metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C28).33D4, (C2×C4).22D28, (C22×D7).2Q8, C22.44(Q8×D7), C14.2(C4⋊1D4), C2.4(C28⋊4D4), (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×C28).33D4
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, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.4Q8, C4⋊Dic7, D14⋊C4, C22×Dic7, C22×C28, C23×D7, C7×C2.C42, C2×C4⋊Dic7, C2×D14⋊C4, (C2×C28).33D4
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C22.D4, C4⋊1D4, D28, C22×D7, C23.4Q8, C2×D28, D4⋊2D7, Q8×D7, C28⋊4D4, C22.D28, D14⋊2Q8, (C2×C28).33D4
►On 224 points
Generators in S224
(1 90)(2 91)(3 92)(4 93)(5 94)(6 95)(7 96)(8 97)(9 98)(10 99)(11 100)(12 101)(13 102)(14 103)(15 104)(16 105)(17 106)(18 107)(19 108)(20 109)(21 110)(22 111)(23 112)(24 85)(25 86)(26 87)(27 88)(28 89)(29 211)(30 212)(31 213)(32 214)(33 215)(34 216)(35 217)(36 218)(37 219)(38 220)(39 221)(40 222)(41 223)(42 224)(43 197)(44 198)(45 199)(46 200)(47 201)(48 202)(49 203)(50 204)(51 205)(52 206)(53 207)(54 208)(55 209)(56 210)(57 125)(58 126)(59 127)(60 128)(61 129)(62 130)(63 131)(64 132)(65 133)(66 134)(67 135)(68 136)(69 137)(70 138)(71 139)(72 140)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)(81 121)(82 122)(83 123)(84 124)(141 182)(142 183)(143 184)(144 185)(145 186)(146 187)(147 188)(148 189)(149 190)(150 191)(151 192)(152 193)(153 194)(154 195)(155 196)(156 169)(157 170)(158 171)(159 172)(160 173)(161 174)(162 175)(163 176)(164 177)(165 178)(166 179)(167 180)(168 181)
(1 132 32 186)(2 65 33 146)(3 134 34 188)(4 67 35 148)(5 136 36 190)(6 69 37 150)(7 138 38 192)(8 71 39 152)(9 140 40 194)(10 73 41 154)(11 114 42 196)(12 75 43 156)(13 116 44 170)(14 77 45 158)(15 118 46 172)(16 79 47 160)(17 120 48 174)(18 81 49 162)(19 122 50 176)(20 83 51 164)(21 124 52 178)(22 57 53 166)(23 126 54 180)(24 59 55 168)(25 128 56 182)(26 61 29 142)(27 130 30 184)(28 63 31 144)(58 208 167 112)(60 210 141 86)(62 212 143 88)(64 214 145 90)(66 216 147 92)(68 218 149 94)(70 220 151 96)(72 222 153 98)(74 224 155 100)(76 198 157 102)(78 200 159 104)(80 202 161 106)(82 204 163 108)(84 206 165 110)(85 127 209 181)(87 129 211 183)(89 131 213 185)(91 133 215 187)(93 135 217 189)(95 137 219 191)(97 139 221 193)(99 113 223 195)(101 115 197 169)(103 117 199 171)(105 119 201 173)(107 121 203 175)(109 123 205 177)(111 125 207 179)
(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 90 89)(2 88 91 27)(3 26 92 87)(4 86 93 25)(5 24 94 85)(6 112 95 23)(7 22 96 111)(8 110 97 21)(9 20 98 109)(10 108 99 19)(11 18 100 107)(12 106 101 17)(13 16 102 105)(14 104 103 15)(29 216 211 34)(30 33 212 215)(31 214 213 32)(35 210 217 56)(36 55 218 209)(37 208 219 54)(38 53 220 207)(39 206 221 52)(40 51 222 205)(41 204 223 50)(42 49 224 203)(43 202 197 48)(44 47 198 201)(45 200 199 46)(57 151 125 192)(58 191 126 150)(59 149 127 190)(60 189 128 148)(61 147 129 188)(62 187 130 146)(63 145 131 186)(64 185 132 144)(65 143 133 184)(66 183 134 142)(67 141 135 182)(68 181 136 168)(69 167 137 180)(70 179 138 166)(71 165 139 178)(72 177 140 164)(73 163 113 176)(74 175 114 162)(75 161 115 174)(76 173 116 160)(77 159 117 172)(78 171 118 158)(79 157 119 170)(80 169 120 156)(81 155 121 196)(82 195 122 154)(83 153 123 194)(84 193 124 152)
G:=sub<Sym(224)| (1,90)(2,91)(3,92)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,101)(13,102)(14,103)(15,104)(16,105)(17,106)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,85)(25,86)(26,87)(27,88)(28,89)(29,211)(30,212)(31,213)(32,214)(33,215)(34,216)(35,217)(36,218)(37,219)(38,220)(39,221)(40,222)(41,223)(42,224)(43,197)(44,198)(45,199)(46,200)(47,201)(48,202)(49,203)(50,204)(51,205)(52,206)(53,207)(54,208)(55,209)(56,210)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(141,182)(142,183)(143,184)(144,185)(145,186)(146,187)(147,188)(148,189)(149,190)(150,191)(151,192)(152,193)(153,194)(154,195)(155,196)(156,169)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181), (1,132,32,186)(2,65,33,146)(3,134,34,188)(4,67,35,148)(5,136,36,190)(6,69,37,150)(7,138,38,192)(8,71,39,152)(9,140,40,194)(10,73,41,154)(11,114,42,196)(12,75,43,156)(13,116,44,170)(14,77,45,158)(15,118,46,172)(16,79,47,160)(17,120,48,174)(18,81,49,162)(19,122,50,176)(20,83,51,164)(21,124,52,178)(22,57,53,166)(23,126,54,180)(24,59,55,168)(25,128,56,182)(26,61,29,142)(27,130,30,184)(28,63,31,144)(58,208,167,112)(60,210,141,86)(62,212,143,88)(64,214,145,90)(66,216,147,92)(68,218,149,94)(70,220,151,96)(72,222,153,98)(74,224,155,100)(76,198,157,102)(78,200,159,104)(80,202,161,106)(82,204,163,108)(84,206,165,110)(85,127,209,181)(87,129,211,183)(89,131,213,185)(91,133,215,187)(93,135,217,189)(95,137,219,191)(97,139,221,193)(99,113,223,195)(101,115,197,169)(103,117,199,171)(105,119,201,173)(107,121,203,175)(109,123,205,177)(111,125,207,179), (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), (1,28,90,89)(2,88,91,27)(3,26,92,87)(4,86,93,25)(5,24,94,85)(6,112,95,23)(7,22,96,111)(8,110,97,21)(9,20,98,109)(10,108,99,19)(11,18,100,107)(12,106,101,17)(13,16,102,105)(14,104,103,15)(29,216,211,34)(30,33,212,215)(31,214,213,32)(35,210,217,56)(36,55,218,209)(37,208,219,54)(38,53,220,207)(39,206,221,52)(40,51,222,205)(41,204,223,50)(42,49,224,203)(43,202,197,48)(44,47,198,201)(45,200,199,46)(57,151,125,192)(58,191,126,150)(59,149,127,190)(60,189,128,148)(61,147,129,188)(62,187,130,146)(63,145,131,186)(64,185,132,144)(65,143,133,184)(66,183,134,142)(67,141,135,182)(68,181,136,168)(69,167,137,180)(70,179,138,166)(71,165,139,178)(72,177,140,164)(73,163,113,176)(74,175,114,162)(75,161,115,174)(76,173,116,160)(77,159,117,172)(78,171,118,158)(79,157,119,170)(80,169,120,156)(81,155,121,196)(82,195,122,154)(83,153,123,194)(84,193,124,152)>;
G:=Group( (1,90)(2,91)(3,92)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,101)(13,102)(14,103)(15,104)(16,105)(17,106)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,85)(25,86)(26,87)(27,88)(28,89)(29,211)(30,212)(31,213)(32,214)(33,215)(34,216)(35,217)(36,218)(37,219)(38,220)(39,221)(40,222)(41,223)(42,224)(43,197)(44,198)(45,199)(46,200)(47,201)(48,202)(49,203)(50,204)(51,205)(52,206)(53,207)(54,208)(55,209)(56,210)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(141,182)(142,183)(143,184)(144,185)(145,186)(146,187)(147,188)(148,189)(149,190)(150,191)(151,192)(152,193)(153,194)(154,195)(155,196)(156,169)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181), (1,132,32,186)(2,65,33,146)(3,134,34,188)(4,67,35,148)(5,136,36,190)(6,69,37,150)(7,138,38,192)(8,71,39,152)(9,140,40,194)(10,73,41,154)(11,114,42,196)(12,75,43,156)(13,116,44,170)(14,77,45,158)(15,118,46,172)(16,79,47,160)(17,120,48,174)(18,81,49,162)(19,122,50,176)(20,83,51,164)(21,124,52,178)(22,57,53,166)(23,126,54,180)(24,59,55,168)(25,128,56,182)(26,61,29,142)(27,130,30,184)(28,63,31,144)(58,208,167,112)(60,210,141,86)(62,212,143,88)(64,214,145,90)(66,216,147,92)(68,218,149,94)(70,220,151,96)(72,222,153,98)(74,224,155,100)(76,198,157,102)(78,200,159,104)(80,202,161,106)(82,204,163,108)(84,206,165,110)(85,127,209,181)(87,129,211,183)(89,131,213,185)(91,133,215,187)(93,135,217,189)(95,137,219,191)(97,139,221,193)(99,113,223,195)(101,115,197,169)(103,117,199,171)(105,119,201,173)(107,121,203,175)(109,123,205,177)(111,125,207,179), (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), (1,28,90,89)(2,88,91,27)(3,26,92,87)(4,86,93,25)(5,24,94,85)(6,112,95,23)(7,22,96,111)(8,110,97,21)(9,20,98,109)(10,108,99,19)(11,18,100,107)(12,106,101,17)(13,16,102,105)(14,104,103,15)(29,216,211,34)(30,33,212,215)(31,214,213,32)(35,210,217,56)(36,55,218,209)(37,208,219,54)(38,53,220,207)(39,206,221,52)(40,51,222,205)(41,204,223,50)(42,49,224,203)(43,202,197,48)(44,47,198,201)(45,200,199,46)(57,151,125,192)(58,191,126,150)(59,149,127,190)(60,189,128,148)(61,147,129,188)(62,187,130,146)(63,145,131,186)(64,185,132,144)(65,143,133,184)(66,183,134,142)(67,141,135,182)(68,181,136,168)(69,167,137,180)(70,179,138,166)(71,165,139,178)(72,177,140,164)(73,163,113,176)(74,175,114,162)(75,161,115,174)(76,173,116,160)(77,159,117,172)(78,171,118,158)(79,157,119,170)(80,169,120,156)(81,155,121,196)(82,195,122,154)(83,153,123,194)(84,193,124,152) );
G=PermutationGroup([[(1,90),(2,91),(3,92),(4,93),(5,94),(6,95),(7,96),(8,97),(9,98),(10,99),(11,100),(12,101),(13,102),(14,103),(15,104),(16,105),(17,106),(18,107),(19,108),(20,109),(21,110),(22,111),(23,112),(24,85),(25,86),(26,87),(27,88),(28,89),(29,211),(30,212),(31,213),(32,214),(33,215),(34,216),(35,217),(36,218),(37,219),(38,220),(39,221),(40,222),(41,223),(42,224),(43,197),(44,198),(45,199),(46,200),(47,201),(48,202),(49,203),(50,204),(51,205),(52,206),(53,207),(54,208),(55,209),(56,210),(57,125),(58,126),(59,127),(60,128),(61,129),(62,130),(63,131),(64,132),(65,133),(66,134),(67,135),(68,136),(69,137),(70,138),(71,139),(72,140),(73,113),(74,114),(75,115),(76,116),(77,117),(78,118),(79,119),(80,120),(81,121),(82,122),(83,123),(84,124),(141,182),(142,183),(143,184),(144,185),(145,186),(146,187),(147,188),(148,189),(149,190),(150,191),(151,192),(152,193),(153,194),(154,195),(155,196),(156,169),(157,170),(158,171),(159,172),(160,173),(161,174),(162,175),(163,176),(164,177),(165,178),(166,179),(167,180),(168,181)], [(1,132,32,186),(2,65,33,146),(3,134,34,188),(4,67,35,148),(5,136,36,190),(6,69,37,150),(7,138,38,192),(8,71,39,152),(9,140,40,194),(10,73,41,154),(11,114,42,196),(12,75,43,156),(13,116,44,170),(14,77,45,158),(15,118,46,172),(16,79,47,160),(17,120,48,174),(18,81,49,162),(19,122,50,176),(20,83,51,164),(21,124,52,178),(22,57,53,166),(23,126,54,180),(24,59,55,168),(25,128,56,182),(26,61,29,142),(27,130,30,184),(28,63,31,144),(58,208,167,112),(60,210,141,86),(62,212,143,88),(64,214,145,90),(66,216,147,92),(68,218,149,94),(70,220,151,96),(72,222,153,98),(74,224,155,100),(76,198,157,102),(78,200,159,104),(80,202,161,106),(82,204,163,108),(84,206,165,110),(85,127,209,181),(87,129,211,183),(89,131,213,185),(91,133,215,187),(93,135,217,189),(95,137,219,191),(97,139,221,193),(99,113,223,195),(101,115,197,169),(103,117,199,171),(105,119,201,173),(107,121,203,175),(109,123,205,177),(111,125,207,179)], [(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)], [(1,28,90,89),(2,88,91,27),(3,26,92,87),(4,86,93,25),(5,24,94,85),(6,112,95,23),(7,22,96,111),(8,110,97,21),(9,20,98,109),(10,108,99,19),(11,18,100,107),(12,106,101,17),(13,16,102,105),(14,104,103,15),(29,216,211,34),(30,33,212,215),(31,214,213,32),(35,210,217,56),(36,55,218,209),(37,208,219,54),(38,53,220,207),(39,206,221,52),(40,51,222,205),(41,204,223,50),(42,49,224,203),(43,202,197,48),(44,47,198,201),(45,200,199,46),(57,151,125,192),(58,191,126,150),(59,149,127,190),(60,189,128,148),(61,147,129,188),(62,187,130,146),(63,145,131,186),(64,185,132,144),(65,143,133,184),(66,183,134,142),(67,141,135,182),(68,181,136,168),(69,167,137,180),(70,179,138,166),(71,165,139,178),(72,177,140,164),(73,163,113,176),(74,175,114,162),(75,161,115,174),(76,173,116,160),(77,159,117,172),(78,171,118,158),(79,157,119,170),(80,169,120,156),(81,155,121,196),(82,195,122,154),(83,153,123,194),(84,193,124,152)]])
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×C28).33D4 | 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×C28).33D4 ►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×C28).33D4 in GAP, Magma, Sage, TeX
(C_2\times C_{28})._{33}D_4 % in TeX
G:=Group("(C2xC28).33D4"); // 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