metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C4⋊3C4, C2.7(C4×D28), C14.25(C4×D4), (C2×C28).235D4, (C2×C4).113D28, C22.64(D4×D7), C2.2(C4⋊D28), (C2×Dic7).85D4, C2.C42⋊9D7, C22.26(C2×D28), (C22×C4).18D14, C14.34(C4⋊D4), C14.C42⋊4C2, (C23×D7).2C22, C14.19(C4.4D4), C22.38(C4○D28), (C22×C28).15C22, C7⋊2(C24.C22), C23.260(C22×D7), C14.21(C42⋊2C2), C14.30(C42⋊C2), C2.10(Dic7⋊4D4), C22.39(D4⋊2D7), (C22×C14).295C23, C2.4(Dic7.D4), C22.20(Q8⋊2D7), C2.2(C22.D28), C14.10(C22.D4), (C22×Dic7).177C22, (C2×C4⋊Dic7)⋊2C2, (C2×C4×Dic7)⋊18C2, (C2×C4).27(C4×D7), C22.93(C2×C4×D7), (C2×C28).35(C2×C4), (C2×D14⋊C4).5C2, C2.4(C4⋊C4⋊D7), C2.8(C4⋊C4⋊7D7), (C2×C14).204(C2×D4), (C22×D7).8(C2×C4), (C2×C14).54(C22×C4), (C2×Dic7).44(C2×C4), (C2×C14).134(C4○D4), (C7×C2.C42)⋊16C2, SmallGroup(448,204)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2.(C4×D28)
G = < a,b,c,d | a2=b4=c28=1, d2=a, cbc-1=ab=ba, ac=ca, ad=da, bd=db, dcd-1=ac-1 >
Subgroups: 988 in 190 conjugacy classes, 69 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2.C42, C2.C42, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.C22, C4×Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C22×Dic7, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×C4×Dic7, C2×C4⋊Dic7, C2×D14⋊C4, C2.(C4×D28)
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, C4×D7, D28, C22×D7, C24.C22, C2×C4×D7, C2×D28, C4○D28, D4×D7, D4⋊2D7, Q8⋊2D7, C4×D28, Dic7⋊4D4, Dic7.D4, C22.D28, C4⋊C4⋊7D7, C4⋊D28, C4⋊C4⋊D7, C2.(C4×D28)
►On 224 points
Generators in S224
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 169)(10 170)(11 171)(12 172)(13 173)(14 174)(15 175)(16 176)(17 177)(18 178)(19 179)(20 180)(21 181)(22 182)(23 183)(24 184)(25 185)(26 186)(27 187)(28 188)(29 112)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 98)(44 99)(45 100)(46 101)(47 102)(48 103)(49 104)(50 105)(51 106)(52 107)(53 108)(54 109)(55 110)(56 111)(57 150)(58 151)(59 152)(60 153)(61 154)(62 155)(63 156)(64 157)(65 158)(66 159)(67 160)(68 161)(69 162)(70 163)(71 164)(72 165)(73 166)(74 167)(75 168)(76 141)(77 142)(78 143)(79 144)(80 145)(81 146)(82 147)(83 148)(84 149)(113 222)(114 223)(115 224)(116 197)(117 198)(118 199)(119 200)(120 201)(121 202)(122 203)(123 204)(124 205)(125 206)(126 207)(127 208)(128 209)(129 210)(130 211)(131 212)(132 213)(133 214)(134 215)(135 216)(136 217)(137 218)(138 219)(139 220)(140 221)
(1 116 141 29)(2 198 142 85)(3 118 143 31)(4 200 144 87)(5 120 145 33)(6 202 146 89)(7 122 147 35)(8 204 148 91)(9 124 149 37)(10 206 150 93)(11 126 151 39)(12 208 152 95)(13 128 153 41)(14 210 154 97)(15 130 155 43)(16 212 156 99)(17 132 157 45)(18 214 158 101)(19 134 159 47)(20 216 160 103)(21 136 161 49)(22 218 162 105)(23 138 163 51)(24 220 164 107)(25 140 165 53)(26 222 166 109)(27 114 167 55)(28 224 168 111)(30 190 117 77)(32 192 119 79)(34 194 121 81)(36 196 123 83)(38 170 125 57)(40 172 127 59)(42 174 129 61)(44 176 131 63)(46 178 133 65)(48 180 135 67)(50 182 137 69)(52 184 139 71)(54 186 113 73)(56 188 115 75)(58 94 171 207)(60 96 173 209)(62 98 175 211)(64 100 177 213)(66 102 179 215)(68 104 181 217)(70 106 183 219)(72 108 185 221)(74 110 187 223)(76 112 189 197)(78 86 191 199)(80 88 193 201)(82 90 195 203)(84 92 169 205)
(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 75 189 168)(2 167 190 74)(3 73 191 166)(4 165 192 72)(5 71 193 164)(6 163 194 70)(7 69 195 162)(8 161 196 68)(9 67 169 160)(10 159 170 66)(11 65 171 158)(12 157 172 64)(13 63 173 156)(14 155 174 62)(15 61 175 154)(16 153 176 60)(17 59 177 152)(18 151 178 58)(19 57 179 150)(20 149 180 84)(21 83 181 148)(22 147 182 82)(23 81 183 146)(24 145 184 80)(25 79 185 144)(26 143 186 78)(27 77 187 142)(28 141 188 76)(29 115 112 224)(30 223 85 114)(31 113 86 222)(32 221 87 140)(33 139 88 220)(34 219 89 138)(35 137 90 218)(36 217 91 136)(37 135 92 216)(38 215 93 134)(39 133 94 214)(40 213 95 132)(41 131 96 212)(42 211 97 130)(43 129 98 210)(44 209 99 128)(45 127 100 208)(46 207 101 126)(47 125 102 206)(48 205 103 124)(49 123 104 204)(50 203 105 122)(51 121 106 202)(52 201 107 120)(53 119 108 200)(54 199 109 118)(55 117 110 198)(56 197 111 116)
G:=sub<Sym(224)| (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,169)(10,170)(11,171)(12,172)(13,173)(14,174)(15,175)(16,176)(17,177)(18,178)(19,179)(20,180)(21,181)(22,182)(23,183)(24,184)(25,185)(26,186)(27,187)(28,188)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,150)(58,151)(59,152)(60,153)(61,154)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,164)(72,165)(73,166)(74,167)(75,168)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(113,222)(114,223)(115,224)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,217)(137,218)(138,219)(139,220)(140,221), (1,116,141,29)(2,198,142,85)(3,118,143,31)(4,200,144,87)(5,120,145,33)(6,202,146,89)(7,122,147,35)(8,204,148,91)(9,124,149,37)(10,206,150,93)(11,126,151,39)(12,208,152,95)(13,128,153,41)(14,210,154,97)(15,130,155,43)(16,212,156,99)(17,132,157,45)(18,214,158,101)(19,134,159,47)(20,216,160,103)(21,136,161,49)(22,218,162,105)(23,138,163,51)(24,220,164,107)(25,140,165,53)(26,222,166,109)(27,114,167,55)(28,224,168,111)(30,190,117,77)(32,192,119,79)(34,194,121,81)(36,196,123,83)(38,170,125,57)(40,172,127,59)(42,174,129,61)(44,176,131,63)(46,178,133,65)(48,180,135,67)(50,182,137,69)(52,184,139,71)(54,186,113,73)(56,188,115,75)(58,94,171,207)(60,96,173,209)(62,98,175,211)(64,100,177,213)(66,102,179,215)(68,104,181,217)(70,106,183,219)(72,108,185,221)(74,110,187,223)(76,112,189,197)(78,86,191,199)(80,88,193,201)(82,90,195,203)(84,92,169,205), (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), (1,75,189,168)(2,167,190,74)(3,73,191,166)(4,165,192,72)(5,71,193,164)(6,163,194,70)(7,69,195,162)(8,161,196,68)(9,67,169,160)(10,159,170,66)(11,65,171,158)(12,157,172,64)(13,63,173,156)(14,155,174,62)(15,61,175,154)(16,153,176,60)(17,59,177,152)(18,151,178,58)(19,57,179,150)(20,149,180,84)(21,83,181,148)(22,147,182,82)(23,81,183,146)(24,145,184,80)(25,79,185,144)(26,143,186,78)(27,77,187,142)(28,141,188,76)(29,115,112,224)(30,223,85,114)(31,113,86,222)(32,221,87,140)(33,139,88,220)(34,219,89,138)(35,137,90,218)(36,217,91,136)(37,135,92,216)(38,215,93,134)(39,133,94,214)(40,213,95,132)(41,131,96,212)(42,211,97,130)(43,129,98,210)(44,209,99,128)(45,127,100,208)(46,207,101,126)(47,125,102,206)(48,205,103,124)(49,123,104,204)(50,203,105,122)(51,121,106,202)(52,201,107,120)(53,119,108,200)(54,199,109,118)(55,117,110,198)(56,197,111,116)>;
G:=Group( (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,169)(10,170)(11,171)(12,172)(13,173)(14,174)(15,175)(16,176)(17,177)(18,178)(19,179)(20,180)(21,181)(22,182)(23,183)(24,184)(25,185)(26,186)(27,187)(28,188)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,150)(58,151)(59,152)(60,153)(61,154)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,164)(72,165)(73,166)(74,167)(75,168)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(113,222)(114,223)(115,224)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,217)(137,218)(138,219)(139,220)(140,221), (1,116,141,29)(2,198,142,85)(3,118,143,31)(4,200,144,87)(5,120,145,33)(6,202,146,89)(7,122,147,35)(8,204,148,91)(9,124,149,37)(10,206,150,93)(11,126,151,39)(12,208,152,95)(13,128,153,41)(14,210,154,97)(15,130,155,43)(16,212,156,99)(17,132,157,45)(18,214,158,101)(19,134,159,47)(20,216,160,103)(21,136,161,49)(22,218,162,105)(23,138,163,51)(24,220,164,107)(25,140,165,53)(26,222,166,109)(27,114,167,55)(28,224,168,111)(30,190,117,77)(32,192,119,79)(34,194,121,81)(36,196,123,83)(38,170,125,57)(40,172,127,59)(42,174,129,61)(44,176,131,63)(46,178,133,65)(48,180,135,67)(50,182,137,69)(52,184,139,71)(54,186,113,73)(56,188,115,75)(58,94,171,207)(60,96,173,209)(62,98,175,211)(64,100,177,213)(66,102,179,215)(68,104,181,217)(70,106,183,219)(72,108,185,221)(74,110,187,223)(76,112,189,197)(78,86,191,199)(80,88,193,201)(82,90,195,203)(84,92,169,205), (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), (1,75,189,168)(2,167,190,74)(3,73,191,166)(4,165,192,72)(5,71,193,164)(6,163,194,70)(7,69,195,162)(8,161,196,68)(9,67,169,160)(10,159,170,66)(11,65,171,158)(12,157,172,64)(13,63,173,156)(14,155,174,62)(15,61,175,154)(16,153,176,60)(17,59,177,152)(18,151,178,58)(19,57,179,150)(20,149,180,84)(21,83,181,148)(22,147,182,82)(23,81,183,146)(24,145,184,80)(25,79,185,144)(26,143,186,78)(27,77,187,142)(28,141,188,76)(29,115,112,224)(30,223,85,114)(31,113,86,222)(32,221,87,140)(33,139,88,220)(34,219,89,138)(35,137,90,218)(36,217,91,136)(37,135,92,216)(38,215,93,134)(39,133,94,214)(40,213,95,132)(41,131,96,212)(42,211,97,130)(43,129,98,210)(44,209,99,128)(45,127,100,208)(46,207,101,126)(47,125,102,206)(48,205,103,124)(49,123,104,204)(50,203,105,122)(51,121,106,202)(52,201,107,120)(53,119,108,200)(54,199,109,118)(55,117,110,198)(56,197,111,116) );
G=PermutationGroup([[(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,169),(10,170),(11,171),(12,172),(13,173),(14,174),(15,175),(16,176),(17,177),(18,178),(19,179),(20,180),(21,181),(22,182),(23,183),(24,184),(25,185),(26,186),(27,187),(28,188),(29,112),(30,85),(31,86),(32,87),(33,88),(34,89),(35,90),(36,91),(37,92),(38,93),(39,94),(40,95),(41,96),(42,97),(43,98),(44,99),(45,100),(46,101),(47,102),(48,103),(49,104),(50,105),(51,106),(52,107),(53,108),(54,109),(55,110),(56,111),(57,150),(58,151),(59,152),(60,153),(61,154),(62,155),(63,156),(64,157),(65,158),(66,159),(67,160),(68,161),(69,162),(70,163),(71,164),(72,165),(73,166),(74,167),(75,168),(76,141),(77,142),(78,143),(79,144),(80,145),(81,146),(82,147),(83,148),(84,149),(113,222),(114,223),(115,224),(116,197),(117,198),(118,199),(119,200),(120,201),(121,202),(122,203),(123,204),(124,205),(125,206),(126,207),(127,208),(128,209),(129,210),(130,211),(131,212),(132,213),(133,214),(134,215),(135,216),(136,217),(137,218),(138,219),(139,220),(140,221)], [(1,116,141,29),(2,198,142,85),(3,118,143,31),(4,200,144,87),(5,120,145,33),(6,202,146,89),(7,122,147,35),(8,204,148,91),(9,124,149,37),(10,206,150,93),(11,126,151,39),(12,208,152,95),(13,128,153,41),(14,210,154,97),(15,130,155,43),(16,212,156,99),(17,132,157,45),(18,214,158,101),(19,134,159,47),(20,216,160,103),(21,136,161,49),(22,218,162,105),(23,138,163,51),(24,220,164,107),(25,140,165,53),(26,222,166,109),(27,114,167,55),(28,224,168,111),(30,190,117,77),(32,192,119,79),(34,194,121,81),(36,196,123,83),(38,170,125,57),(40,172,127,59),(42,174,129,61),(44,176,131,63),(46,178,133,65),(48,180,135,67),(50,182,137,69),(52,184,139,71),(54,186,113,73),(56,188,115,75),(58,94,171,207),(60,96,173,209),(62,98,175,211),(64,100,177,213),(66,102,179,215),(68,104,181,217),(70,106,183,219),(72,108,185,221),(74,110,187,223),(76,112,189,197),(78,86,191,199),(80,88,193,201),(82,90,195,203),(84,92,169,205)], [(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)], [(1,75,189,168),(2,167,190,74),(3,73,191,166),(4,165,192,72),(5,71,193,164),(6,163,194,70),(7,69,195,162),(8,161,196,68),(9,67,169,160),(10,159,170,66),(11,65,171,158),(12,157,172,64),(13,63,173,156),(14,155,174,62),(15,61,175,154),(16,153,176,60),(17,59,177,152),(18,151,178,58),(19,57,179,150),(20,149,180,84),(21,83,181,148),(22,147,182,82),(23,81,183,146),(24,145,184,80),(25,79,185,144),(26,143,186,78),(27,77,187,142),(28,141,188,76),(29,115,112,224),(30,223,85,114),(31,113,86,222),(32,221,87,140),(33,139,88,220),(34,219,89,138),(35,137,90,218),(36,217,91,136),(37,135,92,216),(38,215,93,134),(39,133,94,214),(40,213,95,132),(41,131,96,212),(42,211,97,130),(43,129,98,210),(44,209,99,128),(45,127,100,208),(46,207,101,126),(47,125,102,206),(48,205,103,124),(49,123,104,204),(50,203,105,122),(51,121,106,202),(52,201,107,120),(53,119,108,200),(54,199,109,118),(55,117,110,198),(56,197,111,116)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | C4○D4 | D14 | C4×D7 | D28 | C4○D28 | D4×D7 | D4⋊2D7 | Q8⋊2D7 |
| kernel | C2.(C4×D28) | C14.C42 | C7×C2.C42 | C2×C4×Dic7 | C2×C4⋊Dic7 | C2×D14⋊C4 | D14⋊C4 | C2×Dic7 | C2×C28 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 2 | 2 | 3 | 8 | 9 | 12 | 12 | 12 | 3 | 6 | 3 |
Matrix representation of C2.(C4×D28) ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 20 | 22 | 0 | 0 | 0 | 0 |
| 24 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 24 | 0 | 0 |
| 0 | 0 | 5 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 8 | 16 | 0 | 0 | 0 | 0 |
| 16 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 17 | 0 | 0 |
| 0 | 0 | 2 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[20,24,0,0,0,0,22,25,0,0,0,0,0,0,12,5,0,0,0,0,24,27,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[8,16,0,0,0,0,16,21,0,0,0,0,0,0,5,2,0,0,0,0,17,24,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C2.(C4×D28) in GAP, Magma, Sage, TeX
C_2.(C_4\times D_{28}) % in TeX
G:=Group("C2.(C4xD28)"); // GroupNames label
G:=SmallGroup(448,204);
// by ID
G=gap.SmallGroup(448,204);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,758,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=1,d^2=a,c*b*c^-1=a*b=b*a,a*c=c*a,a*d=d*a,b*d=d*b,d*c*d^-1=a*c^-1>;
// generators/relations