direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C3×C42.2C22, C6.25C4≀C2, C4⋊C4.1C12, C8⋊C4.3C6, C42.2(C2×C6), (C2×C12).446D4, C42.C2.1C6, (C4×C12).242C22, C6.11(C4.10D4), C2.7(C3×C4≀C2), (C3×C4⋊C4).3C4, (C2×C4).98(C3×D4), (C3×C8⋊C4).8C2, (C2×C4).10(C2×C12), (C2×C12).177(C2×C4), C2.3(C3×C4.10D4), (C3×C42.C2).8C2, C22.38(C3×C22⋊C4), (C2×C6).125(C22⋊C4), SmallGroup(192,136)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C42.2C22
G = < a,b,c,d,e | a3=b4=c4=1, d2=c, e2=c2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, dbd-1=bc2, ebe-1=b-1, cd=dc, ece-1=b2c-1, ede-1=b-1c2d >
Subgroups: 98 in 60 conjugacy classes, 30 normal (14 characteristic)
C1, C2, C2, C3, C4, C22, C6, C6, C8, C2×C4, C2×C4, C2×C4, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×C8, C24, C2×C12, C2×C12, C2×C12, C8⋊C4, C42.C2, C4×C12, C3×C4⋊C4, C3×C4⋊C4, C2×C24, C42.2C22, C3×C8⋊C4, C3×C42.C2, C3×C42.2C22
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D4, C12, C2×C6, C22⋊C4, C2×C12, C3×D4, C4.10D4, C4≀C2, C3×C22⋊C4, C42.2C22, C3×C4.10D4, C3×C4≀C2, C3×C42.2C22
►Regular action on 192 points
Generators in S192
(1 31 23)(2 32 24)(3 25 17)(4 26 18)(5 27 19)(6 28 20)(7 29 21)(8 30 22)(9 137 129)(10 138 130)(11 139 131)(12 140 132)(13 141 133)(14 142 134)(15 143 135)(16 144 136)(33 49 41)(34 50 42)(35 51 43)(36 52 44)(37 53 45)(38 54 46)(39 55 47)(40 56 48)(57 73 65)(58 74 66)(59 75 67)(60 76 68)(61 77 69)(62 78 70)(63 79 71)(64 80 72)(81 104 89)(82 97 90)(83 98 91)(84 99 92)(85 100 93)(86 101 94)(87 102 95)(88 103 96)(105 121 113)(106 122 114)(107 123 115)(108 124 116)(109 125 117)(110 126 118)(111 127 119)(112 128 120)(145 161 153)(146 162 154)(147 163 155)(148 164 156)(149 165 157)(150 166 158)(151 167 159)(152 168 160)(169 185 177)(170 186 178)(171 187 179)(172 188 180)(173 189 181)(174 190 182)(175 191 183)(176 192 184)
(1 63 151 111)(2 60 152 108)(3 57 145 105)(4 62 146 110)(5 59 147 107)(6 64 148 112)(7 61 149 109)(8 58 150 106)(9 185 104 49)(10 190 97 54)(11 187 98 51)(12 192 99 56)(13 189 100 53)(14 186 101 50)(15 191 102 55)(16 188 103 52)(17 65 153 113)(18 70 154 118)(19 67 155 115)(20 72 156 120)(21 69 157 117)(22 66 158 114)(23 71 159 119)(24 68 160 116)(25 73 161 121)(26 78 162 126)(27 75 163 123)(28 80 164 128)(29 77 165 125)(30 74 166 122)(31 79 167 127)(32 76 168 124)(33 129 169 81)(34 134 170 86)(35 131 171 83)(36 136 172 88)(37 133 173 85)(38 130 174 82)(39 135 175 87)(40 132 176 84)(41 137 177 89)(42 142 178 94)(43 139 179 91)(44 144 180 96)(45 141 181 93)(46 138 182 90)(47 143 183 95)(48 140 184 92)
(1 3 5 7)(2 4 6 8)(9 11 13 15)(10 12 14 16)(17 19 21 23)(18 20 22 24)(25 27 29 31)(26 28 30 32)(33 35 37 39)(34 36 38 40)(41 43 45 47)(42 44 46 48)(49 51 53 55)(50 52 54 56)(57 59 61 63)(58 60 62 64)(65 67 69 71)(66 68 70 72)(73 75 77 79)(74 76 78 80)(81 83 85 87)(82 84 86 88)(89 91 93 95)(90 92 94 96)(97 99 101 103)(98 100 102 104)(105 107 109 111)(106 108 110 112)(113 115 117 119)(114 116 118 120)(121 123 125 127)(122 124 126 128)(129 131 133 135)(130 132 134 136)(137 139 141 143)(138 140 142 144)(145 147 149 151)(146 148 150 152)(153 155 157 159)(154 156 158 160)(161 163 165 167)(162 164 166 168)(169 171 173 175)(170 172 174 176)(177 179 181 183)(178 180 182 184)(185 187 189 191)(186 188 190 192)
(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)
(1 175 5 171)(2 132 6 136)(3 37 7 33)(4 82 8 86)(9 121 13 125)(10 166 14 162)(11 79 15 75)(12 28 16 32)(17 45 21 41)(18 90 22 94)(19 179 23 183)(20 144 24 140)(25 53 29 49)(26 97 30 101)(27 187 31 191)(34 110 38 106)(35 151 39 147)(36 60 40 64)(42 118 46 114)(43 159 47 155)(44 68 48 72)(50 126 54 122)(51 167 55 163)(52 76 56 80)(57 85 61 81)(58 170 62 174)(59 131 63 135)(65 93 69 89)(66 178 70 182)(67 139 71 143)(73 100 77 104)(74 186 78 190)(83 111 87 107)(84 148 88 152)(91 119 95 115)(92 156 96 160)(98 127 102 123)(99 164 103 168)(105 133 109 129)(108 176 112 172)(113 141 117 137)(116 184 120 180)(124 192 128 188)(130 150 134 146)(138 158 142 154)(145 173 149 169)(153 181 157 177)(161 189 165 185)
G:=sub<Sym(192)| (1,31,23)(2,32,24)(3,25,17)(4,26,18)(5,27,19)(6,28,20)(7,29,21)(8,30,22)(9,137,129)(10,138,130)(11,139,131)(12,140,132)(13,141,133)(14,142,134)(15,143,135)(16,144,136)(33,49,41)(34,50,42)(35,51,43)(36,52,44)(37,53,45)(38,54,46)(39,55,47)(40,56,48)(57,73,65)(58,74,66)(59,75,67)(60,76,68)(61,77,69)(62,78,70)(63,79,71)(64,80,72)(81,104,89)(82,97,90)(83,98,91)(84,99,92)(85,100,93)(86,101,94)(87,102,95)(88,103,96)(105,121,113)(106,122,114)(107,123,115)(108,124,116)(109,125,117)(110,126,118)(111,127,119)(112,128,120)(145,161,153)(146,162,154)(147,163,155)(148,164,156)(149,165,157)(150,166,158)(151,167,159)(152,168,160)(169,185,177)(170,186,178)(171,187,179)(172,188,180)(173,189,181)(174,190,182)(175,191,183)(176,192,184), (1,63,151,111)(2,60,152,108)(3,57,145,105)(4,62,146,110)(5,59,147,107)(6,64,148,112)(7,61,149,109)(8,58,150,106)(9,185,104,49)(10,190,97,54)(11,187,98,51)(12,192,99,56)(13,189,100,53)(14,186,101,50)(15,191,102,55)(16,188,103,52)(17,65,153,113)(18,70,154,118)(19,67,155,115)(20,72,156,120)(21,69,157,117)(22,66,158,114)(23,71,159,119)(24,68,160,116)(25,73,161,121)(26,78,162,126)(27,75,163,123)(28,80,164,128)(29,77,165,125)(30,74,166,122)(31,79,167,127)(32,76,168,124)(33,129,169,81)(34,134,170,86)(35,131,171,83)(36,136,172,88)(37,133,173,85)(38,130,174,82)(39,135,175,87)(40,132,176,84)(41,137,177,89)(42,142,178,94)(43,139,179,91)(44,144,180,96)(45,141,181,93)(46,138,182,90)(47,143,183,95)(48,140,184,92), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96)(97,99,101,103)(98,100,102,104)(105,107,109,111)(106,108,110,112)(113,115,117,119)(114,116,118,120)(121,123,125,127)(122,124,126,128)(129,131,133,135)(130,132,134,136)(137,139,141,143)(138,140,142,144)(145,147,149,151)(146,148,150,152)(153,155,157,159)(154,156,158,160)(161,163,165,167)(162,164,166,168)(169,171,173,175)(170,172,174,176)(177,179,181,183)(178,180,182,184)(185,187,189,191)(186,188,190,192), (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), (1,175,5,171)(2,132,6,136)(3,37,7,33)(4,82,8,86)(9,121,13,125)(10,166,14,162)(11,79,15,75)(12,28,16,32)(17,45,21,41)(18,90,22,94)(19,179,23,183)(20,144,24,140)(25,53,29,49)(26,97,30,101)(27,187,31,191)(34,110,38,106)(35,151,39,147)(36,60,40,64)(42,118,46,114)(43,159,47,155)(44,68,48,72)(50,126,54,122)(51,167,55,163)(52,76,56,80)(57,85,61,81)(58,170,62,174)(59,131,63,135)(65,93,69,89)(66,178,70,182)(67,139,71,143)(73,100,77,104)(74,186,78,190)(83,111,87,107)(84,148,88,152)(91,119,95,115)(92,156,96,160)(98,127,102,123)(99,164,103,168)(105,133,109,129)(108,176,112,172)(113,141,117,137)(116,184,120,180)(124,192,128,188)(130,150,134,146)(138,158,142,154)(145,173,149,169)(153,181,157,177)(161,189,165,185)>;
G:=Group( (1,31,23)(2,32,24)(3,25,17)(4,26,18)(5,27,19)(6,28,20)(7,29,21)(8,30,22)(9,137,129)(10,138,130)(11,139,131)(12,140,132)(13,141,133)(14,142,134)(15,143,135)(16,144,136)(33,49,41)(34,50,42)(35,51,43)(36,52,44)(37,53,45)(38,54,46)(39,55,47)(40,56,48)(57,73,65)(58,74,66)(59,75,67)(60,76,68)(61,77,69)(62,78,70)(63,79,71)(64,80,72)(81,104,89)(82,97,90)(83,98,91)(84,99,92)(85,100,93)(86,101,94)(87,102,95)(88,103,96)(105,121,113)(106,122,114)(107,123,115)(108,124,116)(109,125,117)(110,126,118)(111,127,119)(112,128,120)(145,161,153)(146,162,154)(147,163,155)(148,164,156)(149,165,157)(150,166,158)(151,167,159)(152,168,160)(169,185,177)(170,186,178)(171,187,179)(172,188,180)(173,189,181)(174,190,182)(175,191,183)(176,192,184), (1,63,151,111)(2,60,152,108)(3,57,145,105)(4,62,146,110)(5,59,147,107)(6,64,148,112)(7,61,149,109)(8,58,150,106)(9,185,104,49)(10,190,97,54)(11,187,98,51)(12,192,99,56)(13,189,100,53)(14,186,101,50)(15,191,102,55)(16,188,103,52)(17,65,153,113)(18,70,154,118)(19,67,155,115)(20,72,156,120)(21,69,157,117)(22,66,158,114)(23,71,159,119)(24,68,160,116)(25,73,161,121)(26,78,162,126)(27,75,163,123)(28,80,164,128)(29,77,165,125)(30,74,166,122)(31,79,167,127)(32,76,168,124)(33,129,169,81)(34,134,170,86)(35,131,171,83)(36,136,172,88)(37,133,173,85)(38,130,174,82)(39,135,175,87)(40,132,176,84)(41,137,177,89)(42,142,178,94)(43,139,179,91)(44,144,180,96)(45,141,181,93)(46,138,182,90)(47,143,183,95)(48,140,184,92), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96)(97,99,101,103)(98,100,102,104)(105,107,109,111)(106,108,110,112)(113,115,117,119)(114,116,118,120)(121,123,125,127)(122,124,126,128)(129,131,133,135)(130,132,134,136)(137,139,141,143)(138,140,142,144)(145,147,149,151)(146,148,150,152)(153,155,157,159)(154,156,158,160)(161,163,165,167)(162,164,166,168)(169,171,173,175)(170,172,174,176)(177,179,181,183)(178,180,182,184)(185,187,189,191)(186,188,190,192), (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), (1,175,5,171)(2,132,6,136)(3,37,7,33)(4,82,8,86)(9,121,13,125)(10,166,14,162)(11,79,15,75)(12,28,16,32)(17,45,21,41)(18,90,22,94)(19,179,23,183)(20,144,24,140)(25,53,29,49)(26,97,30,101)(27,187,31,191)(34,110,38,106)(35,151,39,147)(36,60,40,64)(42,118,46,114)(43,159,47,155)(44,68,48,72)(50,126,54,122)(51,167,55,163)(52,76,56,80)(57,85,61,81)(58,170,62,174)(59,131,63,135)(65,93,69,89)(66,178,70,182)(67,139,71,143)(73,100,77,104)(74,186,78,190)(83,111,87,107)(84,148,88,152)(91,119,95,115)(92,156,96,160)(98,127,102,123)(99,164,103,168)(105,133,109,129)(108,176,112,172)(113,141,117,137)(116,184,120,180)(124,192,128,188)(130,150,134,146)(138,158,142,154)(145,173,149,169)(153,181,157,177)(161,189,165,185) );
G=PermutationGroup([[(1,31,23),(2,32,24),(3,25,17),(4,26,18),(5,27,19),(6,28,20),(7,29,21),(8,30,22),(9,137,129),(10,138,130),(11,139,131),(12,140,132),(13,141,133),(14,142,134),(15,143,135),(16,144,136),(33,49,41),(34,50,42),(35,51,43),(36,52,44),(37,53,45),(38,54,46),(39,55,47),(40,56,48),(57,73,65),(58,74,66),(59,75,67),(60,76,68),(61,77,69),(62,78,70),(63,79,71),(64,80,72),(81,104,89),(82,97,90),(83,98,91),(84,99,92),(85,100,93),(86,101,94),(87,102,95),(88,103,96),(105,121,113),(106,122,114),(107,123,115),(108,124,116),(109,125,117),(110,126,118),(111,127,119),(112,128,120),(145,161,153),(146,162,154),(147,163,155),(148,164,156),(149,165,157),(150,166,158),(151,167,159),(152,168,160),(169,185,177),(170,186,178),(171,187,179),(172,188,180),(173,189,181),(174,190,182),(175,191,183),(176,192,184)], [(1,63,151,111),(2,60,152,108),(3,57,145,105),(4,62,146,110),(5,59,147,107),(6,64,148,112),(7,61,149,109),(8,58,150,106),(9,185,104,49),(10,190,97,54),(11,187,98,51),(12,192,99,56),(13,189,100,53),(14,186,101,50),(15,191,102,55),(16,188,103,52),(17,65,153,113),(18,70,154,118),(19,67,155,115),(20,72,156,120),(21,69,157,117),(22,66,158,114),(23,71,159,119),(24,68,160,116),(25,73,161,121),(26,78,162,126),(27,75,163,123),(28,80,164,128),(29,77,165,125),(30,74,166,122),(31,79,167,127),(32,76,168,124),(33,129,169,81),(34,134,170,86),(35,131,171,83),(36,136,172,88),(37,133,173,85),(38,130,174,82),(39,135,175,87),(40,132,176,84),(41,137,177,89),(42,142,178,94),(43,139,179,91),(44,144,180,96),(45,141,181,93),(46,138,182,90),(47,143,183,95),(48,140,184,92)], [(1,3,5,7),(2,4,6,8),(9,11,13,15),(10,12,14,16),(17,19,21,23),(18,20,22,24),(25,27,29,31),(26,28,30,32),(33,35,37,39),(34,36,38,40),(41,43,45,47),(42,44,46,48),(49,51,53,55),(50,52,54,56),(57,59,61,63),(58,60,62,64),(65,67,69,71),(66,68,70,72),(73,75,77,79),(74,76,78,80),(81,83,85,87),(82,84,86,88),(89,91,93,95),(90,92,94,96),(97,99,101,103),(98,100,102,104),(105,107,109,111),(106,108,110,112),(113,115,117,119),(114,116,118,120),(121,123,125,127),(122,124,126,128),(129,131,133,135),(130,132,134,136),(137,139,141,143),(138,140,142,144),(145,147,149,151),(146,148,150,152),(153,155,157,159),(154,156,158,160),(161,163,165,167),(162,164,166,168),(169,171,173,175),(170,172,174,176),(177,179,181,183),(178,180,182,184),(185,187,189,191),(186,188,190,192)], [(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)], [(1,175,5,171),(2,132,6,136),(3,37,7,33),(4,82,8,86),(9,121,13,125),(10,166,14,162),(11,79,15,75),(12,28,16,32),(17,45,21,41),(18,90,22,94),(19,179,23,183),(20,144,24,140),(25,53,29,49),(26,97,30,101),(27,187,31,191),(34,110,38,106),(35,151,39,147),(36,60,40,64),(42,118,46,114),(43,159,47,155),(44,68,48,72),(50,126,54,122),(51,167,55,163),(52,76,56,80),(57,85,61,81),(58,170,62,174),(59,131,63,135),(65,93,69,89),(66,178,70,182),(67,139,71,143),(73,100,77,104),(74,186,78,190),(83,111,87,107),(84,148,88,152),(91,119,95,115),(92,156,96,160),(98,127,102,123),(99,164,103,168),(105,133,109,129),(108,176,112,172),(113,141,117,137),(116,184,120,180),(124,192,128,188),(130,150,134,146),(138,158,142,154),(145,173,149,169),(153,181,157,177),(161,189,165,185)]])
57 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 6A | ··· | 6F | 8A | ··· | 8H | 12A | ··· | 12H | 12I | 12J | 12K | 12L | 12M | 12N | 24A | ··· | 24P |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 12 | ··· | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 1 | ··· | 1 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | - | |||||||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C12 | D4 | C3×D4 | C4≀C2 | C3×C4≀C2 | C4.10D4 | C3×C4.10D4 |
| kernel | C3×C42.2C22 | C3×C8⋊C4 | C3×C42.C2 | C42.2C22 | C3×C4⋊C4 | C8⋊C4 | C42.C2 | C4⋊C4 | C2×C12 | C2×C4 | C6 | C2 | C6 | C2 |
| # reps | 1 | 2 | 1 | 2 | 4 | 4 | 2 | 8 | 2 | 4 | 8 | 16 | 1 | 2 |
Matrix representation of C3×C42.2C22 ►in GL4(𝔽73) generated by
| 8 | 0 | 0 | 0 |
| 0 | 8 | 0 | 0 |
| 0 | 0 | 8 | 0 |
| 0 | 0 | 0 | 8 |
| 72 | 71 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 27 |
| 0 | 0 | 27 | 0 |
| 27 | 0 | 0 | 0 |
| 0 | 27 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 29 | 25 | 0 | 0 |
| 20 | 44 | 0 | 0 |
| 0 | 0 | 60 | 14 |
| 0 | 0 | 14 | 60 |
| 58 | 34 | 0 | 0 |
| 32 | 15 | 0 | 0 |
| 0 | 0 | 43 | 60 |
| 0 | 0 | 13 | 30 |
G:=sub<GL(4,GF(73))| [8,0,0,0,0,8,0,0,0,0,8,0,0,0,0,8],[72,1,0,0,71,1,0,0,0,0,0,27,0,0,27,0],[27,0,0,0,0,27,0,0,0,0,0,1,0,0,1,0],[29,20,0,0,25,44,0,0,0,0,60,14,0,0,14,60],[58,32,0,0,34,15,0,0,0,0,43,13,0,0,60,30] >;
C3×C42.2C22 in GAP, Magma, Sage, TeX
C_3\times C_4^2._2C_2^2
% in TeX
G:=Group("C3xC4^2.2C2^2"); // GroupNames label
G:=SmallGroup(192,136);
// by ID
G=gap.SmallGroup(192,136);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-2,168,197,344,1683,1522,248,2951,102]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^4=c^4=1,d^2=c,e^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,d*b*d^-1=b*c^2,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=b^2*c^-1,e*d*e^-1=b^-1*c^2*d>;
// generators/relations