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G = C2×Dic3⋊Q8order 192 = 26·3

Direct product of C2 and Dic3⋊Q8

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

Aliases: C2×Dic3⋊Q8, C63(C4⋊Q8), Dic33(C2×Q8), (C2×Dic3)⋊10Q8, C12.257(C2×D4), (C2×C12).213D4, (C2×Q8).210D6, C22.35(S3×Q8), C6.51(C22×Q8), (C2×C6).302C24, (C22×C4).291D6, C6.152(C22×D4), (C22×Q8).14S3, (C2×C12).645C23, (C6×Q8).231C22, (C22×C6).420C23, C22.315(S3×C23), C23.349(C22×S3), (C22×Dic6).19C2, Dic3⋊C4.170C22, (C22×C12).282C22, (C2×Dic6).307C22, (C4×Dic3).259C22, (C2×Dic3).156C23, (C22×Dic3).233C22, C34(C2×C4⋊Q8), (Q8×C2×C6).7C2, C2.34(C2×S3×Q8), C4.27(C2×C3⋊D4), (C2×C6).96(C2×Q8), (C2×C6).587(C2×D4), (C2×C4×Dic3).16C2, C2.25(C22×C3⋊D4), (C2×C4).156(C3⋊D4), (C2×Dic3⋊C4).34C2, (C2×C4).241(C22×S3), C22.115(C2×C3⋊D4), SmallGroup(192,1369)

Series: Derived Chief Lower central Upper central

C1C2×C6 — C2×Dic3⋊Q8
C1C3C6C2×C6C2×Dic3C22×Dic3C2×C4×Dic3 — C2×Dic3⋊Q8
C3C2×C6 — C2×Dic3⋊Q8
C1C23C22×Q8

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=b-1, bd=db, be=eb, dcd-1=b3c, ce=ec, ede-1=d-1 >

Subgroups: 584 in 290 conjugacy classes, 143 normal (15 characteristic)
C1, C2, C2 [×6], C3, C4 [×4], C4 [×16], C22, C22 [×6], C6, C6 [×6], C2×C4 [×10], C2×C4 [×24], Q8 [×16], C23, Dic3 [×8], Dic3 [×4], C12 [×4], C12 [×4], C2×C6, C2×C6 [×6], C42 [×4], C4⋊C4 [×16], C22×C4, C22×C4 [×2], C22×C4 [×4], C2×Q8 [×4], C2×Q8 [×12], Dic6 [×8], C2×Dic3 [×16], C2×Dic3 [×4], C2×C12 [×10], C2×C12 [×4], C3×Q8 [×8], C22×C6, C2×C42, C2×C4⋊C4 [×4], C4⋊Q8 [×8], C22×Q8, C22×Q8, C4×Dic3 [×4], Dic3⋊C4 [×16], C2×Dic6 [×4], C2×Dic6 [×4], C22×Dic3 [×4], C22×C12, C22×C12 [×2], C6×Q8 [×4], C6×Q8 [×4], C2×C4⋊Q8, C2×C4×Dic3, C2×Dic3⋊C4 [×4], Dic3⋊Q8 [×8], C22×Dic6, Q8×C2×C6, C2×Dic3⋊Q8
Quotients: C1, C2 [×15], C22 [×35], S3, D4 [×4], Q8 [×8], C23 [×15], D6 [×7], C2×D4 [×6], C2×Q8 [×12], C24, C3⋊D4 [×4], C22×S3 [×7], C4⋊Q8 [×4], C22×D4, C22×Q8 [×2], S3×Q8 [×4], C2×C3⋊D4 [×6], S3×C23, C2×C4⋊Q8, Dic3⋊Q8 [×4], C2×S3×Q8 [×2], C22×C3⋊D4, C2×Dic3⋊Q8

Smallest permutation representation of C2×Dic3⋊Q8
Regular action on 192 points
Generators in S192
(1 52)(2 53)(3 54)(4 49)(5 50)(6 51)(7 58)(8 59)(9 60)(10 55)(11 56)(12 57)(13 64)(14 65)(15 66)(16 61)(17 62)(18 63)(19 70)(20 71)(21 72)(22 67)(23 68)(24 69)(25 76)(26 77)(27 78)(28 73)(29 74)(30 75)(31 82)(32 83)(33 84)(34 79)(35 80)(36 81)(37 88)(38 89)(39 90)(40 85)(41 86)(42 87)(43 94)(44 95)(45 96)(46 91)(47 92)(48 93)(97 148)(98 149)(99 150)(100 145)(101 146)(102 147)(103 154)(104 155)(105 156)(106 151)(107 152)(108 153)(109 160)(110 161)(111 162)(112 157)(113 158)(114 159)(115 166)(116 167)(117 168)(118 163)(119 164)(120 165)(121 172)(122 173)(123 174)(124 169)(125 170)(126 171)(127 178)(128 179)(129 180)(130 175)(131 176)(132 177)(133 184)(134 185)(135 186)(136 181)(137 182)(138 183)(139 190)(140 191)(141 192)(142 187)(143 188)(144 189)
(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 94 7 88)(2 95 8 89)(3 96 9 90)(4 91 10 85)(5 92 11 86)(6 93 12 87)(13 76 19 82)(14 77 20 83)(15 78 21 84)(16 73 22 79)(17 74 23 80)(18 75 24 81)(25 70 31 64)(26 71 32 65)(27 72 33 66)(28 67 34 61)(29 68 35 62)(30 69 36 63)(37 52 43 58)(38 53 44 59)(39 54 45 60)(40 49 46 55)(41 50 47 56)(42 51 48 57)(97 187 103 181)(98 188 104 182)(99 189 105 183)(100 190 106 184)(101 191 107 185)(102 192 108 186)(109 169 115 175)(110 170 116 176)(111 171 117 177)(112 172 118 178)(113 173 119 179)(114 174 120 180)(121 163 127 157)(122 164 128 158)(123 165 129 159)(124 166 130 160)(125 167 131 161)(126 168 132 162)(133 145 139 151)(134 146 140 152)(135 147 141 153)(136 148 142 154)(137 149 143 155)(138 150 144 156)
(1 31 7 25)(2 32 8 26)(3 33 9 27)(4 34 10 28)(5 35 11 29)(6 36 12 30)(13 43 19 37)(14 44 20 38)(15 45 21 39)(16 46 22 40)(17 47 23 41)(18 48 24 42)(49 79 55 73)(50 80 56 74)(51 81 57 75)(52 82 58 76)(53 83 59 77)(54 84 60 78)(61 91 67 85)(62 92 68 86)(63 93 69 87)(64 94 70 88)(65 95 71 89)(66 96 72 90)(97 127 103 121)(98 128 104 122)(99 129 105 123)(100 130 106 124)(101 131 107 125)(102 132 108 126)(109 139 115 133)(110 140 116 134)(111 141 117 135)(112 142 118 136)(113 143 119 137)(114 144 120 138)(145 175 151 169)(146 176 152 170)(147 177 153 171)(148 178 154 172)(149 179 155 173)(150 180 156 174)(157 187 163 181)(158 188 164 182)(159 189 165 183)(160 190 166 184)(161 191 167 185)(162 192 168 186)

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

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

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

48 conjugacy classes

class 1 2A···2G 3 4A4B4C4D4E4F4G4H4I···4P4Q4R4S4T6A···6G12A···12L
order12···23444444444···444446···612···12
size11···12222244446···6121212122···24···4

48 irreducible representations

dim1111112222224
type+++++++-+++-
imageC1C2C2C2C2C2S3Q8D4D6D6C3⋊D4S3×Q8
kernelC2×Dic3⋊Q8C2×C4×Dic3C2×Dic3⋊C4Dic3⋊Q8C22×Dic6Q8×C2×C6C22×Q8C2×Dic3C2×C12C22×C4C2×Q8C2×C4C22
# reps1148111843484

Matrix representation of C2×Dic3⋊Q8 in GL5(𝔽13)

120000
012000
001200
00010
00001
,
10000
01100
012000
00010
00001
,
120000
08000
05500
00010
00001
,
10000
02400
091100
00008
00080
,
10000
01000
00100
00050
00008

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

C2×Dic3⋊Q8 in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_3\rtimes Q_8
% in TeX

G:=Group("C2xDic3:Q8");
// GroupNames label

G:=SmallGroup(192,1369);
// by ID

G=gap.SmallGroup(192,1369);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,100,1123,185,80,6278]);
// 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=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=b^3*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽