metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4).22D28, (C2×C28).33D4, (C22×D7).2Q8, C22.44(Q8×D7), C14.2(C4⋊1D4), C2.4(C4⋊D28), (C22×C4).73D14, C22.84(C2×D28), C7⋊1(C23.4Q8), C2.9(D14⋊2Q8), C2.C42⋊14D7, C14.28(C22⋊Q8), (C23×D7).9C22, (C22×C28).47C22, C23.365(C22×D7), C22.91(D4⋊2D7), (C22×C14).302C23, C2.9(C22.D28), C14.13(C22.D4), (C22×Dic7).24C22, (C2×C4⋊Dic7)⋊4C2, (C2×C14).98(C2×D4), (C2×C14).71(C2×Q8), (C2×D14⋊C4).17C2, (C2×C14).136(C4○D4), (C7×C2.C42)⋊12C2, SmallGroup(448,211)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4).22D28
G = < a,b,c,d | a2=b4=c28=1, d2=a, cbc-1=ab=ba, ac=ca, ad=da, dbd-1=b-1, dcd-1=ac-1 >
Subgroups: 1020 in 186 conjugacy classes, 65 normal (12 characteristic)
C1, C2, C2 [×6], C2 [×2], C4 [×9], C22, C22 [×6], C22 [×10], C7, C2×C4 [×6], C2×C4 [×15], C23, C23 [×8], D7 [×2], C14, C14 [×6], C22⋊C4 [×6], C4⋊C4 [×6], C22×C4 [×3], C22×C4 [×3], C24, Dic7 [×3], C28 [×6], D14 [×10], C2×C14, C2×C14 [×6], C2.C42, C2×C22⋊C4 [×3], C2×C4⋊C4 [×3], C2×Dic7 [×9], C2×C28 [×6], C2×C28 [×6], C22×D7 [×2], C22×D7 [×6], C22×C14, C23.4Q8, C4⋊Dic7 [×6], D14⋊C4 [×6], C22×Dic7 [×3], C22×C28 [×3], C23×D7, C7×C2.C42, C2×C4⋊Dic7 [×3], C2×D14⋊C4 [×3], (C2×C4).22D28
Quotients: C1, C2 [×7], C22 [×7], D4 [×6], Q8 [×2], C23, D7, C2×D4 [×3], C2×Q8, C4○D4 [×3], D14 [×3], C22⋊Q8 [×3], C22.D4 [×3], C4⋊1D4, D28 [×6], C22×D7, C23.4Q8, C2×D28 [×3], D4⋊2D7 [×3], Q8×D7, C4⋊D28, C22.D28 [×3], D14⋊2Q8 [×3], (C2×C4).22D28
►On 224 points
Generators in S224
(1 108)(2 109)(3 110)(4 111)(5 112)(6 85)(7 86)(8 87)(9 88)(10 89)(11 90)(12 91)(13 92)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 100)(22 101)(23 102)(24 103)(25 104)(26 105)(27 106)(28 107)(29 175)(30 176)(31 177)(32 178)(33 179)(34 180)(35 181)(36 182)(37 183)(38 184)(39 185)(40 186)(41 187)(42 188)(43 189)(44 190)(45 191)(46 192)(47 193)(48 194)(49 195)(50 196)(51 169)(52 170)(53 171)(54 172)(55 173)(56 174)(57 148)(58 149)(59 150)(60 151)(61 152)(62 153)(63 154)(64 155)(65 156)(66 157)(67 158)(68 159)(69 160)(70 161)(71 162)(72 163)(73 164)(74 165)(75 166)(76 167)(77 168)(78 141)(79 142)(80 143)(81 144)(82 145)(83 146)(84 147)(113 210)(114 211)(115 212)(116 213)(117 214)(118 215)(119 216)(120 217)(121 218)(122 219)(123 220)(124 221)(125 222)(126 223)(127 224)(128 197)(129 198)(130 199)(131 200)(132 201)(133 202)(134 203)(135 204)(136 205)(137 206)(138 207)(139 208)(140 209)
(1 72 45 140)(2 164 46 210)(3 74 47 114)(4 166 48 212)(5 76 49 116)(6 168 50 214)(7 78 51 118)(8 142 52 216)(9 80 53 120)(10 144 54 218)(11 82 55 122)(12 146 56 220)(13 84 29 124)(14 148 30 222)(15 58 31 126)(16 150 32 224)(17 60 33 128)(18 152 34 198)(19 62 35 130)(20 154 36 200)(21 64 37 132)(22 156 38 202)(23 66 39 134)(24 158 40 204)(25 68 41 136)(26 160 42 206)(27 70 43 138)(28 162 44 208)(57 176 125 93)(59 178 127 95)(61 180 129 97)(63 182 131 99)(65 184 133 101)(67 186 135 103)(69 188 137 105)(71 190 139 107)(73 192 113 109)(75 194 115 111)(77 196 117 85)(79 170 119 87)(81 172 121 89)(83 174 123 91)(86 141 169 215)(88 143 171 217)(90 145 173 219)(92 147 175 221)(94 149 177 223)(96 151 179 197)(98 153 181 199)(100 155 183 201)(102 157 185 203)(104 159 187 205)(106 161 189 207)(108 163 191 209)(110 165 193 211)(112 167 195 213)
(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 28 108 107)(2 106 109 27)(3 26 110 105)(4 104 111 25)(5 24 112 103)(6 102 85 23)(7 22 86 101)(8 100 87 21)(9 20 88 99)(10 98 89 19)(11 18 90 97)(12 96 91 17)(13 16 92 95)(14 94 93 15)(29 32 175 178)(30 177 176 31)(33 56 179 174)(34 173 180 55)(35 54 181 172)(36 171 182 53)(37 52 183 170)(38 169 184 51)(39 50 185 196)(40 195 186 49)(41 48 187 194)(42 193 188 47)(43 46 189 192)(44 191 190 45)(57 126 148 223)(58 222 149 125)(59 124 150 221)(60 220 151 123)(61 122 152 219)(62 218 153 121)(63 120 154 217)(64 216 155 119)(65 118 156 215)(66 214 157 117)(67 116 158 213)(68 212 159 115)(69 114 160 211)(70 210 161 113)(71 140 162 209)(72 208 163 139)(73 138 164 207)(74 206 165 137)(75 136 166 205)(76 204 167 135)(77 134 168 203)(78 202 141 133)(79 132 142 201)(80 200 143 131)(81 130 144 199)(82 198 145 129)(83 128 146 197)(84 224 147 127)
G:=sub<Sym(224)| (1,108)(2,109)(3,110)(4,111)(5,112)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,148)(58,149)(59,150)(60,151)(61,152)(62,153)(63,154)(64,155)(65,156)(66,157)(67,158)(68,159)(69,160)(70,161)(71,162)(72,163)(73,164)(74,165)(75,166)(76,167)(77,168)(78,141)(79,142)(80,143)(81,144)(82,145)(83,146)(84,147)(113,210)(114,211)(115,212)(116,213)(117,214)(118,215)(119,216)(120,217)(121,218)(122,219)(123,220)(124,221)(125,222)(126,223)(127,224)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)(134,203)(135,204)(136,205)(137,206)(138,207)(139,208)(140,209), (1,72,45,140)(2,164,46,210)(3,74,47,114)(4,166,48,212)(5,76,49,116)(6,168,50,214)(7,78,51,118)(8,142,52,216)(9,80,53,120)(10,144,54,218)(11,82,55,122)(12,146,56,220)(13,84,29,124)(14,148,30,222)(15,58,31,126)(16,150,32,224)(17,60,33,128)(18,152,34,198)(19,62,35,130)(20,154,36,200)(21,64,37,132)(22,156,38,202)(23,66,39,134)(24,158,40,204)(25,68,41,136)(26,160,42,206)(27,70,43,138)(28,162,44,208)(57,176,125,93)(59,178,127,95)(61,180,129,97)(63,182,131,99)(65,184,133,101)(67,186,135,103)(69,188,137,105)(71,190,139,107)(73,192,113,109)(75,194,115,111)(77,196,117,85)(79,170,119,87)(81,172,121,89)(83,174,123,91)(86,141,169,215)(88,143,171,217)(90,145,173,219)(92,147,175,221)(94,149,177,223)(96,151,179,197)(98,153,181,199)(100,155,183,201)(102,157,185,203)(104,159,187,205)(106,161,189,207)(108,163,191,209)(110,165,193,211)(112,167,195,213), (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), (1,28,108,107)(2,106,109,27)(3,26,110,105)(4,104,111,25)(5,24,112,103)(6,102,85,23)(7,22,86,101)(8,100,87,21)(9,20,88,99)(10,98,89,19)(11,18,90,97)(12,96,91,17)(13,16,92,95)(14,94,93,15)(29,32,175,178)(30,177,176,31)(33,56,179,174)(34,173,180,55)(35,54,181,172)(36,171,182,53)(37,52,183,170)(38,169,184,51)(39,50,185,196)(40,195,186,49)(41,48,187,194)(42,193,188,47)(43,46,189,192)(44,191,190,45)(57,126,148,223)(58,222,149,125)(59,124,150,221)(60,220,151,123)(61,122,152,219)(62,218,153,121)(63,120,154,217)(64,216,155,119)(65,118,156,215)(66,214,157,117)(67,116,158,213)(68,212,159,115)(69,114,160,211)(70,210,161,113)(71,140,162,209)(72,208,163,139)(73,138,164,207)(74,206,165,137)(75,136,166,205)(76,204,167,135)(77,134,168,203)(78,202,141,133)(79,132,142,201)(80,200,143,131)(81,130,144,199)(82,198,145,129)(83,128,146,197)(84,224,147,127)>;
G:=Group( (1,108)(2,109)(3,110)(4,111)(5,112)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,148)(58,149)(59,150)(60,151)(61,152)(62,153)(63,154)(64,155)(65,156)(66,157)(67,158)(68,159)(69,160)(70,161)(71,162)(72,163)(73,164)(74,165)(75,166)(76,167)(77,168)(78,141)(79,142)(80,143)(81,144)(82,145)(83,146)(84,147)(113,210)(114,211)(115,212)(116,213)(117,214)(118,215)(119,216)(120,217)(121,218)(122,219)(123,220)(124,221)(125,222)(126,223)(127,224)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)(134,203)(135,204)(136,205)(137,206)(138,207)(139,208)(140,209), (1,72,45,140)(2,164,46,210)(3,74,47,114)(4,166,48,212)(5,76,49,116)(6,168,50,214)(7,78,51,118)(8,142,52,216)(9,80,53,120)(10,144,54,218)(11,82,55,122)(12,146,56,220)(13,84,29,124)(14,148,30,222)(15,58,31,126)(16,150,32,224)(17,60,33,128)(18,152,34,198)(19,62,35,130)(20,154,36,200)(21,64,37,132)(22,156,38,202)(23,66,39,134)(24,158,40,204)(25,68,41,136)(26,160,42,206)(27,70,43,138)(28,162,44,208)(57,176,125,93)(59,178,127,95)(61,180,129,97)(63,182,131,99)(65,184,133,101)(67,186,135,103)(69,188,137,105)(71,190,139,107)(73,192,113,109)(75,194,115,111)(77,196,117,85)(79,170,119,87)(81,172,121,89)(83,174,123,91)(86,141,169,215)(88,143,171,217)(90,145,173,219)(92,147,175,221)(94,149,177,223)(96,151,179,197)(98,153,181,199)(100,155,183,201)(102,157,185,203)(104,159,187,205)(106,161,189,207)(108,163,191,209)(110,165,193,211)(112,167,195,213), (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), (1,28,108,107)(2,106,109,27)(3,26,110,105)(4,104,111,25)(5,24,112,103)(6,102,85,23)(7,22,86,101)(8,100,87,21)(9,20,88,99)(10,98,89,19)(11,18,90,97)(12,96,91,17)(13,16,92,95)(14,94,93,15)(29,32,175,178)(30,177,176,31)(33,56,179,174)(34,173,180,55)(35,54,181,172)(36,171,182,53)(37,52,183,170)(38,169,184,51)(39,50,185,196)(40,195,186,49)(41,48,187,194)(42,193,188,47)(43,46,189,192)(44,191,190,45)(57,126,148,223)(58,222,149,125)(59,124,150,221)(60,220,151,123)(61,122,152,219)(62,218,153,121)(63,120,154,217)(64,216,155,119)(65,118,156,215)(66,214,157,117)(67,116,158,213)(68,212,159,115)(69,114,160,211)(70,210,161,113)(71,140,162,209)(72,208,163,139)(73,138,164,207)(74,206,165,137)(75,136,166,205)(76,204,167,135)(77,134,168,203)(78,202,141,133)(79,132,142,201)(80,200,143,131)(81,130,144,199)(82,198,145,129)(83,128,146,197)(84,224,147,127) );
G=PermutationGroup([(1,108),(2,109),(3,110),(4,111),(5,112),(6,85),(7,86),(8,87),(9,88),(10,89),(11,90),(12,91),(13,92),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,100),(22,101),(23,102),(24,103),(25,104),(26,105),(27,106),(28,107),(29,175),(30,176),(31,177),(32,178),(33,179),(34,180),(35,181),(36,182),(37,183),(38,184),(39,185),(40,186),(41,187),(42,188),(43,189),(44,190),(45,191),(46,192),(47,193),(48,194),(49,195),(50,196),(51,169),(52,170),(53,171),(54,172),(55,173),(56,174),(57,148),(58,149),(59,150),(60,151),(61,152),(62,153),(63,154),(64,155),(65,156),(66,157),(67,158),(68,159),(69,160),(70,161),(71,162),(72,163),(73,164),(74,165),(75,166),(76,167),(77,168),(78,141),(79,142),(80,143),(81,144),(82,145),(83,146),(84,147),(113,210),(114,211),(115,212),(116,213),(117,214),(118,215),(119,216),(120,217),(121,218),(122,219),(123,220),(124,221),(125,222),(126,223),(127,224),(128,197),(129,198),(130,199),(131,200),(132,201),(133,202),(134,203),(135,204),(136,205),(137,206),(138,207),(139,208),(140,209)], [(1,72,45,140),(2,164,46,210),(3,74,47,114),(4,166,48,212),(5,76,49,116),(6,168,50,214),(7,78,51,118),(8,142,52,216),(9,80,53,120),(10,144,54,218),(11,82,55,122),(12,146,56,220),(13,84,29,124),(14,148,30,222),(15,58,31,126),(16,150,32,224),(17,60,33,128),(18,152,34,198),(19,62,35,130),(20,154,36,200),(21,64,37,132),(22,156,38,202),(23,66,39,134),(24,158,40,204),(25,68,41,136),(26,160,42,206),(27,70,43,138),(28,162,44,208),(57,176,125,93),(59,178,127,95),(61,180,129,97),(63,182,131,99),(65,184,133,101),(67,186,135,103),(69,188,137,105),(71,190,139,107),(73,192,113,109),(75,194,115,111),(77,196,117,85),(79,170,119,87),(81,172,121,89),(83,174,123,91),(86,141,169,215),(88,143,171,217),(90,145,173,219),(92,147,175,221),(94,149,177,223),(96,151,179,197),(98,153,181,199),(100,155,183,201),(102,157,185,203),(104,159,187,205),(106,161,189,207),(108,163,191,209),(110,165,193,211),(112,167,195,213)], [(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)], [(1,28,108,107),(2,106,109,27),(3,26,110,105),(4,104,111,25),(5,24,112,103),(6,102,85,23),(7,22,86,101),(8,100,87,21),(9,20,88,99),(10,98,89,19),(11,18,90,97),(12,96,91,17),(13,16,92,95),(14,94,93,15),(29,32,175,178),(30,177,176,31),(33,56,179,174),(34,173,180,55),(35,54,181,172),(36,171,182,53),(37,52,183,170),(38,169,184,51),(39,50,185,196),(40,195,186,49),(41,48,187,194),(42,193,188,47),(43,46,189,192),(44,191,190,45),(57,126,148,223),(58,222,149,125),(59,124,150,221),(60,220,151,123),(61,122,152,219),(62,218,153,121),(63,120,154,217),(64,216,155,119),(65,118,156,215),(66,214,157,117),(67,116,158,213),(68,212,159,115),(69,114,160,211),(70,210,161,113),(71,140,162,209),(72,208,163,139),(73,138,164,207),(74,206,165,137),(75,136,166,205),(76,204,167,135),(77,134,168,203),(78,202,141,133),(79,132,142,201),(80,200,143,131),(81,130,144,199),(82,198,145,129),(83,128,146,197),(84,224,147,127)])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4F | 4G | ··· | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | + | - | - | |
| image | C1 | C2 | C2 | C2 | D4 | Q8 | D7 | C4○D4 | D14 | D28 | D4⋊2D7 | Q8×D7 |
| kernel | (C2×C4).22D28 | C7×C2.C42 | C2×C4⋊Dic7 | C2×D14⋊C4 | C2×C28 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 1 | 3 | 3 | 6 | 2 | 3 | 6 | 9 | 36 | 9 | 3 |
Matrix representation of (C2×C4).22D28 ►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 | 28 | 28 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 |
| 0 | 0 | 0 | 0 | 11 | 27 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 7 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 24 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 3 |
| 0 | 0 | 0 | 0 | 26 | 1 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 26 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 3 |
| 0 | 0 | 0 | 0 | 8 | 8 |
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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,28,1,0,0,0,0,0,0,2,11,0,0,0,0,18,27],[26,7,0,0,0,0,22,16,0,0,0,0,0,0,17,24,0,0,0,0,0,12,0,0,0,0,0,0,21,26,0,0,0,0,3,1],[26,26,0,0,0,0,22,3,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,21,8,0,0,0,0,3,8] >;
(C2×C4).22D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)._{22}D_{28} % in TeX
G:=Group("(C2xC4).22D28"); // GroupNames label
G:=SmallGroup(448,211);
// by ID
G=gap.SmallGroup(448,211);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,387,226,18822]);
// 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,d*b*d^-1=b^-1,d*c*d^-1=a*c^-1>;
// generators/relations