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G = C22×Dic3⋊C4order 192 = 26·3

Direct product of C22 and Dic3⋊C4

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

Aliases: C22×Dic3⋊C4, C24.87D6, C23.20Dic6, (C23×C4).12S3, C6.37(C23×C4), C23.73(C4×S3), (C23×C12).9C2, C6.18(C22×Q8), (C22×C6).27Q8, (C2×C6).281C24, Dic35(C22×C4), C6.129(C22×D4), (C22×C4).427D6, (C22×C6).203D4, C2.2(C22×Dic6), (C2×C12).702C23, (C22×Dic3)⋊11C4, C22.39(S3×C23), (C23×Dic3).9C2, C22.38(C2×Dic6), C23.109(C3⋊D4), C23.343(C22×S3), (C23×C6).103C22, (C22×C6).410C23, (C22×C12).506C22, (C2×Dic3).276C23, (C22×Dic3).227C22, C62(C2×C4⋊C4), C32(C22×C4⋊C4), (C2×C6)⋊8(C4⋊C4), C2.37(S3×C22×C4), C22.78(S3×C2×C4), (C2×C6).53(C2×Q8), (C2×C6).570(C2×D4), C2.1(C22×C3⋊D4), (C2×Dic3)⋊24(C2×C4), C22.99(C2×C3⋊D4), (C2×C4).655(C22×S3), (C22×C6).104(C2×C4), (C2×C6).157(C22×C4), SmallGroup(192,1342)

Series: Derived Chief Lower central Upper central

C1C6 — C22×Dic3⋊C4
C1C3C6C2×C6C2×Dic3C22×Dic3C23×Dic3 — C22×Dic3⋊C4
C3C6 — C22×Dic3⋊C4
C1C24C23×C4

Generators and relations for C22×Dic3⋊C4
 G = < a,b,c,d,e | a2=b2=c6=e4=1, d2=c3, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c-1, ce=ec, ede-1=c3d >

Subgroups: 760 in 418 conjugacy classes, 247 normal (17 characteristic)
C1, C2 [×3], C2 [×12], C3, C4 [×16], C22, C22 [×34], C6 [×3], C6 [×12], C2×C4 [×4], C2×C4 [×56], C23 [×15], Dic3 [×8], Dic3 [×4], C12 [×4], C2×C6, C2×C6 [×34], C4⋊C4 [×16], C22×C4 [×6], C22×C4 [×28], C24, C2×Dic3 [×32], C2×Dic3 [×12], C2×C12 [×4], C2×C12 [×12], C22×C6 [×15], C2×C4⋊C4 [×12], C23×C4, C23×C4 [×2], Dic3⋊C4 [×16], C22×Dic3 [×20], C22×Dic3 [×4], C22×C12 [×6], C22×C12 [×4], C23×C6, C22×C4⋊C4, C2×Dic3⋊C4 [×12], C23×Dic3 [×2], C23×C12, C22×Dic3⋊C4
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], S3, C2×C4 [×28], D4 [×4], Q8 [×4], C23 [×15], D6 [×7], C4⋊C4 [×16], C22×C4 [×14], C2×D4 [×6], C2×Q8 [×6], C24, Dic6 [×4], C4×S3 [×4], C3⋊D4 [×4], C22×S3 [×7], C2×C4⋊C4 [×12], C23×C4, C22×D4, C22×Q8, Dic3⋊C4 [×16], C2×Dic6 [×6], S3×C2×C4 [×6], C2×C3⋊D4 [×6], S3×C23, C22×C4⋊C4, C2×Dic3⋊C4 [×12], C22×Dic6, S3×C22×C4, C22×C3⋊D4, C22×Dic3⋊C4

Smallest permutation representation of C22×Dic3⋊C4
Regular action on 192 points
Generators in S192
(1 58)(2 59)(3 60)(4 55)(5 56)(6 57)(7 52)(8 53)(9 54)(10 49)(11 50)(12 51)(13 70)(14 71)(15 72)(16 67)(17 68)(18 69)(19 64)(20 65)(21 66)(22 61)(23 62)(24 63)(25 82)(26 83)(27 84)(28 79)(29 80)(30 81)(31 76)(32 77)(33 78)(34 73)(35 74)(36 75)(37 94)(38 95)(39 96)(40 91)(41 92)(42 93)(43 88)(44 89)(45 90)(46 85)(47 86)(48 87)(97 154)(98 155)(99 156)(100 151)(101 152)(102 153)(103 148)(104 149)(105 150)(106 145)(107 146)(108 147)(109 166)(110 167)(111 168)(112 163)(113 164)(114 165)(115 160)(116 161)(117 162)(118 157)(119 158)(120 159)(121 178)(122 179)(123 180)(124 175)(125 176)(126 177)(127 172)(128 173)(129 174)(130 169)(131 170)(132 171)(133 190)(134 191)(135 192)(136 187)(137 188)(138 189)(139 184)(140 185)(141 186)(142 181)(143 182)(144 183)
(1 34)(2 35)(3 36)(4 31)(5 32)(6 33)(7 28)(8 29)(9 30)(10 25)(11 26)(12 27)(13 46)(14 47)(15 48)(16 43)(17 44)(18 45)(19 40)(20 41)(21 42)(22 37)(23 38)(24 39)(49 82)(50 83)(51 84)(52 79)(53 80)(54 81)(55 76)(56 77)(57 78)(58 73)(59 74)(60 75)(61 94)(62 95)(63 96)(64 91)(65 92)(66 93)(67 88)(68 89)(69 90)(70 85)(71 86)(72 87)(97 130)(98 131)(99 132)(100 127)(101 128)(102 129)(103 124)(104 125)(105 126)(106 121)(107 122)(108 123)(109 142)(110 143)(111 144)(112 139)(113 140)(114 141)(115 136)(116 137)(117 138)(118 133)(119 134)(120 135)(145 178)(146 179)(147 180)(148 175)(149 176)(150 177)(151 172)(152 173)(153 174)(154 169)(155 170)(156 171)(157 190)(158 191)(159 192)(160 187)(161 188)(162 189)(163 184)(164 185)(165 186)(166 181)(167 182)(168 183)
(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)
(1 152 4 155)(2 151 5 154)(3 156 6 153)(7 146 10 149)(8 145 11 148)(9 150 12 147)(13 164 16 167)(14 163 17 166)(15 168 18 165)(19 158 22 161)(20 157 23 160)(21 162 24 159)(25 176 28 179)(26 175 29 178)(27 180 30 177)(31 170 34 173)(32 169 35 172)(33 174 36 171)(37 188 40 191)(38 187 41 190)(39 192 42 189)(43 182 46 185)(44 181 47 184)(45 186 48 183)(49 104 52 107)(50 103 53 106)(51 108 54 105)(55 98 58 101)(56 97 59 100)(57 102 60 99)(61 116 64 119)(62 115 65 118)(63 120 66 117)(67 110 70 113)(68 109 71 112)(69 114 72 111)(73 128 76 131)(74 127 77 130)(75 132 78 129)(79 122 82 125)(80 121 83 124)(81 126 84 123)(85 140 88 143)(86 139 89 142)(87 144 90 141)(91 134 94 137)(92 133 95 136)(93 138 96 135)
(1 91 7 85)(2 92 8 86)(3 93 9 87)(4 94 10 88)(5 95 11 89)(6 96 12 90)(13 73 19 79)(14 74 20 80)(15 75 21 81)(16 76 22 82)(17 77 23 83)(18 78 24 84)(25 67 31 61)(26 68 32 62)(27 69 33 63)(28 70 34 64)(29 71 35 65)(30 72 36 66)(37 49 43 55)(38 50 44 56)(39 51 45 57)(40 52 46 58)(41 53 47 59)(42 54 48 60)(97 190 103 184)(98 191 104 185)(99 192 105 186)(100 187 106 181)(101 188 107 182)(102 189 108 183)(109 172 115 178)(110 173 116 179)(111 174 117 180)(112 169 118 175)(113 170 119 176)(114 171 120 177)(121 166 127 160)(122 167 128 161)(123 168 129 162)(124 163 130 157)(125 164 131 158)(126 165 132 159)(133 148 139 154)(134 149 140 155)(135 150 141 156)(136 145 142 151)(137 146 143 152)(138 147 144 153)

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

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

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

72 conjugacy classes

class 1 2A···2O 3 4A···4H4I···4X6A···6O12A···12P
order12···234···44···46···612···12
size11···122···26···62···22···2

72 irreducible representations

dim1111122222222
type++++++-++-
imageC1C2C2C2C4S3D4Q8D6D6Dic6C4×S3C3⋊D4
kernelC22×Dic3⋊C4C2×Dic3⋊C4C23×Dic3C23×C12C22×Dic3C23×C4C22×C6C22×C6C22×C4C24C23C23C23
# reps112211614461888

Matrix representation of C22×Dic3⋊C4 in GL6(𝔽13)

100000
0120000
001000
000100
0000120
0000012
,
1200000
010000
001000
000100
0000120
0000012
,
100000
010000
0001200
0011200
000011
0000120
,
1200000
0120000
003300
0061000
000005
000050
,
100000
0120000
008000
000800
000024
0000911

G:=sub<GL(6,GF(13))| [1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,12,12,0,0,0,0,0,0,1,12,0,0,0,0,1,0],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,3,6,0,0,0,0,3,10,0,0,0,0,0,0,0,5,0,0,0,0,5,0],[1,0,0,0,0,0,0,12,0,0,0,0,0,0,8,0,0,0,0,0,0,8,0,0,0,0,0,0,2,9,0,0,0,0,4,11] >;

C22×Dic3⋊C4 in GAP, Magma, Sage, TeX

C_2^2\times {\rm Dic}_3\rtimes C_4
% in TeX

G:=Group("C2^2xDic3:C4");
// GroupNames label

G:=SmallGroup(192,1342);
// by ID

G=gap.SmallGroup(192,1342);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,1123,80,6278]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^6=e^4=1,d^2=c^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,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=c^3*d>;
// generators/relations

׿
×
𝔽