metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4)⋊3D28, (C2×C28)⋊22D4, C14.42C22≀C2, (C22×D28).5C2, (C22×D7).33D4, C22.247(D4×D7), C2.25(C4⋊D28), C2.10(C28⋊7D4), C14.62(C4⋊D4), C22.129(C2×D28), (C22×C4).104D14, C7⋊4(C23.10D4), C2.10(C23⋊D14), C14.C42⋊33C2, C2.6(C28.23D4), C14.53(C4.4D4), (C22×C28).68C22, (C23×D7).20C22, C23.380(C22×D7), C2.20(D14.5D4), C22.108(C4○D28), (C22×C14).355C23, C22.51(Q8⋊2D7), C14.53(C22.D4), (C22×Dic7).60C22, (C2×C4⋊C4)⋊9D7, (C14×C4⋊C4)⋊22C2, (C2×D14⋊C4)⋊38C2, (C2×C14).336(C2×D4), (C2×C4).41(C7⋊D4), (C2×C14).86(C4○D4), C22.140(C2×C7⋊D4), SmallGroup(448,525)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4)⋊3D28
G = < a,b,c,d | a2=b4=c28=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd=ab-1, dcd=c-1 >
Subgroups: 1508 in 238 conjugacy classes, 63 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.10D4, D14⋊C4, C7×C4⋊C4, C2×D28, C22×Dic7, C22×C28, C23×D7, C14.C42, C2×D14⋊C4, C14×C4⋊C4, C22×D28, (C2×C4)⋊3D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C22≀C2, C4⋊D4, C22.D4, C4.4D4, D28, C7⋊D4, C22×D7, C23.10D4, C2×D28, C4○D28, D4×D7, Q8⋊2D7, C2×C7⋊D4, D14.5D4, C4⋊D28, C28⋊7D4, C23⋊D14, C28.23D4, (C2×C4)⋊3D28
►On 224 points
Generators in S224
(1 40)(2 41)(3 42)(4 43)(5 44)(6 45)(7 46)(8 47)(9 48)(10 49)(11 50)(12 51)(13 52)(14 53)(15 54)(16 55)(17 56)(18 29)(19 30)(20 31)(21 32)(22 33)(23 34)(24 35)(25 36)(26 37)(27 38)(28 39)(57 107)(58 108)(59 109)(60 110)(61 111)(62 112)(63 85)(64 86)(65 87)(66 88)(67 89)(68 90)(69 91)(70 92)(71 93)(72 94)(73 95)(74 96)(75 97)(76 98)(77 99)(78 100)(79 101)(80 102)(81 103)(82 104)(83 105)(84 106)(113 199)(114 200)(115 201)(116 202)(117 203)(118 204)(119 205)(120 206)(121 207)(122 208)(123 209)(124 210)(125 211)(126 212)(127 213)(128 214)(129 215)(130 216)(131 217)(132 218)(133 219)(134 220)(135 221)(136 222)(137 223)(138 224)(139 197)(140 198)(141 191)(142 192)(143 193)(144 194)(145 195)(146 196)(147 169)(148 170)(149 171)(150 172)(151 173)(152 174)(153 175)(154 176)(155 177)(156 178)(157 179)(158 180)(159 181)(160 182)(161 183)(162 184)(163 185)(164 186)(165 187)(166 188)(167 189)(168 190)
(1 180 60 217)(2 218 61 181)(3 182 62 219)(4 220 63 183)(5 184 64 221)(6 222 65 185)(7 186 66 223)(8 224 67 187)(9 188 68 197)(10 198 69 189)(11 190 70 199)(12 200 71 191)(13 192 72 201)(14 202 73 193)(15 194 74 203)(16 204 75 195)(17 196 76 205)(18 206 77 169)(19 170 78 207)(20 208 79 171)(21 172 80 209)(22 210 81 173)(23 174 82 211)(24 212 83 175)(25 176 84 213)(26 214 57 177)(27 178 58 215)(28 216 59 179)(29 120 99 147)(30 148 100 121)(31 122 101 149)(32 150 102 123)(33 124 103 151)(34 152 104 125)(35 126 105 153)(36 154 106 127)(37 128 107 155)(38 156 108 129)(39 130 109 157)(40 158 110 131)(41 132 111 159)(42 160 112 133)(43 134 85 161)(44 162 86 135)(45 136 87 163)(46 164 88 137)(47 138 89 165)(48 166 90 139)(49 140 91 167)(50 168 92 113)(51 114 93 141)(52 142 94 115)(53 116 95 143)(54 144 96 117)(55 118 97 145)(56 146 98 119)
(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 66)(2 65)(3 64)(4 63)(5 62)(6 61)(7 60)(8 59)(9 58)(10 57)(11 84)(12 83)(13 82)(14 81)(15 80)(16 79)(17 78)(18 77)(19 76)(20 75)(21 74)(22 73)(23 72)(24 71)(25 70)(26 69)(27 68)(28 67)(29 99)(30 98)(31 97)(32 96)(33 95)(34 94)(35 93)(36 92)(37 91)(38 90)(39 89)(40 88)(41 87)(42 86)(43 85)(44 112)(45 111)(46 110)(47 109)(48 108)(49 107)(50 106)(51 105)(52 104)(53 103)(54 102)(55 101)(56 100)(113 213)(114 212)(115 211)(116 210)(117 209)(118 208)(119 207)(120 206)(121 205)(122 204)(123 203)(124 202)(125 201)(126 200)(127 199)(128 198)(129 197)(130 224)(131 223)(132 222)(133 221)(134 220)(135 219)(136 218)(137 217)(138 216)(139 215)(140 214)(141 175)(142 174)(143 173)(144 172)(145 171)(146 170)(147 169)(148 196)(149 195)(150 194)(151 193)(152 192)(153 191)(154 190)(155 189)(156 188)(157 187)(158 186)(159 185)(160 184)(161 183)(162 182)(163 181)(164 180)(165 179)(166 178)(167 177)(168 176)
G:=sub<Sym(224)| (1,40)(2,41)(3,42)(4,43)(5,44)(6,45)(7,46)(8,47)(9,48)(10,49)(11,50)(12,51)(13,52)(14,53)(15,54)(16,55)(17,56)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,85)(64,86)(65,87)(66,88)(67,89)(68,90)(69,91)(70,92)(71,93)(72,94)(73,95)(74,96)(75,97)(76,98)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,197)(140,198)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176)(155,177)(156,178)(157,179)(158,180)(159,181)(160,182)(161,183)(162,184)(163,185)(164,186)(165,187)(166,188)(167,189)(168,190), (1,180,60,217)(2,218,61,181)(3,182,62,219)(4,220,63,183)(5,184,64,221)(6,222,65,185)(7,186,66,223)(8,224,67,187)(9,188,68,197)(10,198,69,189)(11,190,70,199)(12,200,71,191)(13,192,72,201)(14,202,73,193)(15,194,74,203)(16,204,75,195)(17,196,76,205)(18,206,77,169)(19,170,78,207)(20,208,79,171)(21,172,80,209)(22,210,81,173)(23,174,82,211)(24,212,83,175)(25,176,84,213)(26,214,57,177)(27,178,58,215)(28,216,59,179)(29,120,99,147)(30,148,100,121)(31,122,101,149)(32,150,102,123)(33,124,103,151)(34,152,104,125)(35,126,105,153)(36,154,106,127)(37,128,107,155)(38,156,108,129)(39,130,109,157)(40,158,110,131)(41,132,111,159)(42,160,112,133)(43,134,85,161)(44,162,86,135)(45,136,87,163)(46,164,88,137)(47,138,89,165)(48,166,90,139)(49,140,91,167)(50,168,92,113)(51,114,93,141)(52,142,94,115)(53,116,95,143)(54,144,96,117)(55,118,97,145)(56,146,98,119), (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), (1,66)(2,65)(3,64)(4,63)(5,62)(6,61)(7,60)(8,59)(9,58)(10,57)(11,84)(12,83)(13,82)(14,81)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,74)(22,73)(23,72)(24,71)(25,70)(26,69)(27,68)(28,67)(29,99)(30,98)(31,97)(32,96)(33,95)(34,94)(35,93)(36,92)(37,91)(38,90)(39,89)(40,88)(41,87)(42,86)(43,85)(44,112)(45,111)(46,110)(47,109)(48,108)(49,107)(50,106)(51,105)(52,104)(53,103)(54,102)(55,101)(56,100)(113,213)(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)(120,206)(121,205)(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,224)(131,223)(132,222)(133,221)(134,220)(135,219)(136,218)(137,217)(138,216)(139,215)(140,214)(141,175)(142,174)(143,173)(144,172)(145,171)(146,170)(147,169)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,176)>;
G:=Group( (1,40)(2,41)(3,42)(4,43)(5,44)(6,45)(7,46)(8,47)(9,48)(10,49)(11,50)(12,51)(13,52)(14,53)(15,54)(16,55)(17,56)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,85)(64,86)(65,87)(66,88)(67,89)(68,90)(69,91)(70,92)(71,93)(72,94)(73,95)(74,96)(75,97)(76,98)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,197)(140,198)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176)(155,177)(156,178)(157,179)(158,180)(159,181)(160,182)(161,183)(162,184)(163,185)(164,186)(165,187)(166,188)(167,189)(168,190), (1,180,60,217)(2,218,61,181)(3,182,62,219)(4,220,63,183)(5,184,64,221)(6,222,65,185)(7,186,66,223)(8,224,67,187)(9,188,68,197)(10,198,69,189)(11,190,70,199)(12,200,71,191)(13,192,72,201)(14,202,73,193)(15,194,74,203)(16,204,75,195)(17,196,76,205)(18,206,77,169)(19,170,78,207)(20,208,79,171)(21,172,80,209)(22,210,81,173)(23,174,82,211)(24,212,83,175)(25,176,84,213)(26,214,57,177)(27,178,58,215)(28,216,59,179)(29,120,99,147)(30,148,100,121)(31,122,101,149)(32,150,102,123)(33,124,103,151)(34,152,104,125)(35,126,105,153)(36,154,106,127)(37,128,107,155)(38,156,108,129)(39,130,109,157)(40,158,110,131)(41,132,111,159)(42,160,112,133)(43,134,85,161)(44,162,86,135)(45,136,87,163)(46,164,88,137)(47,138,89,165)(48,166,90,139)(49,140,91,167)(50,168,92,113)(51,114,93,141)(52,142,94,115)(53,116,95,143)(54,144,96,117)(55,118,97,145)(56,146,98,119), (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), (1,66)(2,65)(3,64)(4,63)(5,62)(6,61)(7,60)(8,59)(9,58)(10,57)(11,84)(12,83)(13,82)(14,81)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,74)(22,73)(23,72)(24,71)(25,70)(26,69)(27,68)(28,67)(29,99)(30,98)(31,97)(32,96)(33,95)(34,94)(35,93)(36,92)(37,91)(38,90)(39,89)(40,88)(41,87)(42,86)(43,85)(44,112)(45,111)(46,110)(47,109)(48,108)(49,107)(50,106)(51,105)(52,104)(53,103)(54,102)(55,101)(56,100)(113,213)(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)(120,206)(121,205)(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,224)(131,223)(132,222)(133,221)(134,220)(135,219)(136,218)(137,217)(138,216)(139,215)(140,214)(141,175)(142,174)(143,173)(144,172)(145,171)(146,170)(147,169)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,176) );
G=PermutationGroup([[(1,40),(2,41),(3,42),(4,43),(5,44),(6,45),(7,46),(8,47),(9,48),(10,49),(11,50),(12,51),(13,52),(14,53),(15,54),(16,55),(17,56),(18,29),(19,30),(20,31),(21,32),(22,33),(23,34),(24,35),(25,36),(26,37),(27,38),(28,39),(57,107),(58,108),(59,109),(60,110),(61,111),(62,112),(63,85),(64,86),(65,87),(66,88),(67,89),(68,90),(69,91),(70,92),(71,93),(72,94),(73,95),(74,96),(75,97),(76,98),(77,99),(78,100),(79,101),(80,102),(81,103),(82,104),(83,105),(84,106),(113,199),(114,200),(115,201),(116,202),(117,203),(118,204),(119,205),(120,206),(121,207),(122,208),(123,209),(124,210),(125,211),(126,212),(127,213),(128,214),(129,215),(130,216),(131,217),(132,218),(133,219),(134,220),(135,221),(136,222),(137,223),(138,224),(139,197),(140,198),(141,191),(142,192),(143,193),(144,194),(145,195),(146,196),(147,169),(148,170),(149,171),(150,172),(151,173),(152,174),(153,175),(154,176),(155,177),(156,178),(157,179),(158,180),(159,181),(160,182),(161,183),(162,184),(163,185),(164,186),(165,187),(166,188),(167,189),(168,190)], [(1,180,60,217),(2,218,61,181),(3,182,62,219),(4,220,63,183),(5,184,64,221),(6,222,65,185),(7,186,66,223),(8,224,67,187),(9,188,68,197),(10,198,69,189),(11,190,70,199),(12,200,71,191),(13,192,72,201),(14,202,73,193),(15,194,74,203),(16,204,75,195),(17,196,76,205),(18,206,77,169),(19,170,78,207),(20,208,79,171),(21,172,80,209),(22,210,81,173),(23,174,82,211),(24,212,83,175),(25,176,84,213),(26,214,57,177),(27,178,58,215),(28,216,59,179),(29,120,99,147),(30,148,100,121),(31,122,101,149),(32,150,102,123),(33,124,103,151),(34,152,104,125),(35,126,105,153),(36,154,106,127),(37,128,107,155),(38,156,108,129),(39,130,109,157),(40,158,110,131),(41,132,111,159),(42,160,112,133),(43,134,85,161),(44,162,86,135),(45,136,87,163),(46,164,88,137),(47,138,89,165),(48,166,90,139),(49,140,91,167),(50,168,92,113),(51,114,93,141),(52,142,94,115),(53,116,95,143),(54,144,96,117),(55,118,97,145),(56,146,98,119)], [(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)], [(1,66),(2,65),(3,64),(4,63),(5,62),(6,61),(7,60),(8,59),(9,58),(10,57),(11,84),(12,83),(13,82),(14,81),(15,80),(16,79),(17,78),(18,77),(19,76),(20,75),(21,74),(22,73),(23,72),(24,71),(25,70),(26,69),(27,68),(28,67),(29,99),(30,98),(31,97),(32,96),(33,95),(34,94),(35,93),(36,92),(37,91),(38,90),(39,89),(40,88),(41,87),(42,86),(43,85),(44,112),(45,111),(46,110),(47,109),(48,108),(49,107),(50,106),(51,105),(52,104),(53,103),(54,102),(55,101),(56,100),(113,213),(114,212),(115,211),(116,210),(117,209),(118,208),(119,207),(120,206),(121,205),(122,204),(123,203),(124,202),(125,201),(126,200),(127,199),(128,198),(129,197),(130,224),(131,223),(132,222),(133,221),(134,220),(135,219),(136,218),(137,217),(138,216),(139,215),(140,214),(141,175),(142,174),(143,173),(144,172),(145,171),(146,170),(147,169),(148,196),(149,195),(150,194),(151,193),(152,192),(153,191),(154,190),(155,189),(156,188),(157,187),(158,186),(159,185),(160,184),(161,183),(162,182),(163,181),(164,180),(165,179),(166,178),(167,177),(168,176)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 4 | ··· | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D28 | C7⋊D4 | C4○D28 | D4×D7 | Q8⋊2D7 |
| kernel | (C2×C4)⋊3D28 | C14.C42 | C2×D14⋊C4 | C14×C4⋊C4 | C22×D28 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 1 | 4 | 1 | 1 | 4 | 4 | 3 | 6 | 9 | 12 | 12 | 12 | 6 | 6 |
Matrix representation of (C2×C4)⋊3D28 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 27 | 0 | 0 |
| 0 | 0 | 12 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 27 |
| 0 | 0 | 0 | 0 | 5 | 26 |
| 14 | 24 | 0 | 0 | 0 | 0 |
| 22 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 11 | 0 | 0 |
| 0 | 0 | 21 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 26 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 6 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 26 | 1 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,5,12,0,0,0,0,27,24,0,0,0,0,0,0,3,5,0,0,0,0,27,26],[14,22,0,0,0,0,24,15,0,0,0,0,0,0,3,21,0,0,0,0,11,0,0,0,0,0,0,0,28,26,0,0,0,0,0,1],[28,6,0,0,0,0,0,1,0,0,0,0,0,0,0,8,0,0,0,0,11,0,0,0,0,0,0,0,28,26,0,0,0,0,0,1] >;
(C2×C4)⋊3D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)\rtimes_3D_{28} % in TeX
G:=Group("(C2xC4):3D28"); // GroupNames label
G:=SmallGroup(448,525);
// by ID
G=gap.SmallGroup(448,525);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,387,184,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d=a*b^-1,d*c*d=c^-1>;
// generators/relations