,80,210),(74,202,81,209),(75,201,82,208),(76,200,83,207),(77,199,84,206),(85,127,92,134),(86,140,93,133),(87,139,94,132),(88,138,95,131),(89,137,96,130),(90,136,97,129),(91,135,98,128),(99,153,106,146),(100,152,107,145),(101,151,108,144),(102,150,109,143),(103,149,110,142),(104,148,111,141),(105,147,112,154),(113,189,120,196),(114,188,121,195),(115,187,122,194),(116,186,123,193),(117,185,124,192),(118,184,125,191),(119,183,126,190),(169,220,176,213),(170,219,177,212),(171,218,178,211),(172,217,179,224),(173,216,180,223),(174,215,181,222),(175,214,182,221)], [(1,156,204,102,184,180,127,55),(2,157,205,103,185,181,128,56),(3,158,206,104,186,182,129,43),(4,159,207,105,187,169,130,44),(5,160,208,106,188,170,131,45),(6,161,209,107,189,171,132,46),(7,162,210,108,190,172,133,47),(8,163,197,109,191,173,134,48),(9,164,198,110,192,174,135,49),(10,165,199,111,193,175,136,50),(11,166,200,112,194,176,137,51),(12,167,201,99,195,177,138,52),(13,168,202,100,196,178,139,53),(14,155,203,101,183,179,140,54),(15,31,84,141,116,214,97,69),(16,32,71,142,117,215,98,70),(17,33,72,143,118,216,85,57),(18,34,73,144,119,217,86,58),(19,35,74,145,120,218,87,59),(20,36,75,146,121,219,88,60),(21,37,76,147,122,220,89,61),(22,38,77,148,123,221,90,62),(23,39,78,149,124,222,91,63),(24,40,79,150,125,223,92,64),(25,41,80,151,126,224,93,65),(26,42,81,152,113,211,94,66),(27,29,82,153,114,212,95,67),(28,30,83,154,115,213,96,68)], [(1,184),(2,185),(3,186),(4,187),(5,188),(6,189),(7,190),(8,191),(9,192),(10,193),(11,194),(12,195),(13,196),(14,183),(15,116),(16,117),(17,118),(18,119),(19,120),(20,121),(21,122),(22,123),(23,124),(24,125),(25,126),(26,113),(27,114),(28,115),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(71,98),(72,85),(73,86),(74,87),(75,88),(76,89),(77,90),(78,91),(79,92),(80,93),(81,94),(82,95),(83,96),(84,97),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112),(127,204),(128,205),(129,206),(130,207),(131,208),(132,209),(133,210),(134,197),(135,198),(136,199),(137,200),(138,201),(139,202),(140,203),(141,148),(142,149),(143,150),(144,151),(145,152),(146,153),(147,154),(155,162),(156,163),(157,164),(158,165),(159,166),(160,167),(161,168),(169,176),(170,177),(171,178),(172,179),(173,180),(174,181),(175,182),(211,218),(212,219),(213,220),(214,221),(215,222),(216,223),(217,224)]])
100 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4N | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 8A | ··· | 8H | 8I | ··· | 8P | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 7 | ··· | 7 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
100 irreducible representations
| dim | 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 | C4 | C4 | C8 | D7 | M4(2) | C4○D4 | D14 | D14 | C4×D7 | C4×D7 | C8×D7 | D4⋊2D7 | D7×M4(2) |
| kernel | Dic7.5M4(2) | C8×Dic7 | Dic7⋊C8 | C28.55D4 | C7×C22⋊C8 | C2×C4×Dic7 | C4×Dic7 | C22×Dic7 | C2×Dic7 | C22⋊C8 | Dic7 | C28 | C2×C8 | C22×C4 | C2×C4 | C23 | C22 | C4 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 4 | 4 | 16 | 3 | 4 | 4 | 6 | 3 | 6 | 6 | 24 | 6 | 6 |
Matrix representation of Dic7.5M4(2) ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 104 | 112 |
| 0 | 0 | 1 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 42 | 63 |
| 0 | 0 | 24 | 71 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 95 | 0 |
| 0 | 0 | 0 | 95 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,104,1,0,0,112,0],[98,0,0,0,0,98,0,0,0,0,42,24,0,0,63,71],[0,1,0,0,1,0,0,0,0,0,95,0,0,0,0,95],[1,0,0,0,0,112,0,0,0,0,112,0,0,0,0,112] >;
Dic7.5M4(2) in GAP, Magma, Sage, TeX
{\rm Dic}_7._5M_4(2) % in TeX
G:=Group("Dic7.5M4(2)"); // GroupNames label
G:=SmallGroup(448,252);
// by ID
G=gap.SmallGroup(448,252);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=c^8=d^2=1,b^2=a^7,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=a^7*c^5>;
// generators/relations