direct product, metabelian, supersoluble, monomial, A-group
Aliases: C22×C7⋊D7, C14⋊2D14, C142⋊5C2, C72⋊3C23, (C2×C14)⋊3D7, C7⋊2(C22×D7), (C7×C14)⋊3C22, SmallGroup(392,43)
Series: Derived ►Chief ►Lower central ►Upper central
| C72 — C22×C7⋊D7 |
Generators and relations for C22×C7⋊D7
G = < a,b,c,d,e | a2=b2=c7=d7=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece=c-1, ede=d-1 >
Subgroups: 1216 in 160 conjugacy classes, 61 normal (5 characteristic)
C1, C2, C2, C22, C22, C7, C23, D7, C14, D14, C2×C14, C72, C22×D7, C7⋊D7, C7×C14, C2×C7⋊D7, C142, C22×C7⋊D7
Quotients: C1, C2, C22, C23, D7, D14, C22×D7, C7⋊D7, C2×C7⋊D7, C22×C7⋊D7
►On 196 points
Generators in S196
(1 175)(2 169)(3 170)(4 171)(5 172)(6 173)(7 174)(8 105)(9 99)(10 100)(11 101)(12 102)(13 103)(14 104)(15 112)(16 106)(17 107)(18 108)(19 109)(20 110)(21 111)(22 119)(23 113)(24 114)(25 115)(26 116)(27 117)(28 118)(29 126)(30 120)(31 121)(32 122)(33 123)(34 124)(35 125)(36 133)(37 127)(38 128)(39 129)(40 130)(41 131)(42 132)(43 140)(44 134)(45 135)(46 136)(47 137)(48 138)(49 139)(50 148)(51 149)(52 150)(53 151)(54 152)(55 153)(56 154)(57 155)(58 156)(59 157)(60 158)(61 159)(62 160)(63 161)(64 162)(65 163)(66 164)(67 165)(68 166)(69 167)(70 168)(71 144)(72 145)(73 146)(74 147)(75 141)(76 142)(77 143)(78 176)(79 177)(80 178)(81 179)(82 180)(83 181)(84 182)(85 183)(86 184)(87 185)(88 186)(89 187)(90 188)(91 189)(92 190)(93 191)(94 192)(95 193)(96 194)(97 195)(98 196)
(1 126)(2 120)(3 121)(4 122)(5 123)(6 124)(7 125)(8 154)(9 148)(10 149)(11 150)(12 151)(13 152)(14 153)(15 161)(16 155)(17 156)(18 157)(19 158)(20 159)(21 160)(22 168)(23 162)(24 163)(25 164)(26 165)(27 166)(28 167)(29 175)(30 169)(31 170)(32 171)(33 172)(34 173)(35 174)(36 182)(37 176)(38 177)(39 178)(40 179)(41 180)(42 181)(43 189)(44 183)(45 184)(46 185)(47 186)(48 187)(49 188)(50 99)(51 100)(52 101)(53 102)(54 103)(55 104)(56 105)(57 106)(58 107)(59 108)(60 109)(61 110)(62 111)(63 112)(64 113)(65 114)(66 115)(67 116)(68 117)(69 118)(70 119)(71 95)(72 96)(73 97)(74 98)(75 92)(76 93)(77 94)(78 127)(79 128)(80 129)(81 130)(82 131)(83 132)(84 133)(85 134)(86 135)(87 136)(88 137)(89 138)(90 139)(91 140)(141 190)(142 191)(143 192)(144 193)(145 194)(146 195)(147 196)
(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)
(1 74 50 58 66 87 82)(2 75 51 59 67 88 83)(3 76 52 60 68 89 84)(4 77 53 61 69 90 78)(5 71 54 62 70 91 79)(6 72 55 63 64 85 80)(7 73 56 57 65 86 81)(8 16 24 45 40 35 195)(9 17 25 46 41 29 196)(10 18 26 47 42 30 190)(11 19 27 48 36 31 191)(12 20 28 49 37 32 192)(13 21 22 43 38 33 193)(14 15 23 44 39 34 194)(92 100 108 116 137 132 120)(93 101 109 117 138 133 121)(94 102 110 118 139 127 122)(95 103 111 119 140 128 123)(96 104 112 113 134 129 124)(97 105 106 114 135 130 125)(98 99 107 115 136 131 126)(141 149 157 165 186 181 169)(142 150 158 166 187 182 170)(143 151 159 167 188 176 171)(144 152 160 168 189 177 172)(145 153 161 162 183 178 173)(146 154 155 163 184 179 174)(147 148 156 164 185 180 175)
(1 131)(2 130)(3 129)(4 128)(5 127)(6 133)(7 132)(8 165)(9 164)(10 163)(11 162)(12 168)(13 167)(14 166)(15 158)(16 157)(17 156)(18 155)(19 161)(20 160)(21 159)(22 151)(23 150)(24 149)(25 148)(26 154)(27 153)(28 152)(29 180)(30 179)(31 178)(32 177)(33 176)(34 182)(35 181)(36 173)(37 172)(38 171)(39 170)(40 169)(41 175)(42 174)(43 143)(44 142)(45 141)(46 147)(47 146)(48 145)(49 144)(50 115)(51 114)(52 113)(53 119)(54 118)(55 117)(56 116)(57 108)(58 107)(59 106)(60 112)(61 111)(62 110)(63 109)(64 101)(65 100)(66 99)(67 105)(68 104)(69 103)(70 102)(71 139)(72 138)(73 137)(74 136)(75 135)(76 134)(77 140)(78 123)(79 122)(80 121)(81 120)(82 126)(83 125)(84 124)(85 93)(86 92)(87 98)(88 97)(89 96)(90 95)(91 94)(183 191)(184 190)(185 196)(186 195)(187 194)(188 193)(189 192)
G:=sub<Sym(196)| (1,175)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,105)(9,99)(10,100)(11,101)(12,102)(13,103)(14,104)(15,112)(16,106)(17,107)(18,108)(19,109)(20,110)(21,111)(22,119)(23,113)(24,114)(25,115)(26,116)(27,117)(28,118)(29,126)(30,120)(31,121)(32,122)(33,123)(34,124)(35,125)(36,133)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,140)(44,134)(45,135)(46,136)(47,137)(48,138)(49,139)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,161)(64,162)(65,163)(66,164)(67,165)(68,166)(69,167)(70,168)(71,144)(72,145)(73,146)(74,147)(75,141)(76,142)(77,143)(78,176)(79,177)(80,178)(81,179)(82,180)(83,181)(84,182)(85,183)(86,184)(87,185)(88,186)(89,187)(90,188)(91,189)(92,190)(93,191)(94,192)(95,193)(96,194)(97,195)(98,196), (1,126)(2,120)(3,121)(4,122)(5,123)(6,124)(7,125)(8,154)(9,148)(10,149)(11,150)(12,151)(13,152)(14,153)(15,161)(16,155)(17,156)(18,157)(19,158)(20,159)(21,160)(22,168)(23,162)(24,163)(25,164)(26,165)(27,166)(28,167)(29,175)(30,169)(31,170)(32,171)(33,172)(34,173)(35,174)(36,182)(37,176)(38,177)(39,178)(40,179)(41,180)(42,181)(43,189)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,109)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,117)(69,118)(70,119)(71,95)(72,96)(73,97)(74,98)(75,92)(76,93)(77,94)(78,127)(79,128)(80,129)(81,130)(82,131)(83,132)(84,133)(85,134)(86,135)(87,136)(88,137)(89,138)(90,139)(91,140)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196), (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), (1,74,50,58,66,87,82)(2,75,51,59,67,88,83)(3,76,52,60,68,89,84)(4,77,53,61,69,90,78)(5,71,54,62,70,91,79)(6,72,55,63,64,85,80)(7,73,56,57,65,86,81)(8,16,24,45,40,35,195)(9,17,25,46,41,29,196)(10,18,26,47,42,30,190)(11,19,27,48,36,31,191)(12,20,28,49,37,32,192)(13,21,22,43,38,33,193)(14,15,23,44,39,34,194)(92,100,108,116,137,132,120)(93,101,109,117,138,133,121)(94,102,110,118,139,127,122)(95,103,111,119,140,128,123)(96,104,112,113,134,129,124)(97,105,106,114,135,130,125)(98,99,107,115,136,131,126)(141,149,157,165,186,181,169)(142,150,158,166,187,182,170)(143,151,159,167,188,176,171)(144,152,160,168,189,177,172)(145,153,161,162,183,178,173)(146,154,155,163,184,179,174)(147,148,156,164,185,180,175), (1,131)(2,130)(3,129)(4,128)(5,127)(6,133)(7,132)(8,165)(9,164)(10,163)(11,162)(12,168)(13,167)(14,166)(15,158)(16,157)(17,156)(18,155)(19,161)(20,160)(21,159)(22,151)(23,150)(24,149)(25,148)(26,154)(27,153)(28,152)(29,180)(30,179)(31,178)(32,177)(33,176)(34,182)(35,181)(36,173)(37,172)(38,171)(39,170)(40,169)(41,175)(42,174)(43,143)(44,142)(45,141)(46,147)(47,146)(48,145)(49,144)(50,115)(51,114)(52,113)(53,119)(54,118)(55,117)(56,116)(57,108)(58,107)(59,106)(60,112)(61,111)(62,110)(63,109)(64,101)(65,100)(66,99)(67,105)(68,104)(69,103)(70,102)(71,139)(72,138)(73,137)(74,136)(75,135)(76,134)(77,140)(78,123)(79,122)(80,121)(81,120)(82,126)(83,125)(84,124)(85,93)(86,92)(87,98)(88,97)(89,96)(90,95)(91,94)(183,191)(184,190)(185,196)(186,195)(187,194)(188,193)(189,192)>;
G:=Group( (1,175)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,105)(9,99)(10,100)(11,101)(12,102)(13,103)(14,104)(15,112)(16,106)(17,107)(18,108)(19,109)(20,110)(21,111)(22,119)(23,113)(24,114)(25,115)(26,116)(27,117)(28,118)(29,126)(30,120)(31,121)(32,122)(33,123)(34,124)(35,125)(36,133)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,140)(44,134)(45,135)(46,136)(47,137)(48,138)(49,139)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,161)(64,162)(65,163)(66,164)(67,165)(68,166)(69,167)(70,168)(71,144)(72,145)(73,146)(74,147)(75,141)(76,142)(77,143)(78,176)(79,177)(80,178)(81,179)(82,180)(83,181)(84,182)(85,183)(86,184)(87,185)(88,186)(89,187)(90,188)(91,189)(92,190)(93,191)(94,192)(95,193)(96,194)(97,195)(98,196), (1,126)(2,120)(3,121)(4,122)(5,123)(6,124)(7,125)(8,154)(9,148)(10,149)(11,150)(12,151)(13,152)(14,153)(15,161)(16,155)(17,156)(18,157)(19,158)(20,159)(21,160)(22,168)(23,162)(24,163)(25,164)(26,165)(27,166)(28,167)(29,175)(30,169)(31,170)(32,171)(33,172)(34,173)(35,174)(36,182)(37,176)(38,177)(39,178)(40,179)(41,180)(42,181)(43,189)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,109)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,117)(69,118)(70,119)(71,95)(72,96)(73,97)(74,98)(75,92)(76,93)(77,94)(78,127)(79,128)(80,129)(81,130)(82,131)(83,132)(84,133)(85,134)(86,135)(87,136)(88,137)(89,138)(90,139)(91,140)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196), (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), (1,74,50,58,66,87,82)(2,75,51,59,67,88,83)(3,76,52,60,68,89,84)(4,77,53,61,69,90,78)(5,71,54,62,70,91,79)(6,72,55,63,64,85,80)(7,73,56,57,65,86,81)(8,16,24,45,40,35,195)(9,17,25,46,41,29,196)(10,18,26,47,42,30,190)(11,19,27,48,36,31,191)(12,20,28,49,37,32,192)(13,21,22,43,38,33,193)(14,15,23,44,39,34,194)(92,100,108,116,137,132,120)(93,101,109,117,138,133,121)(94,102,110,118,139,127,122)(95,103,111,119,140,128,123)(96,104,112,113,134,129,124)(97,105,106,114,135,130,125)(98,99,107,115,136,131,126)(141,149,157,165,186,181,169)(142,150,158,166,187,182,170)(143,151,159,167,188,176,171)(144,152,160,168,189,177,172)(145,153,161,162,183,178,173)(146,154,155,163,184,179,174)(147,148,156,164,185,180,175), (1,131)(2,130)(3,129)(4,128)(5,127)(6,133)(7,132)(8,165)(9,164)(10,163)(11,162)(12,168)(13,167)(14,166)(15,158)(16,157)(17,156)(18,155)(19,161)(20,160)(21,159)(22,151)(23,150)(24,149)(25,148)(26,154)(27,153)(28,152)(29,180)(30,179)(31,178)(32,177)(33,176)(34,182)(35,181)(36,173)(37,172)(38,171)(39,170)(40,169)(41,175)(42,174)(43,143)(44,142)(45,141)(46,147)(47,146)(48,145)(49,144)(50,115)(51,114)(52,113)(53,119)(54,118)(55,117)(56,116)(57,108)(58,107)(59,106)(60,112)(61,111)(62,110)(63,109)(64,101)(65,100)(66,99)(67,105)(68,104)(69,103)(70,102)(71,139)(72,138)(73,137)(74,136)(75,135)(76,134)(77,140)(78,123)(79,122)(80,121)(81,120)(82,126)(83,125)(84,124)(85,93)(86,92)(87,98)(88,97)(89,96)(90,95)(91,94)(183,191)(184,190)(185,196)(186,195)(187,194)(188,193)(189,192) );
G=PermutationGroup([[(1,175),(2,169),(3,170),(4,171),(5,172),(6,173),(7,174),(8,105),(9,99),(10,100),(11,101),(12,102),(13,103),(14,104),(15,112),(16,106),(17,107),(18,108),(19,109),(20,110),(21,111),(22,119),(23,113),(24,114),(25,115),(26,116),(27,117),(28,118),(29,126),(30,120),(31,121),(32,122),(33,123),(34,124),(35,125),(36,133),(37,127),(38,128),(39,129),(40,130),(41,131),(42,132),(43,140),(44,134),(45,135),(46,136),(47,137),(48,138),(49,139),(50,148),(51,149),(52,150),(53,151),(54,152),(55,153),(56,154),(57,155),(58,156),(59,157),(60,158),(61,159),(62,160),(63,161),(64,162),(65,163),(66,164),(67,165),(68,166),(69,167),(70,168),(71,144),(72,145),(73,146),(74,147),(75,141),(76,142),(77,143),(78,176),(79,177),(80,178),(81,179),(82,180),(83,181),(84,182),(85,183),(86,184),(87,185),(88,186),(89,187),(90,188),(91,189),(92,190),(93,191),(94,192),(95,193),(96,194),(97,195),(98,196)], [(1,126),(2,120),(3,121),(4,122),(5,123),(6,124),(7,125),(8,154),(9,148),(10,149),(11,150),(12,151),(13,152),(14,153),(15,161),(16,155),(17,156),(18,157),(19,158),(20,159),(21,160),(22,168),(23,162),(24,163),(25,164),(26,165),(27,166),(28,167),(29,175),(30,169),(31,170),(32,171),(33,172),(34,173),(35,174),(36,182),(37,176),(38,177),(39,178),(40,179),(41,180),(42,181),(43,189),(44,183),(45,184),(46,185),(47,186),(48,187),(49,188),(50,99),(51,100),(52,101),(53,102),(54,103),(55,104),(56,105),(57,106),(58,107),(59,108),(60,109),(61,110),(62,111),(63,112),(64,113),(65,114),(66,115),(67,116),(68,117),(69,118),(70,119),(71,95),(72,96),(73,97),(74,98),(75,92),(76,93),(77,94),(78,127),(79,128),(80,129),(81,130),(82,131),(83,132),(84,133),(85,134),(86,135),(87,136),(88,137),(89,138),(90,139),(91,140),(141,190),(142,191),(143,192),(144,193),(145,194),(146,195),(147,196)], [(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)], [(1,74,50,58,66,87,82),(2,75,51,59,67,88,83),(3,76,52,60,68,89,84),(4,77,53,61,69,90,78),(5,71,54,62,70,91,79),(6,72,55,63,64,85,80),(7,73,56,57,65,86,81),(8,16,24,45,40,35,195),(9,17,25,46,41,29,196),(10,18,26,47,42,30,190),(11,19,27,48,36,31,191),(12,20,28,49,37,32,192),(13,21,22,43,38,33,193),(14,15,23,44,39,34,194),(92,100,108,116,137,132,120),(93,101,109,117,138,133,121),(94,102,110,118,139,127,122),(95,103,111,119,140,128,123),(96,104,112,113,134,129,124),(97,105,106,114,135,130,125),(98,99,107,115,136,131,126),(141,149,157,165,186,181,169),(142,150,158,166,187,182,170),(143,151,159,167,188,176,171),(144,152,160,168,189,177,172),(145,153,161,162,183,178,173),(146,154,155,163,184,179,174),(147,148,156,164,185,180,175)], [(1,131),(2,130),(3,129),(4,128),(5,127),(6,133),(7,132),(8,165),(9,164),(10,163),(11,162),(12,168),(13,167),(14,166),(15,158),(16,157),(17,156),(18,155),(19,161),(20,160),(21,159),(22,151),(23,150),(24,149),(25,148),(26,154),(27,153),(28,152),(29,180),(30,179),(31,178),(32,177),(33,176),(34,182),(35,181),(36,173),(37,172),(38,171),(39,170),(40,169),(41,175),(42,174),(43,143),(44,142),(45,141),(46,147),(47,146),(48,145),(49,144),(50,115),(51,114),(52,113),(53,119),(54,118),(55,117),(56,116),(57,108),(58,107),(59,106),(60,112),(61,111),(62,110),(63,109),(64,101),(65,100),(66,99),(67,105),(68,104),(69,103),(70,102),(71,139),(72,138),(73,137),(74,136),(75,135),(76,134),(77,140),(78,123),(79,122),(80,121),(81,120),(82,126),(83,125),(84,124),(85,93),(86,92),(87,98),(88,97),(89,96),(90,95),(91,94),(183,191),(184,190),(185,196),(186,195),(187,194),(188,193),(189,192)]])
104 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 7A | ··· | 7X | 14A | ··· | 14BT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 7 | ··· | 7 | 14 | ··· | 14 |
| size | 1 | 1 | 1 | 1 | 49 | 49 | 49 | 49 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | C2 | D7 | D14 |
| kernel | C22×C7⋊D7 | C2×C7⋊D7 | C142 | C2×C14 | C14 |
| # reps | 1 | 6 | 1 | 24 | 72 |
Matrix representation of C22×C7⋊D7 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 18 | 0 | 0 |
| 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 0 | 11 | 1 |
| 0 | 0 | 0 | 13 | 25 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 28 | 18 | 0 | 0 |
| 0 | 0 | 0 | 11 | 1 |
| 0 | 0 | 0 | 13 | 25 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 1 |
| 0 | 0 | 0 | 14 | 25 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[1,0,0,0,0,0,28,11,0,0,0,18,4,0,0,0,0,0,11,13,0,0,0,1,25],[1,0,0,0,0,0,0,28,0,0,0,1,18,0,0,0,0,0,11,13,0,0,0,1,25],[28,0,0,0,0,0,0,28,0,0,0,28,0,0,0,0,0,0,4,14,0,0,0,1,25] >;
C22×C7⋊D7 in GAP, Magma, Sage, TeX
C_2^2\times C_7\rtimes D_7
% in TeX
G:=Group("C2^2xC7:D7"); // GroupNames label
G:=SmallGroup(392,43);
// by ID
G=gap.SmallGroup(392,43);
# by ID
G:=PCGroup([5,-2,-2,-2,-7,-7,963,8404]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^7=d^7=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations