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G = Dic3×C22×C4  order 192 = 26·3

Direct product of C22×C4 and Dic3

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: Dic3×C22×C4, C24.86D6, (C2×C6)⋊4C42, C6⋊2(C2×C42), C12⋊9(C22×C4), C3⋊2(C22×C42), (C22×C12)⋊18C4, C6.36(C23×C4), C23.72(C4×S3), (C23×C4).21S3, (C2×C6).280C24, (C23×C12).21C2, (C22×C4).489D6, C2.2(C23×Dic3), (C2×C12).884C23, C22.38(S3×C23), C23.49(C2×Dic3), (C22×C6).409C23, C23.342(C22×S3), (C23×C6).102C22, (C23×Dic3).12C2, (C22×C12).569C22, (C2×Dic3).314C23, C22.29(C22×Dic3), (C22×Dic3).244C22, (C2×C12)⋊38(C2×C4), C2.3(S3×C22×C4), C22.77(S3×C2×C4), (C22×C6).141(C2×C4), (C2×C4).828(C22×S3), (C2×C6).206(C22×C4), SmallGroup(192,1341)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C3 — Dic3×C22×C4
Chief series
C1 — C3 — C6 — C2×C6 — C2×Dic3 — C22×Dic3 — C23×Dic3 — Dic3×C22×C4
Lower central
C3 — Dic3×C22×C4

Subgroups: 760 in 498 conjugacy classes, 367 normal (11 characteristic)
C1, C2, C2 [×14], C3, C4 [×8], C4 [×16], C22, C22 [×34], C6, C6 [×14], C2×C4 [×28], C2×C4 [×56], C23 [×15], Dic3 [×16], C12 [×8], C2×C6, C2×C6 [×34], C42 [×16], C22×C4 [×14], C22×C4 [×28], C24, C2×Dic3 [×56], C2×C12 [×28], C22×C6 [×15], C2×C42 [×12], C23×C4, C23×C4 [×2], C4×Dic3 [×16], C22×Dic3 [×28], C22×C12 [×14], C23×C6, C22×C42, C2×C4×Dic3 [×12], C23×Dic3 [×2], C23×C12, Dic3×C22×C4

Quotients:
C1, C2 [×15], C4 [×24], C22 [×35], S3, C2×C4 [×84], C23 [×15], Dic3 [×8], D6 [×7], C42 [×16], C22×C4 [×42], C24, C4×S3 [×8], C2×Dic3 [×28], C22×S3 [×7], C2×C42 [×12], C23×C4 [×3], C4×Dic3 [×16], S3×C2×C4 [×12], C22×Dic3 [×14], S3×C23, C22×C42, C2×C4×Dic3 [×12], S3×C22×C4 [×2], C23×Dic3, Dic3×C22×C4

Generators and relations
 G = < a,b,c,d,e | a2=b2=c4=d6=1, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Smallest permutation representation
►Regular action on 192 points
Generators in S192
(1 61)(2 62)(3 63)(4 64)(5 65)(6 66)(7 144)(8 139)(9 140)(10 141)(11 142)(12 143)(13 60)(14 55)(15 56)(16 57)(17 58)(18 59)(19 74)(20 75)(21 76)(22 77)(23 78)(24 73)(25 72)(26 67)(27 68)(28 69)(29 70)(30 71)(31 86)(32 87)(33 88)(34 89)(35 90)(36 85)(37 84)(38 79)(39 80)(40 81)(41 82)(42 83)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 96)(50 91)(51 92)(52 93)(53 94)(54 95)(103 159)(104 160)(105 161)(106 162)(107 157)(108 158)(109 155)(110 156)(111 151)(112 152)(113 153)(114 154)(115 171)(116 172)(117 173)(118 174)(119 169)(120 170)(121 167)(122 168)(123 163)(124 164)(125 165)(126 166)(127 183)(128 184)(129 185)(130 186)(131 181)(132 182)(133 179)(134 180)(135 175)(136 176)(137 177)(138 178)(145 191)(146 192)(147 187)(148 188)(149 189)(150 190)

(1 37)(2 38)(3 39)(4 40)(5 41)(6 42)(7 168)(8 163)(9 164)(10 165)(11 166)(12 167)(13 36)(14 31)(15 32)(16 33)(17 34)(18 35)(19 50)(20 51)(21 52)(22 53)(23 54)(24 49)(25 48)(26 43)(27 44)(28 45)(29 46)(30 47)(55 86)(56 87)(57 88)(58 89)(59 90)(60 85)(61 84)(62 79)(63 80)(64 81)(65 82)(66 83)(67 97)(68 98)(69 99)(70 100)(71 101)(72 102)(73 96)(74 91)(75 92)(76 93)(77 94)(78 95)(103 135)(104 136)(105 137)(106 138)(107 133)(108 134)(109 131)(110 132)(111 127)(112 128)(113 129)(114 130)(115 147)(116 148)(117 149)(118 150)(119 145)(120 146)(121 143)(122 144)(123 139)(124 140)(125 141)(126 142)(151 183)(152 184)(153 185)(154 186)(155 181)(156 182)(157 179)(158 180)(159 175)(160 176)(161 177)(162 178)(169 191)(170 192)(171 187)(172 188)(173 189)(174 190)

(1 28 16 24)(2 29 17 19)(3 30 18 20)(4 25 13 21)(5 26 14 22)(6 27 15 23)(7 182 189 177)(8 183 190 178)(9 184 191 179)(10 185 192 180)(11 186 187 175)(12 181 188 176)(31 53 41 43)(32 54 42 44)(33 49 37 45)(34 50 38 46)(35 51 39 47)(36 52 40 48)(55 77 65 67)(56 78 66 68)(57 73 61 69)(58 74 62 70)(59 75 63 71)(60 76 64 72)(79 100 89 91)(80 101 90 92)(81 102 85 93)(82 97 86 94)(83 98 87 95)(84 99 88 96)(103 126 114 115)(104 121 109 116)(105 122 110 117)(106 123 111 118)(107 124 112 119)(108 125 113 120)(127 150 138 139)(128 145 133 140)(129 146 134 141)(130 147 135 142)(131 148 136 143)(132 149 137 144)(151 174 162 163)(152 169 157 164)(153 170 158 165)(154 171 159 166)(155 172 160 167)(156 173 161 168)

(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)

(1 177 4 180)(2 176 5 179)(3 175 6 178)(7 25 10 28)(8 30 11 27)(9 29 12 26)(13 185 16 182)(14 184 17 181)(15 183 18 186)(19 188 22 191)(20 187 23 190)(21 192 24 189)(31 152 34 155)(32 151 35 154)(33 156 36 153)(37 161 40 158)(38 160 41 157)(39 159 42 162)(43 164 46 167)(44 163 47 166)(45 168 48 165)(49 173 52 170)(50 172 53 169)(51 171 54 174)(55 128 58 131)(56 127 59 130)(57 132 60 129)(61 137 64 134)(62 136 65 133)(63 135 66 138)(67 140 70 143)(68 139 71 142)(69 144 72 141)(73 149 76 146)(74 148 77 145)(75 147 78 150)(79 104 82 107)(80 103 83 106)(81 108 84 105)(85 113 88 110)(86 112 89 109)(87 111 90 114)(91 116 94 119)(92 115 95 118)(93 120 96 117)(97 124 100 121)(98 123 101 126)(99 122 102 125)
 
G:=sub<Sym(192)| (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,144)(8,139)(9,140)(10,141)(11,142)(12,143)(13,60)(14,55)(15,56)(16,57)(17,58)(18,59)(19,74)(20,75)(21,76)(22,77)(23,78)(24,73)(25,72)(26,67)(27,68)(28,69)(29,70)(30,71)(31,86)(32,87)(33,88)(34,89)(35,90)(36,85)(37,84)(38,79)(39,80)(40,81)(41,82)(42,83)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,96)(50,91)(51,92)(52,93)(53,94)(54,95)(103,159)(104,160)(105,161)(106,162)(107,157)(108,158)(109,155)(110,156)(111,151)(112,152)(113,153)(114,154)(115,171)(116,172)(117,173)(118,174)(119,169)(120,170)(121,167)(122,168)(123,163)(124,164)(125,165)(126,166)(127,183)(128,184)(129,185)(130,186)(131,181)(132,182)(133,179)(134,180)(135,175)(136,176)(137,177)(138,178)(145,191)(146,192)(147,187)(148,188)(149,189)(150,190), (1,37)(2,38)(3,39)(4,40)(5,41)(6,42)(7,168)(8,163)(9,164)(10,165)(11,166)(12,167)(13,36)(14,31)(15,32)(16,33)(17,34)(18,35)(19,50)(20,51)(21,52)(22,53)(23,54)(24,49)(25,48)(26,43)(27,44)(28,45)(29,46)(30,47)(55,86)(56,87)(57,88)(58,89)(59,90)(60,85)(61,84)(62,79)(63,80)(64,81)(65,82)(66,83)(67,97)(68,98)(69,99)(70,100)(71,101)(72,102)(73,96)(74,91)(75,92)(76,93)(77,94)(78,95)(103,135)(104,136)(105,137)(106,138)(107,133)(108,134)(109,131)(110,132)(111,127)(112,128)(113,129)(114,130)(115,147)(116,148)(117,149)(118,150)(119,145)(120,146)(121,143)(122,144)(123,139)(124,140)(125,141)(126,142)(151,183)(152,184)(153,185)(154,186)(155,181)(156,182)(157,179)(158,180)(159,175)(160,176)(161,177)(162,178)(169,191)(170,192)(171,187)(172,188)(173,189)(174,190), (1,28,16,24)(2,29,17,19)(3,30,18,20)(4,25,13,21)(5,26,14,22)(6,27,15,23)(7,182,189,177)(8,183,190,178)(9,184,191,179)(10,185,192,180)(11,186,187,175)(12,181,188,176)(31,53,41,43)(32,54,42,44)(33,49,37,45)(34,50,38,46)(35,51,39,47)(36,52,40,48)(55,77,65,67)(56,78,66,68)(57,73,61,69)(58,74,62,70)(59,75,63,71)(60,76,64,72)(79,100,89,91)(80,101,90,92)(81,102,85,93)(82,97,86,94)(83,98,87,95)(84,99,88,96)(103,126,114,115)(104,121,109,116)(105,122,110,117)(106,123,111,118)(107,124,112,119)(108,125,113,120)(127,150,138,139)(128,145,133,140)(129,146,134,141)(130,147,135,142)(131,148,136,143)(132,149,137,144)(151,174,162,163)(152,169,157,164)(153,170,158,165)(154,171,159,166)(155,172,160,167)(156,173,161,168), (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), (1,177,4,180)(2,176,5,179)(3,175,6,178)(7,25,10,28)(8,30,11,27)(9,29,12,26)(13,185,16,182)(14,184,17,181)(15,183,18,186)(19,188,22,191)(20,187,23,190)(21,192,24,189)(31,152,34,155)(32,151,35,154)(33,156,36,153)(37,161,40,158)(38,160,41,157)(39,159,42,162)(43,164,46,167)(44,163,47,166)(45,168,48,165)(49,173,52,170)(50,172,53,169)(51,171,54,174)(55,128,58,131)(56,127,59,130)(57,132,60,129)(61,137,64,134)(62,136,65,133)(63,135,66,138)(67,140,70,143)(68,139,71,142)(69,144,72,141)(73,149,76,146)(74,148,77,145)(75,147,78,150)(79,104,82,107)(80,103,83,106)(81,108,84,105)(85,113,88,110)(86,112,89,109)(87,111,90,114)(91,116,94,119)(92,115,95,118)(93,120,96,117)(97,124,100,121)(98,123,101,126)(99,122,102,125)>;
 
G:=Group( (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,144)(8,139)(9,140)(10,141)(11,142)(12,143)(13,60)(14,55)(15,56)(16,57)(17,58)(18,59)(19,74)(20,75)(21,76)(22,77)(23,78)(24,73)(25,72)(26,67)(27,68)(28,69)(29,70)(30,71)(31,86)(32,87)(33,88)(34,89)(35,90)(36,85)(37,84)(38,79)(39,80)(40,81)(41,82)(42,83)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,96)(50,91)(51,92)(52,93)(53,94)(54,95)(103,159)(104,160)(105,161)(106,162)(107,157)(108,158)(109,155)(110,156)(111,151)(112,152)(113,153)(114,154)(115,171)(116,172)(117,173)(118,174)(119,169)(120,170)(121,167)(122,168)(123,163)(124,164)(125,165)(126,166)(127,183)(128,184)(129,185)(130,186)(131,181)(132,182)(133,179)(134,180)(135,175)(136,176)(137,177)(138,178)(145,191)(146,192)(147,187)(148,188)(149,189)(150,190), (1,37)(2,38)(3,39)(4,40)(5,41)(6,42)(7,168)(8,163)(9,164)(10,165)(11,166)(12,167)(13,36)(14,31)(15,32)(16,33)(17,34)(18,35)(19,50)(20,51)(21,52)(22,53)(23,54)(24,49)(25,48)(26,43)(27,44)(28,45)(29,46)(30,47)(55,86)(56,87)(57,88)(58,89)(59,90)(60,85)(61,84)(62,79)(63,80)(64,81)(65,82)(66,83)(67,97)(68,98)(69,99)(70,100)(71,101)(72,102)(73,96)(74,91)(75,92)(76,93)(77,94)(78,95)(103,135)(104,136)(105,137)(106,138)(107,133)(108,134)(109,131)(110,132)(111,127)(112,128)(113,129)(114,130)(115,147)(116,148)(117,149)(118,150)(119,145)(120,146)(121,143)(122,144)(123,139)(124,140)(125,141)(126,142)(151,183)(152,184)(153,185)(154,186)(155,181)(156,182)(157,179)(158,180)(159,175)(160,176)(161,177)(162,178)(169,191)(170,192)(171,187)(172,188)(173,189)(174,190), (1,28,16,24)(2,29,17,19)(3,30,18,20)(4,25,13,21)(5,26,14,22)(6,27,15,23)(7,182,189,177)(8,183,190,178)(9,184,191,179)(10,185,192,180)(11,186,187,175)(12,181,188,176)(31,53,41,43)(32,54,42,44)(33,49,37,45)(34,50,38,46)(35,51,39,47)(36,52,40,48)(55,77,65,67)(56,78,66,68)(57,73,61,69)(58,74,62,70)(59,75,63,71)(60,76,64,72)(79,100,89,91)(80,101,90,92)(81,102,85,93)(82,97,86,94)(83,98,87,95)(84,99,88,96)(103,126,114,115)(104,121,109,116)(105,122,110,117)(106,123,111,118)(107,124,112,119)(108,125,113,120)(127,150,138,139)(128,145,133,140)(129,146,134,141)(130,147,135,142)(131,148,136,143)(132,149,137,144)(151,174,162,163)(152,169,157,164)(153,170,158,165)(154,171,159,166)(155,172,160,167)(156,173,161,168), (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), (1,177,4,180)(2,176,5,179)(3,175,6,178)(7,25,10,28)(8,30,11,27)(9,29,12,26)(13,185,16,182)(14,184,17,181)(15,183,18,186)(19,188,22,191)(20,187,23,190)(21,192,24,189)(31,152,34,155)(32,151,35,154)(33,156,36,153)(37,161,40,158)(38,160,41,157)(39,159,42,162)(43,164,46,167)(44,163,47,166)(45,168,48,165)(49,173,52,170)(50,172,53,169)(51,171,54,174)(55,128,58,131)(56,127,59,130)(57,132,60,129)(61,137,64,134)(62,136,65,133)(63,135,66,138)(67,140,70,143)(68,139,71,142)(69,144,72,141)(73,149,76,146)(74,148,77,145)(75,147,78,150)(79,104,82,107)(80,103,83,106)(81,108,84,105)(85,113,88,110)(86,112,89,109)(87,111,90,114)(91,116,94,119)(92,115,95,118)(93,120,96,117)(97,124,100,121)(98,123,101,126)(99,122,102,125) );
 
G=PermutationGroup([(1,61),(2,62),(3,63),(4,64),(5,65),(6,66),(7,144),(8,139),(9,140),(10,141),(11,142),(12,143),(13,60),(14,55),(15,56),(16,57),(17,58),(18,59),(19,74),(20,75),(21,76),(22,77),(23,78),(24,73),(25,72),(26,67),(27,68),(28,69),(29,70),(30,71),(31,86),(32,87),(33,88),(34,89),(35,90),(36,85),(37,84),(38,79),(39,80),(40,81),(41,82),(42,83),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,96),(50,91),(51,92),(52,93),(53,94),(54,95),(103,159),(104,160),(105,161),(106,162),(107,157),(108,158),(109,155),(110,156),(111,151),(112,152),(113,153),(114,154),(115,171),(116,172),(117,173),(118,174),(119,169),(120,170),(121,167),(122,168),(123,163),(124,164),(125,165),(126,166),(127,183),(128,184),(129,185),(130,186),(131,181),(132,182),(133,179),(134,180),(135,175),(136,176),(137,177),(138,178),(145,191),(146,192),(147,187),(148,188),(149,189),(150,190)], [(1,37),(2,38),(3,39),(4,40),(5,41),(6,42),(7,168),(8,163),(9,164),(10,165),(11,166),(12,167),(13,36),(14,31),(15,32),(16,33),(17,34),(18,35),(19,50),(20,51),(21,52),(22,53),(23,54),(24,49),(25,48),(26,43),(27,44),(28,45),(29,46),(30,47),(55,86),(56,87),(57,88),(58,89),(59,90),(60,85),(61,84),(62,79),(63,80),(64,81),(65,82),(66,83),(67,97),(68,98),(69,99),(70,100),(71,101),(72,102),(73,96),(74,91),(75,92),(76,93),(77,94),(78,95),(103,135),(104,136),(105,137),(106,138),(107,133),(108,134),(109,131),(110,132),(111,127),(112,128),(113,129),(114,130),(115,147),(116,148),(117,149),(118,150),(119,145),(120,146),(121,143),(122,144),(123,139),(124,140),(125,141),(126,142),(151,183),(152,184),(153,185),(154,186),(155,181),(156,182),(157,179),(158,180),(159,175),(160,176),(161,177),(162,178),(169,191),(170,192),(171,187),(172,188),(173,189),(174,190)], [(1,28,16,24),(2,29,17,19),(3,30,18,20),(4,25,13,21),(5,26,14,22),(6,27,15,23),(7,182,189,177),(8,183,190,178),(9,184,191,179),(10,185,192,180),(11,186,187,175),(12,181,188,176),(31,53,41,43),(32,54,42,44),(33,49,37,45),(34,50,38,46),(35,51,39,47),(36,52,40,48),(55,77,65,67),(56,78,66,68),(57,73,61,69),(58,74,62,70),(59,75,63,71),(60,76,64,72),(79,100,89,91),(80,101,90,92),(81,102,85,93),(82,97,86,94),(83,98,87,95),(84,99,88,96),(103,126,114,115),(104,121,109,116),(105,122,110,117),(106,123,111,118),(107,124,112,119),(108,125,113,120),(127,150,138,139),(128,145,133,140),(129,146,134,141),(130,147,135,142),(131,148,136,143),(132,149,137,144),(151,174,162,163),(152,169,157,164),(153,170,158,165),(154,171,159,166),(155,172,160,167),(156,173,161,168)], [(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)], [(1,177,4,180),(2,176,5,179),(3,175,6,178),(7,25,10,28),(8,30,11,27),(9,29,12,26),(13,185,16,182),(14,184,17,181),(15,183,18,186),(19,188,22,191),(20,187,23,190),(21,192,24,189),(31,152,34,155),(32,151,35,154),(33,156,36,153),(37,161,40,158),(38,160,41,157),(39,159,42,162),(43,164,46,167),(44,163,47,166),(45,168,48,165),(49,173,52,170),(50,172,53,169),(51,171,54,174),(55,128,58,131),(56,127,59,130),(57,132,60,129),(61,137,64,134),(62,136,65,133),(63,135,66,138),(67,140,70,143),(68,139,71,142),(69,144,72,141),(73,149,76,146),(74,148,77,145),(75,147,78,150),(79,104,82,107),(80,103,83,106),(81,108,84,105),(85,113,88,110),(86,112,89,109),(87,111,90,114),(91,116,94,119),(92,115,95,118),(93,120,96,117),(97,124,100,121),(98,123,101,126),(99,122,102,125)])
 

Matrix representation ►G ⊆ GL5(𝔽13)

10000
01000
00100
000120
000012
,
120000
01000
001200
00010
00001
,
10000
05000
001200
000120
000012
,
120000
012000
00100
000121
000120
,
80000
08000
00100
0001010
00073

G:=sub<GL(5,GF(13))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,0,12],[12,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,5,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,12],[12,0,0,0,0,0,12,0,0,0,0,0,1,0,0,0,0,0,12,12,0,0,0,1,0],[8,0,0,0,0,0,8,0,0,0,0,0,1,0,0,0,0,0,10,7,0,0,0,10,3] >;
 

96 conjugacy classes

class 1 2A···2O 3 4A···4P4Q···4AV6A···6O12A···12P
order12···234···44···46···612···12
size11···121···13···32···22···2

96 irreducible representations

dim11111122222
type+++++-++
imageC1C2C2C2C4C4S3Dic3D6D6C4×S3
kernelDic3×C22×C4C2×C4×Dic3C23×Dic3C23×C12C22×Dic3C22×C12C23×C4C22×C4C22×C4C24C23
# reps112213216186116

In GAP, Magma, Sage, TeX 

Dic_3\times C_2^2\times C_4
 
% in TeX
 
G:=Group("Dic3xC2^2xC4");
 
// GroupNames label
 
G:=SmallGroup(192,1341);
 
// by ID
 
G=gap.SmallGroup(192,1341);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,136,6278]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^6=1,e^2=d^3,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,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

׿
×
⋊
ℤ
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