direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C4⋊Dic3, C24.88D6, C23.68D12, C23.21Dic6, C12⋊8(C22×C4), (C22×C12)⋊15C4, (C23×C4).17S3, C6.42(C23×C4), C4⋊2(C22×Dic3), C2.2(C22×D12), C6.31(C22×D4), (C22×C6).28Q8, C6.20(C22×Q8), (C2×C6).283C24, (C23×C12).13C2, (C22×C4)⋊11Dic3, (C22×C6).148D4, (C22×C4).463D6, C22.75(C2×D12), C2.3(C22×Dic6), C2.4(C23×Dic3), (C2×C12).789C23, C22.40(S3×C23), C23.50(C2×Dic3), C22.39(C2×Dic6), C23.344(C22×S3), (C23×C6).105C22, (C22×C6).412C23, (C23×Dic3).10C2, (C22×C12).529C22, (C2×Dic3).277C23, C22.30(C22×Dic3), (C22×Dic3).228C22, C6⋊3(C2×C4⋊C4), C3⋊3(C22×C4⋊C4), (C2×C6)⋊9(C4⋊C4), (C2×C12)⋊36(C2×C4), (C2×C6).54(C2×Q8), (C2×C4)⋊10(C2×Dic3), (C2×C6).181(C2×D4), (C2×C6).207(C22×C4), (C2×C4).739(C22×S3), (C22×C6).142(C2×C4), SmallGroup(192,1344)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22×C4⋊Dic3
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, ece-1=c-1, ede-1=d-1 >
Subgroups: 760 in 418 conjugacy classes, 287 normal (15 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C2×C4, C2×C4, C23, Dic3, C12, C2×C6, C2×C6, C4⋊C4, C22×C4, C22×C4, C24, C2×Dic3, C2×Dic3, C2×C12, C22×C6, C2×C4⋊C4, C23×C4, C23×C4, C4⋊Dic3, C22×Dic3, C22×Dic3, C22×C12, C23×C6, C22×C4⋊C4, C2×C4⋊Dic3, C23×Dic3, C23×C12, C22×C4⋊Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, C23, Dic3, D6, C4⋊C4, C22×C4, C2×D4, C2×Q8, C24, Dic6, D12, C2×Dic3, C22×S3, C2×C4⋊C4, C23×C4, C22×D4, C22×Q8, C4⋊Dic3, C2×Dic6, C2×D12, C22×Dic3, S3×C23, C22×C4⋊C4, C2×C4⋊Dic3, C22×Dic6, C22×D12, C23×Dic3, C22×C4⋊Dic3
►Regular action on 192 points
Generators in S192
(1 65)(2 66)(3 61)(4 62)(5 63)(6 64)(7 144)(8 139)(9 140)(10 141)(11 142)(12 143)(13 56)(14 57)(15 58)(16 59)(17 60)(18 55)(19 78)(20 73)(21 74)(22 75)(23 76)(24 77)(25 68)(26 69)(27 70)(28 71)(29 72)(30 67)(31 90)(32 85)(33 86)(34 87)(35 88)(36 89)(37 80)(38 81)(39 82)(40 83)(41 84)(42 79)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 92)(50 93)(51 94)(52 95)(53 96)(54 91)(103 161)(104 162)(105 157)(106 158)(107 159)(108 160)(109 153)(110 154)(111 155)(112 156)(113 151)(114 152)(115 173)(116 174)(117 169)(118 170)(119 171)(120 172)(121 165)(122 166)(123 167)(124 168)(125 163)(126 164)(127 185)(128 186)(129 181)(130 182)(131 183)(132 184)(133 177)(134 178)(135 179)(136 180)(137 175)(138 176)(145 189)(146 190)(147 191)(148 192)(149 187)(150 188)
(1 33)(2 34)(3 35)(4 36)(5 31)(6 32)(7 169)(8 170)(9 171)(10 172)(11 173)(12 174)(13 40)(14 41)(15 42)(16 37)(17 38)(18 39)(19 46)(20 47)(21 48)(22 43)(23 44)(24 45)(25 52)(26 53)(27 54)(28 49)(29 50)(30 51)(55 82)(56 83)(57 84)(58 79)(59 80)(60 81)(61 88)(62 89)(63 90)(64 85)(65 86)(66 87)(67 94)(68 95)(69 96)(70 91)(71 92)(72 93)(73 101)(74 102)(75 97)(76 98)(77 99)(78 100)(103 130)(104 131)(105 132)(106 127)(107 128)(108 129)(109 136)(110 137)(111 138)(112 133)(113 134)(114 135)(115 142)(116 143)(117 144)(118 139)(119 140)(120 141)(121 148)(122 149)(123 150)(124 145)(125 146)(126 147)(151 178)(152 179)(153 180)(154 175)(155 176)(156 177)(157 184)(158 185)(159 186)(160 181)(161 182)(162 183)(163 190)(164 191)(165 192)(166 187)(167 188)(168 189)
(1 102 17 96)(2 97 18 91)(3 98 13 92)(4 99 14 93)(5 100 15 94)(6 101 16 95)(7 108 192 112)(8 103 187 113)(9 104 188 114)(10 105 189 109)(11 106 190 110)(12 107 191 111)(19 79 30 90)(20 80 25 85)(21 81 26 86)(22 82 27 87)(23 83 28 88)(24 84 29 89)(31 78 42 67)(32 73 37 68)(33 74 38 69)(34 75 39 70)(35 76 40 71)(36 77 41 72)(43 55 54 66)(44 56 49 61)(45 57 50 62)(46 58 51 63)(47 59 52 64)(48 60 53 65)(115 185 125 175)(116 186 126 176)(117 181 121 177)(118 182 122 178)(119 183 123 179)(120 184 124 180)(127 163 137 173)(128 164 138 174)(129 165 133 169)(130 166 134 170)(131 167 135 171)(132 168 136 172)(139 161 149 151)(140 162 150 152)(141 157 145 153)(142 158 146 154)(143 159 147 155)(144 160 148 156)
(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)
(1 117 4 120)(2 116 5 119)(3 115 6 118)(7 89 10 86)(8 88 11 85)(9 87 12 90)(13 125 16 122)(14 124 17 121)(15 123 18 126)(19 114 22 111)(20 113 23 110)(21 112 24 109)(25 103 28 106)(26 108 29 105)(27 107 30 104)(31 140 34 143)(32 139 35 142)(33 144 36 141)(37 149 40 146)(38 148 41 145)(39 147 42 150)(43 138 46 135)(44 137 47 134)(45 136 48 133)(49 127 52 130)(50 132 53 129)(51 131 54 128)(55 164 58 167)(56 163 59 166)(57 168 60 165)(61 173 64 170)(62 172 65 169)(63 171 66 174)(67 162 70 159)(68 161 71 158)(69 160 72 157)(73 151 76 154)(74 156 77 153)(75 155 78 152)(79 188 82 191)(80 187 83 190)(81 192 84 189)(91 186 94 183)(92 185 95 182)(93 184 96 181)(97 176 100 179)(98 175 101 178)(99 180 102 177)
G:=sub<Sym(192)| (1,65)(2,66)(3,61)(4,62)(5,63)(6,64)(7,144)(8,139)(9,140)(10,141)(11,142)(12,143)(13,56)(14,57)(15,58)(16,59)(17,60)(18,55)(19,78)(20,73)(21,74)(22,75)(23,76)(24,77)(25,68)(26,69)(27,70)(28,71)(29,72)(30,67)(31,90)(32,85)(33,86)(34,87)(35,88)(36,89)(37,80)(38,81)(39,82)(40,83)(41,84)(42,79)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,92)(50,93)(51,94)(52,95)(53,96)(54,91)(103,161)(104,162)(105,157)(106,158)(107,159)(108,160)(109,153)(110,154)(111,155)(112,156)(113,151)(114,152)(115,173)(116,174)(117,169)(118,170)(119,171)(120,172)(121,165)(122,166)(123,167)(124,168)(125,163)(126,164)(127,185)(128,186)(129,181)(130,182)(131,183)(132,184)(133,177)(134,178)(135,179)(136,180)(137,175)(138,176)(145,189)(146,190)(147,191)(148,192)(149,187)(150,188), (1,33)(2,34)(3,35)(4,36)(5,31)(6,32)(7,169)(8,170)(9,171)(10,172)(11,173)(12,174)(13,40)(14,41)(15,42)(16,37)(17,38)(18,39)(19,46)(20,47)(21,48)(22,43)(23,44)(24,45)(25,52)(26,53)(27,54)(28,49)(29,50)(30,51)(55,82)(56,83)(57,84)(58,79)(59,80)(60,81)(61,88)(62,89)(63,90)(64,85)(65,86)(66,87)(67,94)(68,95)(69,96)(70,91)(71,92)(72,93)(73,101)(74,102)(75,97)(76,98)(77,99)(78,100)(103,130)(104,131)(105,132)(106,127)(107,128)(108,129)(109,136)(110,137)(111,138)(112,133)(113,134)(114,135)(115,142)(116,143)(117,144)(118,139)(119,140)(120,141)(121,148)(122,149)(123,150)(124,145)(125,146)(126,147)(151,178)(152,179)(153,180)(154,175)(155,176)(156,177)(157,184)(158,185)(159,186)(160,181)(161,182)(162,183)(163,190)(164,191)(165,192)(166,187)(167,188)(168,189), (1,102,17,96)(2,97,18,91)(3,98,13,92)(4,99,14,93)(5,100,15,94)(6,101,16,95)(7,108,192,112)(8,103,187,113)(9,104,188,114)(10,105,189,109)(11,106,190,110)(12,107,191,111)(19,79,30,90)(20,80,25,85)(21,81,26,86)(22,82,27,87)(23,83,28,88)(24,84,29,89)(31,78,42,67)(32,73,37,68)(33,74,38,69)(34,75,39,70)(35,76,40,71)(36,77,41,72)(43,55,54,66)(44,56,49,61)(45,57,50,62)(46,58,51,63)(47,59,52,64)(48,60,53,65)(115,185,125,175)(116,186,126,176)(117,181,121,177)(118,182,122,178)(119,183,123,179)(120,184,124,180)(127,163,137,173)(128,164,138,174)(129,165,133,169)(130,166,134,170)(131,167,135,171)(132,168,136,172)(139,161,149,151)(140,162,150,152)(141,157,145,153)(142,158,146,154)(143,159,147,155)(144,160,148,156), (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), (1,117,4,120)(2,116,5,119)(3,115,6,118)(7,89,10,86)(8,88,11,85)(9,87,12,90)(13,125,16,122)(14,124,17,121)(15,123,18,126)(19,114,22,111)(20,113,23,110)(21,112,24,109)(25,103,28,106)(26,108,29,105)(27,107,30,104)(31,140,34,143)(32,139,35,142)(33,144,36,141)(37,149,40,146)(38,148,41,145)(39,147,42,150)(43,138,46,135)(44,137,47,134)(45,136,48,133)(49,127,52,130)(50,132,53,129)(51,131,54,128)(55,164,58,167)(56,163,59,166)(57,168,60,165)(61,173,64,170)(62,172,65,169)(63,171,66,174)(67,162,70,159)(68,161,71,158)(69,160,72,157)(73,151,76,154)(74,156,77,153)(75,155,78,152)(79,188,82,191)(80,187,83,190)(81,192,84,189)(91,186,94,183)(92,185,95,182)(93,184,96,181)(97,176,100,179)(98,175,101,178)(99,180,102,177)>;
G:=Group( (1,65)(2,66)(3,61)(4,62)(5,63)(6,64)(7,144)(8,139)(9,140)(10,141)(11,142)(12,143)(13,56)(14,57)(15,58)(16,59)(17,60)(18,55)(19,78)(20,73)(21,74)(22,75)(23,76)(24,77)(25,68)(26,69)(27,70)(28,71)(29,72)(30,67)(31,90)(32,85)(33,86)(34,87)(35,88)(36,89)(37,80)(38,81)(39,82)(40,83)(41,84)(42,79)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,92)(50,93)(51,94)(52,95)(53,96)(54,91)(103,161)(104,162)(105,157)(106,158)(107,159)(108,160)(109,153)(110,154)(111,155)(112,156)(113,151)(114,152)(115,173)(116,174)(117,169)(118,170)(119,171)(120,172)(121,165)(122,166)(123,167)(124,168)(125,163)(126,164)(127,185)(128,186)(129,181)(130,182)(131,183)(132,184)(133,177)(134,178)(135,179)(136,180)(137,175)(138,176)(145,189)(146,190)(147,191)(148,192)(149,187)(150,188), (1,33)(2,34)(3,35)(4,36)(5,31)(6,32)(7,169)(8,170)(9,171)(10,172)(11,173)(12,174)(13,40)(14,41)(15,42)(16,37)(17,38)(18,39)(19,46)(20,47)(21,48)(22,43)(23,44)(24,45)(25,52)(26,53)(27,54)(28,49)(29,50)(30,51)(55,82)(56,83)(57,84)(58,79)(59,80)(60,81)(61,88)(62,89)(63,90)(64,85)(65,86)(66,87)(67,94)(68,95)(69,96)(70,91)(71,92)(72,93)(73,101)(74,102)(75,97)(76,98)(77,99)(78,100)(103,130)(104,131)(105,132)(106,127)(107,128)(108,129)(109,136)(110,137)(111,138)(112,133)(113,134)(114,135)(115,142)(116,143)(117,144)(118,139)(119,140)(120,141)(121,148)(122,149)(123,150)(124,145)(125,146)(126,147)(151,178)(152,179)(153,180)(154,175)(155,176)(156,177)(157,184)(158,185)(159,186)(160,181)(161,182)(162,183)(163,190)(164,191)(165,192)(166,187)(167,188)(168,189), (1,102,17,96)(2,97,18,91)(3,98,13,92)(4,99,14,93)(5,100,15,94)(6,101,16,95)(7,108,192,112)(8,103,187,113)(9,104,188,114)(10,105,189,109)(11,106,190,110)(12,107,191,111)(19,79,30,90)(20,80,25,85)(21,81,26,86)(22,82,27,87)(23,83,28,88)(24,84,29,89)(31,78,42,67)(32,73,37,68)(33,74,38,69)(34,75,39,70)(35,76,40,71)(36,77,41,72)(43,55,54,66)(44,56,49,61)(45,57,50,62)(46,58,51,63)(47,59,52,64)(48,60,53,65)(115,185,125,175)(116,186,126,176)(117,181,121,177)(118,182,122,178)(119,183,123,179)(120,184,124,180)(127,163,137,173)(128,164,138,174)(129,165,133,169)(130,166,134,170)(131,167,135,171)(132,168,136,172)(139,161,149,151)(140,162,150,152)(141,157,145,153)(142,158,146,154)(143,159,147,155)(144,160,148,156), (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), (1,117,4,120)(2,116,5,119)(3,115,6,118)(7,89,10,86)(8,88,11,85)(9,87,12,90)(13,125,16,122)(14,124,17,121)(15,123,18,126)(19,114,22,111)(20,113,23,110)(21,112,24,109)(25,103,28,106)(26,108,29,105)(27,107,30,104)(31,140,34,143)(32,139,35,142)(33,144,36,141)(37,149,40,146)(38,148,41,145)(39,147,42,150)(43,138,46,135)(44,137,47,134)(45,136,48,133)(49,127,52,130)(50,132,53,129)(51,131,54,128)(55,164,58,167)(56,163,59,166)(57,168,60,165)(61,173,64,170)(62,172,65,169)(63,171,66,174)(67,162,70,159)(68,161,71,158)(69,160,72,157)(73,151,76,154)(74,156,77,153)(75,155,78,152)(79,188,82,191)(80,187,83,190)(81,192,84,189)(91,186,94,183)(92,185,95,182)(93,184,96,181)(97,176,100,179)(98,175,101,178)(99,180,102,177) );
G=PermutationGroup([[(1,65),(2,66),(3,61),(4,62),(5,63),(6,64),(7,144),(8,139),(9,140),(10,141),(11,142),(12,143),(13,56),(14,57),(15,58),(16,59),(17,60),(18,55),(19,78),(20,73),(21,74),(22,75),(23,76),(24,77),(25,68),(26,69),(27,70),(28,71),(29,72),(30,67),(31,90),(32,85),(33,86),(34,87),(35,88),(36,89),(37,80),(38,81),(39,82),(40,83),(41,84),(42,79),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,92),(50,93),(51,94),(52,95),(53,96),(54,91),(103,161),(104,162),(105,157),(106,158),(107,159),(108,160),(109,153),(110,154),(111,155),(112,156),(113,151),(114,152),(115,173),(116,174),(117,169),(118,170),(119,171),(120,172),(121,165),(122,166),(123,167),(124,168),(125,163),(126,164),(127,185),(128,186),(129,181),(130,182),(131,183),(132,184),(133,177),(134,178),(135,179),(136,180),(137,175),(138,176),(145,189),(146,190),(147,191),(148,192),(149,187),(150,188)], [(1,33),(2,34),(3,35),(4,36),(5,31),(6,32),(7,169),(8,170),(9,171),(10,172),(11,173),(12,174),(13,40),(14,41),(15,42),(16,37),(17,38),(18,39),(19,46),(20,47),(21,48),(22,43),(23,44),(24,45),(25,52),(26,53),(27,54),(28,49),(29,50),(30,51),(55,82),(56,83),(57,84),(58,79),(59,80),(60,81),(61,88),(62,89),(63,90),(64,85),(65,86),(66,87),(67,94),(68,95),(69,96),(70,91),(71,92),(72,93),(73,101),(74,102),(75,97),(76,98),(77,99),(78,100),(103,130),(104,131),(105,132),(106,127),(107,128),(108,129),(109,136),(110,137),(111,138),(112,133),(113,134),(114,135),(115,142),(116,143),(117,144),(118,139),(119,140),(120,141),(121,148),(122,149),(123,150),(124,145),(125,146),(126,147),(151,178),(152,179),(153,180),(154,175),(155,176),(156,177),(157,184),(158,185),(159,186),(160,181),(161,182),(162,183),(163,190),(164,191),(165,192),(166,187),(167,188),(168,189)], [(1,102,17,96),(2,97,18,91),(3,98,13,92),(4,99,14,93),(5,100,15,94),(6,101,16,95),(7,108,192,112),(8,103,187,113),(9,104,188,114),(10,105,189,109),(11,106,190,110),(12,107,191,111),(19,79,30,90),(20,80,25,85),(21,81,26,86),(22,82,27,87),(23,83,28,88),(24,84,29,89),(31,78,42,67),(32,73,37,68),(33,74,38,69),(34,75,39,70),(35,76,40,71),(36,77,41,72),(43,55,54,66),(44,56,49,61),(45,57,50,62),(46,58,51,63),(47,59,52,64),(48,60,53,65),(115,185,125,175),(116,186,126,176),(117,181,121,177),(118,182,122,178),(119,183,123,179),(120,184,124,180),(127,163,137,173),(128,164,138,174),(129,165,133,169),(130,166,134,170),(131,167,135,171),(132,168,136,172),(139,161,149,151),(140,162,150,152),(141,157,145,153),(142,158,146,154),(143,159,147,155),(144,160,148,156)], [(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)], [(1,117,4,120),(2,116,5,119),(3,115,6,118),(7,89,10,86),(8,88,11,85),(9,87,12,90),(13,125,16,122),(14,124,17,121),(15,123,18,126),(19,114,22,111),(20,113,23,110),(21,112,24,109),(25,103,28,106),(26,108,29,105),(27,107,30,104),(31,140,34,143),(32,139,35,142),(33,144,36,141),(37,149,40,146),(38,148,41,145),(39,147,42,150),(43,138,46,135),(44,137,47,134),(45,136,48,133),(49,127,52,130),(50,132,53,129),(51,131,54,128),(55,164,58,167),(56,163,59,166),(57,168,60,165),(61,173,64,170),(62,172,65,169),(63,171,66,174),(67,162,70,159),(68,161,71,158),(69,160,72,157),(73,151,76,154),(74,156,77,153),(75,155,78,152),(79,188,82,191),(80,187,83,190),(81,192,84,189),(91,186,94,183),(92,185,95,182),(93,184,96,181),(97,176,100,179),(98,175,101,178),(99,180,102,177)]])
72 conjugacy classes
| class | 1 | 2A | ··· | 2O | 3 | 4A | ··· | 4H | 4I | ··· | 4X | 6A | ··· | 6O | 12A | ··· | 12P |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | - | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C4 | S3 | D4 | Q8 | Dic3 | D6 | D6 | Dic6 | D12 |
| kernel | C22×C4⋊Dic3 | C2×C4⋊Dic3 | C23×Dic3 | C23×C12 | C22×C12 | C23×C4 | C22×C6 | C22×C6 | C22×C4 | C22×C4 | C24 | C23 | C23 |
| # reps | 1 | 12 | 2 | 1 | 16 | 1 | 4 | 4 | 8 | 6 | 1 | 8 | 8 |
Matrix representation of C22×C4⋊Dic3 ►in GL6(𝔽13)
| 1 | 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 7 |
| 0 | 0 | 0 | 0 | 6 | 10 |
| 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 | 0 | 12 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 8 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 | 12 |
G:=sub<GL(6,GF(13))| [1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,0,0,0,0,0,0,5,0,0,0,0,0,0,3,6,0,0,0,0,7,10],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,1,0,0,0,0,12,12],[1,0,0,0,0,0,0,12,0,0,0,0,0,0,0,8,0,0,0,0,8,0,0,0,0,0,0,0,1,1,0,0,0,0,0,12] >;
C22×C4⋊Dic3 in GAP, Magma, Sage, TeX
C_2^2\times C_4\rtimes {\rm Dic}_3 % in TeX
G:=Group("C2^2xC4:Dic3"); // GroupNames label
G:=SmallGroup(192,1344);
// by ID
G=gap.SmallGroup(192,1344);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,1123,136,6278]);
// 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,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
// generators/relations