direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8⋊2Dic3, (C6×Q8)⋊5C4, Q8⋊4(C2×Dic3), (C2×Q8)⋊5Dic3, (C2×C6).18Q16, C6.46(C2×Q16), C6⋊3(Q8⋊C4), (C2×C12).192D4, C12.207(C2×D4), (C2×Q8).189D6, (C2×C6).42SD16, C6.79(C2×SD16), (C22×Q8).7S3, C12.81(C22×C4), (C22×C6).198D4, (C22×C4).370D6, C12.33(C22⋊C4), (C2×C12).474C23, (C6×Q8).200C22, C4.11(C22×Dic3), C22.9(C3⋊Q16), C4.10(C6.D4), C23.108(C3⋊D4), C4⋊Dic3.352C22, (C22×C12).200C22, C22.12(Q8⋊2S3), C22.35(C6.D4), (Q8×C2×C6).1C2, C3⋊4(C2×Q8⋊C4), (C3×Q8)⋊15(C2×C4), C4.91(C2×C3⋊D4), C2.4(C2×C3⋊Q16), (C2×C6).558(C2×D4), C6.77(C2×C22⋊C4), (C22×C3⋊C8).13C2, C2.4(C2×Q8⋊2S3), (C2×C12).119(C2×C4), (C2×C3⋊C8).281C22, (C2×C4⋊Dic3).40C2, (C2×C4).51(C2×Dic3), C22.93(C2×C3⋊D4), (C2×C4).149(C3⋊D4), (C2×C4).560(C22×S3), C2.13(C2×C6.D4), (C2×C6).114(C22⋊C4), SmallGroup(192,783)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q8⋊2Dic3
G = < a,b,c,d,e | a2=b4=d6=1, c2=b2, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d-1 >
Subgroups: 328 in 162 conjugacy classes, 87 normal (27 characteristic)
C1, C2, C2, C3, C4, C4, C4, C22, C22, C6, C6, C8, C2×C4, C2×C4, C2×C4, Q8, Q8, C23, Dic3, C12, C12, C12, C2×C6, C2×C6, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×Q8, C2×Q8, C3⋊C8, C2×Dic3, C2×C12, C2×C12, C2×C12, C3×Q8, C3×Q8, C22×C6, Q8⋊C4, C2×C4⋊C4, C22×C8, C22×Q8, C2×C3⋊C8, C2×C3⋊C8, C4⋊Dic3, C4⋊Dic3, C22×Dic3, C22×C12, C22×C12, C6×Q8, C6×Q8, C2×Q8⋊C4, Q8⋊2Dic3, C22×C3⋊C8, C2×C4⋊Dic3, Q8×C2×C6, C2×Q8⋊2Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, Dic3, D6, C22⋊C4, SD16, Q16, C22×C4, C2×D4, C2×Dic3, C3⋊D4, C22×S3, Q8⋊C4, C2×C22⋊C4, C2×SD16, C2×Q16, Q8⋊2S3, C3⋊Q16, C6.D4, C22×Dic3, C2×C3⋊D4, C2×Q8⋊C4, Q8⋊2Dic3, C2×Q8⋊2S3, C2×C3⋊Q16, C2×C6.D4, C2×Q8⋊2Dic3
►Regular action on 192 points
Generators in S192
(1 58)(2 59)(3 60)(4 55)(5 56)(6 57)(7 63)(8 64)(9 65)(10 66)(11 61)(12 62)(13 145)(14 146)(15 147)(16 148)(17 149)(18 150)(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)(49 101)(50 102)(51 97)(52 98)(53 99)(54 100)(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 29 19 7)(2 30 20 8)(3 25 21 9)(4 26 22 10)(5 27 23 11)(6 28 24 12)(13 191 186 176)(14 192 181 177)(15 187 182 178)(16 188 183 179)(17 189 184 180)(18 190 185 175)(31 42 43 53)(32 37 44 54)(33 38 45 49)(34 39 46 50)(35 40 47 51)(36 41 48 52)(55 77 67 66)(56 78 68 61)(57 73 69 62)(58 74 70 63)(59 75 71 64)(60 76 72 65)(79 90 91 102)(80 85 92 97)(81 86 93 98)(82 87 94 99)(83 88 95 100)(84 89 96 101)(103 113 118 123)(104 114 119 124)(105 109 120 125)(106 110 115 126)(107 111 116 121)(108 112 117 122)(127 147 142 137)(128 148 143 138)(129 149 144 133)(130 150 139 134)(131 145 140 135)(132 146 141 136)(151 161 166 171)(152 162 167 172)(153 157 168 173)(154 158 163 174)(155 159 164 169)(156 160 165 170)
(1 46 19 34)(2 47 20 35)(3 48 21 36)(4 43 22 31)(5 44 23 32)(6 45 24 33)(7 50 29 39)(8 51 30 40)(9 52 25 41)(10 53 26 42)(11 54 27 37)(12 49 28 38)(13 164 186 155)(14 165 181 156)(15 166 182 151)(16 167 183 152)(17 168 184 153)(18 163 185 154)(55 94 67 82)(56 95 68 83)(57 96 69 84)(58 91 70 79)(59 92 71 80)(60 93 72 81)(61 100 78 88)(62 101 73 89)(63 102 74 90)(64 97 75 85)(65 98 76 86)(66 99 77 87)(103 150 118 134)(104 145 119 135)(105 146 120 136)(106 147 115 137)(107 148 116 138)(108 149 117 133)(109 132 125 141)(110 127 126 142)(111 128 121 143)(112 129 122 144)(113 130 123 139)(114 131 124 140)(157 180 173 189)(158 175 174 190)(159 176 169 191)(160 177 170 192)(161 178 171 187)(162 179 172 188)
(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)
(1 155 4 152)(2 154 5 151)(3 153 6 156)(7 159 10 162)(8 158 11 161)(9 157 12 160)(13 53 16 50)(14 52 17 49)(15 51 18 54)(19 164 22 167)(20 163 23 166)(21 168 24 165)(25 173 28 170)(26 172 29 169)(27 171 30 174)(31 179 34 176)(32 178 35 175)(33 177 36 180)(37 182 40 185)(38 181 41 184)(39 186 42 183)(43 188 46 191)(44 187 47 190)(45 192 48 189)(55 107 58 104)(56 106 59 103)(57 105 60 108)(61 110 64 113)(62 109 65 112)(63 114 66 111)(67 116 70 119)(68 115 71 118)(69 120 72 117)(73 125 76 122)(74 124 77 121)(75 123 78 126)(79 131 82 128)(80 130 83 127)(81 129 84 132)(85 134 88 137)(86 133 89 136)(87 138 90 135)(91 140 94 143)(92 139 95 142)(93 144 96 141)(97 150 100 147)(98 149 101 146)(99 148 102 145)
G:=sub<Sym(192)| (1,58)(2,59)(3,60)(4,55)(5,56)(6,57)(7,63)(8,64)(9,65)(10,66)(11,61)(12,62)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(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)(49,101)(50,102)(51,97)(52,98)(53,99)(54,100)(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), (1,29,19,7)(2,30,20,8)(3,25,21,9)(4,26,22,10)(5,27,23,11)(6,28,24,12)(13,191,186,176)(14,192,181,177)(15,187,182,178)(16,188,183,179)(17,189,184,180)(18,190,185,175)(31,42,43,53)(32,37,44,54)(33,38,45,49)(34,39,46,50)(35,40,47,51)(36,41,48,52)(55,77,67,66)(56,78,68,61)(57,73,69,62)(58,74,70,63)(59,75,71,64)(60,76,72,65)(79,90,91,102)(80,85,92,97)(81,86,93,98)(82,87,94,99)(83,88,95,100)(84,89,96,101)(103,113,118,123)(104,114,119,124)(105,109,120,125)(106,110,115,126)(107,111,116,121)(108,112,117,122)(127,147,142,137)(128,148,143,138)(129,149,144,133)(130,150,139,134)(131,145,140,135)(132,146,141,136)(151,161,166,171)(152,162,167,172)(153,157,168,173)(154,158,163,174)(155,159,164,169)(156,160,165,170), (1,46,19,34)(2,47,20,35)(3,48,21,36)(4,43,22,31)(5,44,23,32)(6,45,24,33)(7,50,29,39)(8,51,30,40)(9,52,25,41)(10,53,26,42)(11,54,27,37)(12,49,28,38)(13,164,186,155)(14,165,181,156)(15,166,182,151)(16,167,183,152)(17,168,184,153)(18,163,185,154)(55,94,67,82)(56,95,68,83)(57,96,69,84)(58,91,70,79)(59,92,71,80)(60,93,72,81)(61,100,78,88)(62,101,73,89)(63,102,74,90)(64,97,75,85)(65,98,76,86)(66,99,77,87)(103,150,118,134)(104,145,119,135)(105,146,120,136)(106,147,115,137)(107,148,116,138)(108,149,117,133)(109,132,125,141)(110,127,126,142)(111,128,121,143)(112,129,122,144)(113,130,123,139)(114,131,124,140)(157,180,173,189)(158,175,174,190)(159,176,169,191)(160,177,170,192)(161,178,171,187)(162,179,172,188), (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), (1,155,4,152)(2,154,5,151)(3,153,6,156)(7,159,10,162)(8,158,11,161)(9,157,12,160)(13,53,16,50)(14,52,17,49)(15,51,18,54)(19,164,22,167)(20,163,23,166)(21,168,24,165)(25,173,28,170)(26,172,29,169)(27,171,30,174)(31,179,34,176)(32,178,35,175)(33,177,36,180)(37,182,40,185)(38,181,41,184)(39,186,42,183)(43,188,46,191)(44,187,47,190)(45,192,48,189)(55,107,58,104)(56,106,59,103)(57,105,60,108)(61,110,64,113)(62,109,65,112)(63,114,66,111)(67,116,70,119)(68,115,71,118)(69,120,72,117)(73,125,76,122)(74,124,77,121)(75,123,78,126)(79,131,82,128)(80,130,83,127)(81,129,84,132)(85,134,88,137)(86,133,89,136)(87,138,90,135)(91,140,94,143)(92,139,95,142)(93,144,96,141)(97,150,100,147)(98,149,101,146)(99,148,102,145)>;
G:=Group( (1,58)(2,59)(3,60)(4,55)(5,56)(6,57)(7,63)(8,64)(9,65)(10,66)(11,61)(12,62)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(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)(49,101)(50,102)(51,97)(52,98)(53,99)(54,100)(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), (1,29,19,7)(2,30,20,8)(3,25,21,9)(4,26,22,10)(5,27,23,11)(6,28,24,12)(13,191,186,176)(14,192,181,177)(15,187,182,178)(16,188,183,179)(17,189,184,180)(18,190,185,175)(31,42,43,53)(32,37,44,54)(33,38,45,49)(34,39,46,50)(35,40,47,51)(36,41,48,52)(55,77,67,66)(56,78,68,61)(57,73,69,62)(58,74,70,63)(59,75,71,64)(60,76,72,65)(79,90,91,102)(80,85,92,97)(81,86,93,98)(82,87,94,99)(83,88,95,100)(84,89,96,101)(103,113,118,123)(104,114,119,124)(105,109,120,125)(106,110,115,126)(107,111,116,121)(108,112,117,122)(127,147,142,137)(128,148,143,138)(129,149,144,133)(130,150,139,134)(131,145,140,135)(132,146,141,136)(151,161,166,171)(152,162,167,172)(153,157,168,173)(154,158,163,174)(155,159,164,169)(156,160,165,170), (1,46,19,34)(2,47,20,35)(3,48,21,36)(4,43,22,31)(5,44,23,32)(6,45,24,33)(7,50,29,39)(8,51,30,40)(9,52,25,41)(10,53,26,42)(11,54,27,37)(12,49,28,38)(13,164,186,155)(14,165,181,156)(15,166,182,151)(16,167,183,152)(17,168,184,153)(18,163,185,154)(55,94,67,82)(56,95,68,83)(57,96,69,84)(58,91,70,79)(59,92,71,80)(60,93,72,81)(61,100,78,88)(62,101,73,89)(63,102,74,90)(64,97,75,85)(65,98,76,86)(66,99,77,87)(103,150,118,134)(104,145,119,135)(105,146,120,136)(106,147,115,137)(107,148,116,138)(108,149,117,133)(109,132,125,141)(110,127,126,142)(111,128,121,143)(112,129,122,144)(113,130,123,139)(114,131,124,140)(157,180,173,189)(158,175,174,190)(159,176,169,191)(160,177,170,192)(161,178,171,187)(162,179,172,188), (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), (1,155,4,152)(2,154,5,151)(3,153,6,156)(7,159,10,162)(8,158,11,161)(9,157,12,160)(13,53,16,50)(14,52,17,49)(15,51,18,54)(19,164,22,167)(20,163,23,166)(21,168,24,165)(25,173,28,170)(26,172,29,169)(27,171,30,174)(31,179,34,176)(32,178,35,175)(33,177,36,180)(37,182,40,185)(38,181,41,184)(39,186,42,183)(43,188,46,191)(44,187,47,190)(45,192,48,189)(55,107,58,104)(56,106,59,103)(57,105,60,108)(61,110,64,113)(62,109,65,112)(63,114,66,111)(67,116,70,119)(68,115,71,118)(69,120,72,117)(73,125,76,122)(74,124,77,121)(75,123,78,126)(79,131,82,128)(80,130,83,127)(81,129,84,132)(85,134,88,137)(86,133,89,136)(87,138,90,135)(91,140,94,143)(92,139,95,142)(93,144,96,141)(97,150,100,147)(98,149,101,146)(99,148,102,145) );
G=PermutationGroup([[(1,58),(2,59),(3,60),(4,55),(5,56),(6,57),(7,63),(8,64),(9,65),(10,66),(11,61),(12,62),(13,145),(14,146),(15,147),(16,148),(17,149),(18,150),(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),(49,101),(50,102),(51,97),(52,98),(53,99),(54,100),(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)], [(1,29,19,7),(2,30,20,8),(3,25,21,9),(4,26,22,10),(5,27,23,11),(6,28,24,12),(13,191,186,176),(14,192,181,177),(15,187,182,178),(16,188,183,179),(17,189,184,180),(18,190,185,175),(31,42,43,53),(32,37,44,54),(33,38,45,49),(34,39,46,50),(35,40,47,51),(36,41,48,52),(55,77,67,66),(56,78,68,61),(57,73,69,62),(58,74,70,63),(59,75,71,64),(60,76,72,65),(79,90,91,102),(80,85,92,97),(81,86,93,98),(82,87,94,99),(83,88,95,100),(84,89,96,101),(103,113,118,123),(104,114,119,124),(105,109,120,125),(106,110,115,126),(107,111,116,121),(108,112,117,122),(127,147,142,137),(128,148,143,138),(129,149,144,133),(130,150,139,134),(131,145,140,135),(132,146,141,136),(151,161,166,171),(152,162,167,172),(153,157,168,173),(154,158,163,174),(155,159,164,169),(156,160,165,170)], [(1,46,19,34),(2,47,20,35),(3,48,21,36),(4,43,22,31),(5,44,23,32),(6,45,24,33),(7,50,29,39),(8,51,30,40),(9,52,25,41),(10,53,26,42),(11,54,27,37),(12,49,28,38),(13,164,186,155),(14,165,181,156),(15,166,182,151),(16,167,183,152),(17,168,184,153),(18,163,185,154),(55,94,67,82),(56,95,68,83),(57,96,69,84),(58,91,70,79),(59,92,71,80),(60,93,72,81),(61,100,78,88),(62,101,73,89),(63,102,74,90),(64,97,75,85),(65,98,76,86),(66,99,77,87),(103,150,118,134),(104,145,119,135),(105,146,120,136),(106,147,115,137),(107,148,116,138),(108,149,117,133),(109,132,125,141),(110,127,126,142),(111,128,121,143),(112,129,122,144),(113,130,123,139),(114,131,124,140),(157,180,173,189),(158,175,174,190),(159,176,169,191),(160,177,170,192),(161,178,171,187),(162,179,172,188)], [(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)], [(1,155,4,152),(2,154,5,151),(3,153,6,156),(7,159,10,162),(8,158,11,161),(9,157,12,160),(13,53,16,50),(14,52,17,49),(15,51,18,54),(19,164,22,167),(20,163,23,166),(21,168,24,165),(25,173,28,170),(26,172,29,169),(27,171,30,174),(31,179,34,176),(32,178,35,175),(33,177,36,180),(37,182,40,185),(38,181,41,184),(39,186,42,183),(43,188,46,191),(44,187,47,190),(45,192,48,189),(55,107,58,104),(56,106,59,103),(57,105,60,108),(61,110,64,113),(62,109,65,112),(63,114,66,111),(67,116,70,119),(68,115,71,118),(69,120,72,117),(73,125,76,122),(74,124,77,121),(75,123,78,126),(79,131,82,128),(80,130,83,127),(81,129,84,132),(85,134,88,137),(86,133,89,136),(87,138,90,135),(91,140,94,143),(92,139,95,142),(93,144,96,141),(97,150,100,147),(98,149,101,146),(99,148,102,145)]])
48 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 6A | ··· | 6G | 8A | ··· | 8H | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D4 | D6 | Dic3 | D6 | SD16 | Q16 | C3⋊D4 | C3⋊D4 | Q8⋊2S3 | C3⋊Q16 |
| kernel | C2×Q8⋊2Dic3 | Q8⋊2Dic3 | C22×C3⋊C8 | C2×C4⋊Dic3 | Q8×C2×C6 | C6×Q8 | C22×Q8 | C2×C12 | C22×C6 | C22×C4 | C2×Q8 | C2×Q8 | C2×C6 | C2×C6 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 1 | 3 | 1 | 1 | 4 | 2 | 4 | 4 | 6 | 2 | 2 | 2 |
Matrix representation of C2×Q8⋊2Dic3 ►in GL6(𝔽73)
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 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 |
| 1 | 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 | 71 |
| 0 | 0 | 0 | 0 | 1 | 72 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 35 |
| 0 | 0 | 0 | 0 | 21 | 33 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 27 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 31 | 70 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 64 |
| 0 | 0 | 0 | 0 | 56 | 49 |
G:=sub<GL(6,GF(73))| [72,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,71,72],[1,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,40,21,0,0,0,0,35,33],[72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,72,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[27,0,0,0,0,0,0,72,0,0,0,0,0,0,3,31,0,0,0,0,28,70,0,0,0,0,0,0,24,56,0,0,0,0,64,49] >;
C2×Q8⋊2Dic3 in GAP, Magma, Sage, TeX
C_2\times Q_8\rtimes_2{\rm Dic}_3 % in TeX
G:=Group("C2xQ8:2Dic3"); // GroupNames label
G:=SmallGroup(192,783);
// by ID
G=gap.SmallGroup(192,783);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,56,422,184,1684,438,102,6278]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=d^6=1,c^2=b^2,e^2=d^3,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,c*d=d*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^-1>;
// generators/relations