direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic3.Q8, C4⋊C4.259D6, (C2×C6).42C24, Dic3.1(C2×Q8), C6⋊2(C42.C2), C22.31(S3×Q8), C6.22(C22×Q8), (C2×Dic3).20Q8, (C22×C4).190D6, (C2×C12).133C23, C22.80(S3×C23), C22.75(C4○D12), C4⋊Dic3.291C22, C23.332(C22×S3), (C22×C6).391C23, C22.71(D4⋊2S3), Dic3⋊C4.103C22, (C22×C12).356C22, (C4×Dic3).290C22, (C2×Dic3).182C23, (C22×Dic3).207C22, C2.6(C2×S3×Q8), (C6×C4⋊C4).18C2, (C2×C4⋊C4).25S3, C3⋊2(C2×C42.C2), C6.18(C2×C4○D4), (C2×C6).91(C2×Q8), C2.20(C2×C4○D12), (C2×C4×Dic3).41C2, C2.13(C2×D4⋊2S3), (C2×C4⋊Dic3).26C2, (C2×C6).105(C4○D4), (C3×C4⋊C4).291C22, (C2×Dic3⋊C4).29C2, (C2×C4).138(C22×S3), SmallGroup(192,1057)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic3.Q8
G = < a,b,c,d,e | a2=b6=d4=1, c2=b3, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, dcd-1=b3c, ce=ec, ede-1=b3d-1 >
Subgroups: 440 in 226 conjugacy classes, 119 normal (31 characteristic)
C1, C2, C2, C3, C4, C22, C22, C6, C6, C2×C4, C2×C4, C23, Dic3, Dic3, C12, C2×C6, C2×C6, C42, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×C6, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C42.C2, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C3×C4⋊C4, C22×Dic3, C22×C12, C2×C42.C2, Dic3.Q8, C2×C4×Dic3, C2×Dic3⋊C4, C2×C4⋊Dic3, C6×C4⋊C4, C2×Dic3.Q8
Quotients: C1, C2, C22, S3, Q8, C23, D6, C2×Q8, C4○D4, C24, C22×S3, C42.C2, C22×Q8, C2×C4○D4, C4○D12, D4⋊2S3, S3×Q8, S3×C23, C2×C42.C2, Dic3.Q8, C2×C4○D12, C2×D4⋊2S3, C2×S3×Q8, C2×Dic3.Q8
►Regular action on 192 points
Generators in S192
(1 58)(2 59)(3 60)(4 55)(5 56)(6 57)(7 143)(8 144)(9 139)(10 140)(11 141)(12 142)(13 63)(14 64)(15 65)(16 66)(17 61)(18 62)(19 77)(20 78)(21 73)(22 74)(23 75)(24 76)(25 69)(26 70)(27 71)(28 72)(29 67)(30 68)(31 89)(32 90)(33 85)(34 86)(35 87)(36 88)(37 81)(38 82)(39 83)(40 84)(41 79)(42 80)(43 102)(44 97)(45 98)(46 99)(47 100)(48 101)(49 93)(50 94)(51 95)(52 96)(53 91)(54 92)(103 162)(104 157)(105 158)(106 159)(107 160)(108 161)(109 152)(110 153)(111 154)(112 155)(113 156)(114 151)(115 174)(116 169)(117 170)(118 171)(119 172)(120 173)(121 164)(122 165)(123 166)(124 167)(125 168)(126 163)(127 186)(128 181)(129 182)(130 183)(131 184)(132 185)(133 176)(134 177)(135 178)(136 179)(137 180)(138 175)(145 188)(146 189)(147 190)(148 191)(149 192)(150 187)
(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)
(1 131 4 128)(2 130 5 127)(3 129 6 132)(7 67 10 70)(8 72 11 69)(9 71 12 68)(13 135 16 138)(14 134 17 137)(15 133 18 136)(19 145 22 148)(20 150 23 147)(21 149 24 146)(25 144 28 141)(26 143 29 140)(27 142 30 139)(31 107 34 104)(32 106 35 103)(33 105 36 108)(37 110 40 113)(38 109 41 112)(39 114 42 111)(43 119 46 116)(44 118 47 115)(45 117 48 120)(49 122 52 125)(50 121 53 124)(51 126 54 123)(55 181 58 184)(56 186 59 183)(57 185 60 182)(61 180 64 177)(62 179 65 176)(63 178 66 175)(73 192 76 189)(74 191 77 188)(75 190 78 187)(79 155 82 152)(80 154 83 151)(81 153 84 156)(85 158 88 161)(86 157 89 160)(87 162 90 159)(91 167 94 164)(92 166 95 163)(93 165 96 168)(97 171 100 174)(98 170 101 173)(99 169 102 172)
(1 77 18 67)(2 78 13 68)(3 73 14 69)(4 74 15 70)(5 75 16 71)(6 76 17 72)(7 131 191 136)(8 132 192 137)(9 127 187 138)(10 128 188 133)(11 129 189 134)(12 130 190 135)(19 62 29 58)(20 63 30 59)(21 64 25 60)(22 65 26 55)(23 66 27 56)(24 61 28 57)(31 99 41 94)(32 100 42 95)(33 101 37 96)(34 102 38 91)(35 97 39 92)(36 98 40 93)(43 82 53 86)(44 83 54 87)(45 84 49 88)(46 79 50 89)(47 80 51 90)(48 81 52 85)(103 174 114 163)(104 169 109 164)(105 170 110 165)(106 171 111 166)(107 172 112 167)(108 173 113 168)(115 151 126 162)(116 152 121 157)(117 153 122 158)(118 154 123 159)(119 155 124 160)(120 156 125 161)(139 186 150 175)(140 181 145 176)(141 182 146 177)(142 183 147 178)(143 184 148 179)(144 185 149 180)
(1 104 18 109)(2 103 13 114)(3 108 14 113)(4 107 15 112)(5 106 16 111)(6 105 17 110)(7 102 191 91)(8 101 192 96)(9 100 187 95)(10 99 188 94)(11 98 189 93)(12 97 190 92)(19 124 29 119)(20 123 30 118)(21 122 25 117)(22 121 26 116)(23 126 27 115)(24 125 28 120)(31 136 41 131)(32 135 42 130)(33 134 37 129)(34 133 38 128)(35 138 39 127)(36 137 40 132)(43 148 53 143)(44 147 54 142)(45 146 49 141)(46 145 50 140)(47 150 51 139)(48 149 52 144)(55 160 65 155)(56 159 66 154)(57 158 61 153)(58 157 62 152)(59 162 63 151)(60 161 64 156)(67 172 77 167)(68 171 78 166)(69 170 73 165)(70 169 74 164)(71 174 75 163)(72 173 76 168)(79 184 89 179)(80 183 90 178)(81 182 85 177)(82 181 86 176)(83 186 87 175)(84 185 88 180)
G:=sub<Sym(192)| (1,58)(2,59)(3,60)(4,55)(5,56)(6,57)(7,143)(8,144)(9,139)(10,140)(11,141)(12,142)(13,63)(14,64)(15,65)(16,66)(17,61)(18,62)(19,77)(20,78)(21,73)(22,74)(23,75)(24,76)(25,69)(26,70)(27,71)(28,72)(29,67)(30,68)(31,89)(32,90)(33,85)(34,86)(35,87)(36,88)(37,81)(38,82)(39,83)(40,84)(41,79)(42,80)(43,102)(44,97)(45,98)(46,99)(47,100)(48,101)(49,93)(50,94)(51,95)(52,96)(53,91)(54,92)(103,162)(104,157)(105,158)(106,159)(107,160)(108,161)(109,152)(110,153)(111,154)(112,155)(113,156)(114,151)(115,174)(116,169)(117,170)(118,171)(119,172)(120,173)(121,164)(122,165)(123,166)(124,167)(125,168)(126,163)(127,186)(128,181)(129,182)(130,183)(131,184)(132,185)(133,176)(134,177)(135,178)(136,179)(137,180)(138,175)(145,188)(146,189)(147,190)(148,191)(149,192)(150,187), (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), (1,131,4,128)(2,130,5,127)(3,129,6,132)(7,67,10,70)(8,72,11,69)(9,71,12,68)(13,135,16,138)(14,134,17,137)(15,133,18,136)(19,145,22,148)(20,150,23,147)(21,149,24,146)(25,144,28,141)(26,143,29,140)(27,142,30,139)(31,107,34,104)(32,106,35,103)(33,105,36,108)(37,110,40,113)(38,109,41,112)(39,114,42,111)(43,119,46,116)(44,118,47,115)(45,117,48,120)(49,122,52,125)(50,121,53,124)(51,126,54,123)(55,181,58,184)(56,186,59,183)(57,185,60,182)(61,180,64,177)(62,179,65,176)(63,178,66,175)(73,192,76,189)(74,191,77,188)(75,190,78,187)(79,155,82,152)(80,154,83,151)(81,153,84,156)(85,158,88,161)(86,157,89,160)(87,162,90,159)(91,167,94,164)(92,166,95,163)(93,165,96,168)(97,171,100,174)(98,170,101,173)(99,169,102,172), (1,77,18,67)(2,78,13,68)(3,73,14,69)(4,74,15,70)(5,75,16,71)(6,76,17,72)(7,131,191,136)(8,132,192,137)(9,127,187,138)(10,128,188,133)(11,129,189,134)(12,130,190,135)(19,62,29,58)(20,63,30,59)(21,64,25,60)(22,65,26,55)(23,66,27,56)(24,61,28,57)(31,99,41,94)(32,100,42,95)(33,101,37,96)(34,102,38,91)(35,97,39,92)(36,98,40,93)(43,82,53,86)(44,83,54,87)(45,84,49,88)(46,79,50,89)(47,80,51,90)(48,81,52,85)(103,174,114,163)(104,169,109,164)(105,170,110,165)(106,171,111,166)(107,172,112,167)(108,173,113,168)(115,151,126,162)(116,152,121,157)(117,153,122,158)(118,154,123,159)(119,155,124,160)(120,156,125,161)(139,186,150,175)(140,181,145,176)(141,182,146,177)(142,183,147,178)(143,184,148,179)(144,185,149,180), (1,104,18,109)(2,103,13,114)(3,108,14,113)(4,107,15,112)(5,106,16,111)(6,105,17,110)(7,102,191,91)(8,101,192,96)(9,100,187,95)(10,99,188,94)(11,98,189,93)(12,97,190,92)(19,124,29,119)(20,123,30,118)(21,122,25,117)(22,121,26,116)(23,126,27,115)(24,125,28,120)(31,136,41,131)(32,135,42,130)(33,134,37,129)(34,133,38,128)(35,138,39,127)(36,137,40,132)(43,148,53,143)(44,147,54,142)(45,146,49,141)(46,145,50,140)(47,150,51,139)(48,149,52,144)(55,160,65,155)(56,159,66,154)(57,158,61,153)(58,157,62,152)(59,162,63,151)(60,161,64,156)(67,172,77,167)(68,171,78,166)(69,170,73,165)(70,169,74,164)(71,174,75,163)(72,173,76,168)(79,184,89,179)(80,183,90,178)(81,182,85,177)(82,181,86,176)(83,186,87,175)(84,185,88,180)>;
G:=Group( (1,58)(2,59)(3,60)(4,55)(5,56)(6,57)(7,143)(8,144)(9,139)(10,140)(11,141)(12,142)(13,63)(14,64)(15,65)(16,66)(17,61)(18,62)(19,77)(20,78)(21,73)(22,74)(23,75)(24,76)(25,69)(26,70)(27,71)(28,72)(29,67)(30,68)(31,89)(32,90)(33,85)(34,86)(35,87)(36,88)(37,81)(38,82)(39,83)(40,84)(41,79)(42,80)(43,102)(44,97)(45,98)(46,99)(47,100)(48,101)(49,93)(50,94)(51,95)(52,96)(53,91)(54,92)(103,162)(104,157)(105,158)(106,159)(107,160)(108,161)(109,152)(110,153)(111,154)(112,155)(113,156)(114,151)(115,174)(116,169)(117,170)(118,171)(119,172)(120,173)(121,164)(122,165)(123,166)(124,167)(125,168)(126,163)(127,186)(128,181)(129,182)(130,183)(131,184)(132,185)(133,176)(134,177)(135,178)(136,179)(137,180)(138,175)(145,188)(146,189)(147,190)(148,191)(149,192)(150,187), (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), (1,131,4,128)(2,130,5,127)(3,129,6,132)(7,67,10,70)(8,72,11,69)(9,71,12,68)(13,135,16,138)(14,134,17,137)(15,133,18,136)(19,145,22,148)(20,150,23,147)(21,149,24,146)(25,144,28,141)(26,143,29,140)(27,142,30,139)(31,107,34,104)(32,106,35,103)(33,105,36,108)(37,110,40,113)(38,109,41,112)(39,114,42,111)(43,119,46,116)(44,118,47,115)(45,117,48,120)(49,122,52,125)(50,121,53,124)(51,126,54,123)(55,181,58,184)(56,186,59,183)(57,185,60,182)(61,180,64,177)(62,179,65,176)(63,178,66,175)(73,192,76,189)(74,191,77,188)(75,190,78,187)(79,155,82,152)(80,154,83,151)(81,153,84,156)(85,158,88,161)(86,157,89,160)(87,162,90,159)(91,167,94,164)(92,166,95,163)(93,165,96,168)(97,171,100,174)(98,170,101,173)(99,169,102,172), (1,77,18,67)(2,78,13,68)(3,73,14,69)(4,74,15,70)(5,75,16,71)(6,76,17,72)(7,131,191,136)(8,132,192,137)(9,127,187,138)(10,128,188,133)(11,129,189,134)(12,130,190,135)(19,62,29,58)(20,63,30,59)(21,64,25,60)(22,65,26,55)(23,66,27,56)(24,61,28,57)(31,99,41,94)(32,100,42,95)(33,101,37,96)(34,102,38,91)(35,97,39,92)(36,98,40,93)(43,82,53,86)(44,83,54,87)(45,84,49,88)(46,79,50,89)(47,80,51,90)(48,81,52,85)(103,174,114,163)(104,169,109,164)(105,170,110,165)(106,171,111,166)(107,172,112,167)(108,173,113,168)(115,151,126,162)(116,152,121,157)(117,153,122,158)(118,154,123,159)(119,155,124,160)(120,156,125,161)(139,186,150,175)(140,181,145,176)(141,182,146,177)(142,183,147,178)(143,184,148,179)(144,185,149,180), (1,104,18,109)(2,103,13,114)(3,108,14,113)(4,107,15,112)(5,106,16,111)(6,105,17,110)(7,102,191,91)(8,101,192,96)(9,100,187,95)(10,99,188,94)(11,98,189,93)(12,97,190,92)(19,124,29,119)(20,123,30,118)(21,122,25,117)(22,121,26,116)(23,126,27,115)(24,125,28,120)(31,136,41,131)(32,135,42,130)(33,134,37,129)(34,133,38,128)(35,138,39,127)(36,137,40,132)(43,148,53,143)(44,147,54,142)(45,146,49,141)(46,145,50,140)(47,150,51,139)(48,149,52,144)(55,160,65,155)(56,159,66,154)(57,158,61,153)(58,157,62,152)(59,162,63,151)(60,161,64,156)(67,172,77,167)(68,171,78,166)(69,170,73,165)(70,169,74,164)(71,174,75,163)(72,173,76,168)(79,184,89,179)(80,183,90,178)(81,182,85,177)(82,181,86,176)(83,186,87,175)(84,185,88,180) );
G=PermutationGroup([[(1,58),(2,59),(3,60),(4,55),(5,56),(6,57),(7,143),(8,144),(9,139),(10,140),(11,141),(12,142),(13,63),(14,64),(15,65),(16,66),(17,61),(18,62),(19,77),(20,78),(21,73),(22,74),(23,75),(24,76),(25,69),(26,70),(27,71),(28,72),(29,67),(30,68),(31,89),(32,90),(33,85),(34,86),(35,87),(36,88),(37,81),(38,82),(39,83),(40,84),(41,79),(42,80),(43,102),(44,97),(45,98),(46,99),(47,100),(48,101),(49,93),(50,94),(51,95),(52,96),(53,91),(54,92),(103,162),(104,157),(105,158),(106,159),(107,160),(108,161),(109,152),(110,153),(111,154),(112,155),(113,156),(114,151),(115,174),(116,169),(117,170),(118,171),(119,172),(120,173),(121,164),(122,165),(123,166),(124,167),(125,168),(126,163),(127,186),(128,181),(129,182),(130,183),(131,184),(132,185),(133,176),(134,177),(135,178),(136,179),(137,180),(138,175),(145,188),(146,189),(147,190),(148,191),(149,192),(150,187)], [(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)], [(1,131,4,128),(2,130,5,127),(3,129,6,132),(7,67,10,70),(8,72,11,69),(9,71,12,68),(13,135,16,138),(14,134,17,137),(15,133,18,136),(19,145,22,148),(20,150,23,147),(21,149,24,146),(25,144,28,141),(26,143,29,140),(27,142,30,139),(31,107,34,104),(32,106,35,103),(33,105,36,108),(37,110,40,113),(38,109,41,112),(39,114,42,111),(43,119,46,116),(44,118,47,115),(45,117,48,120),(49,122,52,125),(50,121,53,124),(51,126,54,123),(55,181,58,184),(56,186,59,183),(57,185,60,182),(61,180,64,177),(62,179,65,176),(63,178,66,175),(73,192,76,189),(74,191,77,188),(75,190,78,187),(79,155,82,152),(80,154,83,151),(81,153,84,156),(85,158,88,161),(86,157,89,160),(87,162,90,159),(91,167,94,164),(92,166,95,163),(93,165,96,168),(97,171,100,174),(98,170,101,173),(99,169,102,172)], [(1,77,18,67),(2,78,13,68),(3,73,14,69),(4,74,15,70),(5,75,16,71),(6,76,17,72),(7,131,191,136),(8,132,192,137),(9,127,187,138),(10,128,188,133),(11,129,189,134),(12,130,190,135),(19,62,29,58),(20,63,30,59),(21,64,25,60),(22,65,26,55),(23,66,27,56),(24,61,28,57),(31,99,41,94),(32,100,42,95),(33,101,37,96),(34,102,38,91),(35,97,39,92),(36,98,40,93),(43,82,53,86),(44,83,54,87),(45,84,49,88),(46,79,50,89),(47,80,51,90),(48,81,52,85),(103,174,114,163),(104,169,109,164),(105,170,110,165),(106,171,111,166),(107,172,112,167),(108,173,113,168),(115,151,126,162),(116,152,121,157),(117,153,122,158),(118,154,123,159),(119,155,124,160),(120,156,125,161),(139,186,150,175),(140,181,145,176),(141,182,146,177),(142,183,147,178),(143,184,148,179),(144,185,149,180)], [(1,104,18,109),(2,103,13,114),(3,108,14,113),(4,107,15,112),(5,106,16,111),(6,105,17,110),(7,102,191,91),(8,101,192,96),(9,100,187,95),(10,99,188,94),(11,98,189,93),(12,97,190,92),(19,124,29,119),(20,123,30,118),(21,122,25,117),(22,121,26,116),(23,126,27,115),(24,125,28,120),(31,136,41,131),(32,135,42,130),(33,134,37,129),(34,133,38,128),(35,138,39,127),(36,137,40,132),(43,148,53,143),(44,147,54,142),(45,146,49,141),(46,145,50,140),(47,150,51,139),(48,149,52,144),(55,160,65,155),(56,159,66,154),(57,158,61,153),(58,157,62,152),(59,162,63,151),(60,161,64,156),(67,172,77,167),(68,171,78,166),(69,170,73,165),(70,169,74,164),(71,174,75,163),(72,173,76,168),(79,184,89,179),(80,183,90,178),(81,182,85,177),(82,181,86,176),(83,186,87,175),(84,185,88,180)]])
48 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 4T | 6A | ··· | 6G | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | 12 | 12 | 12 | 2 | ··· | 2 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | Q8 | D6 | D6 | C4○D4 | C4○D12 | D4⋊2S3 | S3×Q8 |
| kernel | C2×Dic3.Q8 | Dic3.Q8 | C2×C4×Dic3 | C2×Dic3⋊C4 | C2×C4⋊Dic3 | C6×C4⋊C4 | C2×C4⋊C4 | C2×Dic3 | C4⋊C4 | C22×C4 | C2×C6 | C22 | C22 | C22 |
| # reps | 1 | 8 | 1 | 4 | 1 | 1 | 1 | 4 | 4 | 3 | 8 | 8 | 2 | 2 |
Matrix representation of C2×Dic3.Q8 ►in GL6(𝔽13)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 9 | 3 | 0 | 0 | 0 | 0 |
| 3 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 2 | 0 | 0 |
| 0 | 0 | 12 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 8 | 0 | 0 | 0 | 0 | 0 |
| 0 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 8 | 0 | 0 |
| 0 | 0 | 3 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(13))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,12,12],[9,3,0,0,0,0,3,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,12,0,0,0,0,12,0],[0,1,0,0,0,0,12,0,0,0,0,0,0,0,1,12,0,0,0,0,2,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[8,0,0,0,0,0,0,8,0,0,0,0,0,0,1,3,0,0,0,0,8,12,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C2×Dic3.Q8 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_3.Q_8 % in TeX
G:=Group("C2xDic3.Q8"); // GroupNames label
G:=SmallGroup(192,1057);
// by ID
G=gap.SmallGroup(192,1057);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,100,675,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^6=d^4=1,c^2=b^3,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=b^3*c,c*e=e*c,e*d*e^-1=b^3*d^-1>;
// generators/relations