direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4.12D28, M4(2).32D14, (C2×C4).53D28, C4.67(C2×D28), (C2×C28).176D4, C28.422(C2×D4), C23.56(C4×D7), C4.29(D14⋊C4), C14⋊1(C4.10D4), C28.54(C22⋊C4), (C2×C28).418C23, (C2×Dic14).15C4, (C22×C4).144D14, (C2×M4(2)).17D7, (C22×Dic7).5C4, C22.51(D14⋊C4), (C14×M4(2)).28C2, C4.Dic7.43C22, (C22×C28).191C22, (C22×Dic14).15C2, (C7×M4(2)).35C22, (C2×Dic14).279C22, (C2×C4).55(C4×D7), C7⋊2(C2×C4.10D4), C22.22(C2×C4×D7), C2.33(C2×D14⋊C4), C4.115(C2×C7⋊D4), (C2×C28).111(C2×C4), C14.61(C2×C22⋊C4), (C2×Dic7).6(C2×C4), (C2×C4).257(C7⋊D4), (C22×C14).72(C2×C4), (C2×C14).16(C22×C4), (C2×C4).122(C22×D7), (C2×C4.Dic7).26C2, (C2×C14).67(C22⋊C4), SmallGroup(448,670)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C4.12D28
G = < a,b,c,d | a2=b28=1, c4=d2=b14, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b21c3 >
Subgroups: 612 in 146 conjugacy classes, 63 normal (39 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C2×C8, M4(2), M4(2), C22×C4, C22×C4, C2×Q8, Dic7, C28, C2×C14, C2×C14, C4.10D4, C2×M4(2), C2×M4(2), C22×Q8, C7⋊C8, C56, Dic14, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C2×C4.10D4, C2×C7⋊C8, C4.Dic7, C4.Dic7, C2×C56, C7×M4(2), C7×M4(2), C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C4.12D28, C2×C4.Dic7, C14×M4(2), C22×Dic14, C2×C4.12D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C4.10D4, C2×C22⋊C4, C4×D7, D28, C7⋊D4, C22×D7, C2×C4.10D4, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C4.12D28, C2×D14⋊C4, C2×C4.12D28
►On 224 points
Generators in S224
(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)(14 169)(15 170)(16 171)(17 172)(18 173)(19 174)(20 175)(21 176)(22 177)(23 178)(24 179)(25 180)(26 181)(27 182)(28 183)(29 155)(30 156)(31 157)(32 158)(33 159)(34 160)(35 161)(36 162)(37 163)(38 164)(39 165)(40 166)(41 167)(42 168)(43 141)(44 142)(45 143)(46 144)(47 145)(48 146)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 153)(56 154)(57 104)(58 105)(59 106)(60 107)(61 108)(62 109)(63 110)(64 111)(65 112)(66 85)(67 86)(68 87)(69 88)(70 89)(71 90)(72 91)(73 92)(74 93)(75 94)(76 95)(77 96)(78 97)(79 98)(80 99)(81 100)(82 101)(83 102)(84 103)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)(121 197)(122 198)(123 199)(124 200)(125 201)(126 202)(127 203)(128 204)(129 205)(130 206)(131 207)(132 208)(133 209)(134 210)(135 211)(136 212)(137 213)(138 214)(139 215)(140 216)
(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)
(1 118 177 201 15 132 191 215)(2 117 178 200 16 131 192 214)(3 116 179 199 17 130 193 213)(4 115 180 198 18 129 194 212)(5 114 181 197 19 128 195 211)(6 113 182 224 20 127 196 210)(7 140 183 223 21 126 169 209)(8 139 184 222 22 125 170 208)(9 138 185 221 23 124 171 207)(10 137 186 220 24 123 172 206)(11 136 187 219 25 122 173 205)(12 135 188 218 26 121 174 204)(13 134 189 217 27 120 175 203)(14 133 190 216 28 119 176 202)(29 92 162 66 43 106 148 80)(30 91 163 65 44 105 149 79)(31 90 164 64 45 104 150 78)(32 89 165 63 46 103 151 77)(33 88 166 62 47 102 152 76)(34 87 167 61 48 101 153 75)(35 86 168 60 49 100 154 74)(36 85 141 59 50 99 155 73)(37 112 142 58 51 98 156 72)(38 111 143 57 52 97 157 71)(39 110 144 84 53 96 158 70)(40 109 145 83 54 95 159 69)(41 108 146 82 55 94 160 68)(42 107 147 81 56 93 161 67)
(1 80 15 66)(2 79 16 65)(3 78 17 64)(4 77 18 63)(5 76 19 62)(6 75 20 61)(7 74 21 60)(8 73 22 59)(9 72 23 58)(10 71 24 57)(11 70 25 84)(12 69 26 83)(13 68 27 82)(14 67 28 81)(29 222 43 208)(30 221 44 207)(31 220 45 206)(32 219 46 205)(33 218 47 204)(34 217 48 203)(35 216 49 202)(36 215 50 201)(37 214 51 200)(38 213 52 199)(39 212 53 198)(40 211 54 197)(41 210 55 224)(42 209 56 223)(85 184 99 170)(86 183 100 169)(87 182 101 196)(88 181 102 195)(89 180 103 194)(90 179 104 193)(91 178 105 192)(92 177 106 191)(93 176 107 190)(94 175 108 189)(95 174 109 188)(96 173 110 187)(97 172 111 186)(98 171 112 185)(113 146 127 160)(114 145 128 159)(115 144 129 158)(116 143 130 157)(117 142 131 156)(118 141 132 155)(119 168 133 154)(120 167 134 153)(121 166 135 152)(122 165 136 151)(123 164 137 150)(124 163 138 149)(125 162 139 148)(126 161 140 147)
G:=sub<Sym(224)| (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)(14,169)(15,170)(16,171)(17,172)(18,173)(19,174)(20,175)(21,176)(22,177)(23,178)(24,179)(25,180)(26,181)(27,182)(28,183)(29,155)(30,156)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,163)(38,164)(39,165)(40,166)(41,167)(42,168)(43,141)(44,142)(45,143)(46,144)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,104)(58,105)(59,106)(60,107)(61,108)(62,109)(63,110)(64,111)(65,112)(66,85)(67,86)(68,87)(69,88)(70,89)(71,90)(72,91)(73,92)(74,93)(75,94)(76,95)(77,96)(78,97)(79,98)(80,99)(81,100)(82,101)(83,102)(84,103)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,197)(122,198)(123,199)(124,200)(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)(132,208)(133,209)(134,210)(135,211)(136,212)(137,213)(138,214)(139,215)(140,216), (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), (1,118,177,201,15,132,191,215)(2,117,178,200,16,131,192,214)(3,116,179,199,17,130,193,213)(4,115,180,198,18,129,194,212)(5,114,181,197,19,128,195,211)(6,113,182,224,20,127,196,210)(7,140,183,223,21,126,169,209)(8,139,184,222,22,125,170,208)(9,138,185,221,23,124,171,207)(10,137,186,220,24,123,172,206)(11,136,187,219,25,122,173,205)(12,135,188,218,26,121,174,204)(13,134,189,217,27,120,175,203)(14,133,190,216,28,119,176,202)(29,92,162,66,43,106,148,80)(30,91,163,65,44,105,149,79)(31,90,164,64,45,104,150,78)(32,89,165,63,46,103,151,77)(33,88,166,62,47,102,152,76)(34,87,167,61,48,101,153,75)(35,86,168,60,49,100,154,74)(36,85,141,59,50,99,155,73)(37,112,142,58,51,98,156,72)(38,111,143,57,52,97,157,71)(39,110,144,84,53,96,158,70)(40,109,145,83,54,95,159,69)(41,108,146,82,55,94,160,68)(42,107,147,81,56,93,161,67), (1,80,15,66)(2,79,16,65)(3,78,17,64)(4,77,18,63)(5,76,19,62)(6,75,20,61)(7,74,21,60)(8,73,22,59)(9,72,23,58)(10,71,24,57)(11,70,25,84)(12,69,26,83)(13,68,27,82)(14,67,28,81)(29,222,43,208)(30,221,44,207)(31,220,45,206)(32,219,46,205)(33,218,47,204)(34,217,48,203)(35,216,49,202)(36,215,50,201)(37,214,51,200)(38,213,52,199)(39,212,53,198)(40,211,54,197)(41,210,55,224)(42,209,56,223)(85,184,99,170)(86,183,100,169)(87,182,101,196)(88,181,102,195)(89,180,103,194)(90,179,104,193)(91,178,105,192)(92,177,106,191)(93,176,107,190)(94,175,108,189)(95,174,109,188)(96,173,110,187)(97,172,111,186)(98,171,112,185)(113,146,127,160)(114,145,128,159)(115,144,129,158)(116,143,130,157)(117,142,131,156)(118,141,132,155)(119,168,133,154)(120,167,134,153)(121,166,135,152)(122,165,136,151)(123,164,137,150)(124,163,138,149)(125,162,139,148)(126,161,140,147)>;
G:=Group( (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)(14,169)(15,170)(16,171)(17,172)(18,173)(19,174)(20,175)(21,176)(22,177)(23,178)(24,179)(25,180)(26,181)(27,182)(28,183)(29,155)(30,156)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,163)(38,164)(39,165)(40,166)(41,167)(42,168)(43,141)(44,142)(45,143)(46,144)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,104)(58,105)(59,106)(60,107)(61,108)(62,109)(63,110)(64,111)(65,112)(66,85)(67,86)(68,87)(69,88)(70,89)(71,90)(72,91)(73,92)(74,93)(75,94)(76,95)(77,96)(78,97)(79,98)(80,99)(81,100)(82,101)(83,102)(84,103)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,197)(122,198)(123,199)(124,200)(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)(132,208)(133,209)(134,210)(135,211)(136,212)(137,213)(138,214)(139,215)(140,216), (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), (1,118,177,201,15,132,191,215)(2,117,178,200,16,131,192,214)(3,116,179,199,17,130,193,213)(4,115,180,198,18,129,194,212)(5,114,181,197,19,128,195,211)(6,113,182,224,20,127,196,210)(7,140,183,223,21,126,169,209)(8,139,184,222,22,125,170,208)(9,138,185,221,23,124,171,207)(10,137,186,220,24,123,172,206)(11,136,187,219,25,122,173,205)(12,135,188,218,26,121,174,204)(13,134,189,217,27,120,175,203)(14,133,190,216,28,119,176,202)(29,92,162,66,43,106,148,80)(30,91,163,65,44,105,149,79)(31,90,164,64,45,104,150,78)(32,89,165,63,46,103,151,77)(33,88,166,62,47,102,152,76)(34,87,167,61,48,101,153,75)(35,86,168,60,49,100,154,74)(36,85,141,59,50,99,155,73)(37,112,142,58,51,98,156,72)(38,111,143,57,52,97,157,71)(39,110,144,84,53,96,158,70)(40,109,145,83,54,95,159,69)(41,108,146,82,55,94,160,68)(42,107,147,81,56,93,161,67), (1,80,15,66)(2,79,16,65)(3,78,17,64)(4,77,18,63)(5,76,19,62)(6,75,20,61)(7,74,21,60)(8,73,22,59)(9,72,23,58)(10,71,24,57)(11,70,25,84)(12,69,26,83)(13,68,27,82)(14,67,28,81)(29,222,43,208)(30,221,44,207)(31,220,45,206)(32,219,46,205)(33,218,47,204)(34,217,48,203)(35,216,49,202)(36,215,50,201)(37,214,51,200)(38,213,52,199)(39,212,53,198)(40,211,54,197)(41,210,55,224)(42,209,56,223)(85,184,99,170)(86,183,100,169)(87,182,101,196)(88,181,102,195)(89,180,103,194)(90,179,104,193)(91,178,105,192)(92,177,106,191)(93,176,107,190)(94,175,108,189)(95,174,109,188)(96,173,110,187)(97,172,111,186)(98,171,112,185)(113,146,127,160)(114,145,128,159)(115,144,129,158)(116,143,130,157)(117,142,131,156)(118,141,132,155)(119,168,133,154)(120,167,134,153)(121,166,135,152)(122,165,136,151)(123,164,137,150)(124,163,138,149)(125,162,139,148)(126,161,140,147) );
G=PermutationGroup([[(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),(14,169),(15,170),(16,171),(17,172),(18,173),(19,174),(20,175),(21,176),(22,177),(23,178),(24,179),(25,180),(26,181),(27,182),(28,183),(29,155),(30,156),(31,157),(32,158),(33,159),(34,160),(35,161),(36,162),(37,163),(38,164),(39,165),(40,166),(41,167),(42,168),(43,141),(44,142),(45,143),(46,144),(47,145),(48,146),(49,147),(50,148),(51,149),(52,150),(53,151),(54,152),(55,153),(56,154),(57,104),(58,105),(59,106),(60,107),(61,108),(62,109),(63,110),(64,111),(65,112),(66,85),(67,86),(68,87),(69,88),(70,89),(71,90),(72,91),(73,92),(74,93),(75,94),(76,95),(77,96),(78,97),(79,98),(80,99),(81,100),(82,101),(83,102),(84,103),(113,217),(114,218),(115,219),(116,220),(117,221),(118,222),(119,223),(120,224),(121,197),(122,198),(123,199),(124,200),(125,201),(126,202),(127,203),(128,204),(129,205),(130,206),(131,207),(132,208),(133,209),(134,210),(135,211),(136,212),(137,213),(138,214),(139,215),(140,216)], [(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)], [(1,118,177,201,15,132,191,215),(2,117,178,200,16,131,192,214),(3,116,179,199,17,130,193,213),(4,115,180,198,18,129,194,212),(5,114,181,197,19,128,195,211),(6,113,182,224,20,127,196,210),(7,140,183,223,21,126,169,209),(8,139,184,222,22,125,170,208),(9,138,185,221,23,124,171,207),(10,137,186,220,24,123,172,206),(11,136,187,219,25,122,173,205),(12,135,188,218,26,121,174,204),(13,134,189,217,27,120,175,203),(14,133,190,216,28,119,176,202),(29,92,162,66,43,106,148,80),(30,91,163,65,44,105,149,79),(31,90,164,64,45,104,150,78),(32,89,165,63,46,103,151,77),(33,88,166,62,47,102,152,76),(34,87,167,61,48,101,153,75),(35,86,168,60,49,100,154,74),(36,85,141,59,50,99,155,73),(37,112,142,58,51,98,156,72),(38,111,143,57,52,97,157,71),(39,110,144,84,53,96,158,70),(40,109,145,83,54,95,159,69),(41,108,146,82,55,94,160,68),(42,107,147,81,56,93,161,67)], [(1,80,15,66),(2,79,16,65),(3,78,17,64),(4,77,18,63),(5,76,19,62),(6,75,20,61),(7,74,21,60),(8,73,22,59),(9,72,23,58),(10,71,24,57),(11,70,25,84),(12,69,26,83),(13,68,27,82),(14,67,28,81),(29,222,43,208),(30,221,44,207),(31,220,45,206),(32,219,46,205),(33,218,47,204),(34,217,48,203),(35,216,49,202),(36,215,50,201),(37,214,51,200),(38,213,52,199),(39,212,53,198),(40,211,54,197),(41,210,55,224),(42,209,56,223),(85,184,99,170),(86,183,100,169),(87,182,101,196),(88,181,102,195),(89,180,103,194),(90,179,104,193),(91,178,105,192),(92,177,106,191),(93,176,107,190),(94,175,108,189),(95,174,109,188),(96,173,110,187),(97,172,111,186),(98,171,112,185),(113,146,127,160),(114,145,128,159),(115,144,129,158),(116,143,130,157),(117,142,131,156),(118,141,132,155),(119,168,133,154),(120,167,134,153),(121,166,135,152),(122,165,136,151),(123,164,137,150),(124,163,138,149),(125,162,139,148),(126,161,140,147)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 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 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | D4 | D7 | D14 | D14 | C4×D7 | D28 | C7⋊D4 | C4×D7 | C4.10D4 | C4.12D28 |
| kernel | C2×C4.12D28 | C4.12D28 | C2×C4.Dic7 | C14×M4(2) | C22×Dic14 | C2×Dic14 | C22×Dic7 | C2×C28 | C2×M4(2) | M4(2) | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C14 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 4 | 4 | 3 | 6 | 3 | 6 | 12 | 12 | 6 | 2 | 12 |
Matrix representation of C2×C4.12D28 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 10 | 89 | 0 | 0 | 0 | 0 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 100 | 0 | 0 |
| 0 | 0 | 13 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 100 |
| 0 | 0 | 0 | 0 | 13 | 9 |
| 107 | 64 | 0 | 0 | 0 | 0 |
| 33 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 79 | 112 | 62 | 69 |
| 0 | 0 | 25 | 34 | 108 | 51 |
| 0 | 0 | 43 | 38 | 79 | 112 |
| 0 | 0 | 45 | 70 | 25 | 34 |
| 107 | 64 | 0 | 0 | 0 | 0 |
| 33 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 22 | 0 | 0 |
| 0 | 0 | 59 | 31 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 91 |
| 0 | 0 | 0 | 0 | 54 | 82 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[10,24,0,0,0,0,89,112,0,0,0,0,0,0,19,13,0,0,0,0,100,9,0,0,0,0,0,0,19,13,0,0,0,0,100,9],[107,33,0,0,0,0,64,6,0,0,0,0,0,0,79,25,43,45,0,0,112,34,38,70,0,0,62,108,79,25,0,0,69,51,112,34],[107,33,0,0,0,0,64,6,0,0,0,0,0,0,82,59,0,0,0,0,22,31,0,0,0,0,0,0,31,54,0,0,0,0,91,82] >;
C2×C4.12D28 in GAP, Magma, Sage, TeX
C_2\times C_4._{12}D_{28} % in TeX
G:=Group("C2xC4.12D28"); // GroupNames label
G:=SmallGroup(448,670);
// by ID
G=gap.SmallGroup(448,670);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,422,58,1123,136,438,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=1,c^4=d^2=b^14,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^21*c^3>;
// generators/relations