direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8×Dic3, C6⋊3(C4×Q8), (C6×Q8)⋊11C4, C6.46(C23×C4), (C2×Q8).230D6, C6.52(C22×Q8), C22.36(S3×Q8), C12.95(C22×C4), (C2×C6).303C24, (C22×C4).399D6, (C22×Q8).16S3, C2.8(C23×Dic3), (C2×C12).550C23, C22.46(S3×C23), (C6×Q8).232C22, C4.18(C22×Dic3), C4⋊Dic3.388C22, C23.350(C22×S3), (C22×C6).421C23, (C22×C12).283C22, C22.38(Q8⋊3S3), (C2×Dic3).287C23, (C4×Dic3).260C22, C22.32(C22×Dic3), (C22×Dic3).245C22, C3⋊4(C2×C4×Q8), C2.4(C2×S3×Q8), (Q8×C2×C6).8C2, (C3×Q8)⋊18(C2×C4), (C2×C6).97(C2×Q8), C6.126(C2×C4○D4), C2.4(C2×Q8⋊3S3), (C2×C4×Dic3).17C2, (C2×C12).133(C2×C4), (C2×C4⋊Dic3).45C2, (C2×C4).55(C2×Dic3), (C2×C6).199(C4○D4), (C2×C4).631(C22×S3), (C2×C6).209(C22×C4), SmallGroup(192,1370)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q8×Dic3
G = < a,b,c,d,e | a2=b4=d6=1, c2=b2, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 488 in 298 conjugacy classes, 215 normal (16 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C2×C4, C2×C4, Q8, C23, Dic3, Dic3, C12, C2×C6, C2×C6, C42, C4⋊C4, C22×C4, C22×C4, C2×Q8, C2×Dic3, C2×Dic3, C2×C12, C3×Q8, C22×C6, C2×C42, C2×C4⋊C4, C4×Q8, C22×Q8, C4×Dic3, C4⋊Dic3, C22×Dic3, C22×Dic3, C22×C12, C6×Q8, C2×C4×Q8, C2×C4×Dic3, C2×C4⋊Dic3, Q8×Dic3, Q8×C2×C6, C2×Q8×Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, Q8, C23, Dic3, D6, C22×C4, C2×Q8, C4○D4, C24, C2×Dic3, C22×S3, C4×Q8, C23×C4, C22×Q8, C2×C4○D4, S3×Q8, Q8⋊3S3, C22×Dic3, S3×C23, C2×C4×Q8, Q8×Dic3, C2×S3×Q8, C2×Q8⋊3S3, C23×Dic3, C2×Q8×Dic3
►Regular action on 192 points
Generators in S192
(1 64)(2 65)(3 66)(4 61)(5 62)(6 63)(7 141)(8 142)(9 143)(10 144)(11 139)(12 140)(13 57)(14 58)(15 59)(16 60)(17 55)(18 56)(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)(43 100)(44 101)(45 102)(46 97)(47 98)(48 99)(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 25 16 21)(2 26 17 22)(3 27 18 23)(4 28 13 24)(5 29 14 19)(6 30 15 20)(7 180 189 185)(8 175 190 186)(9 176 191 181)(10 177 192 182)(11 178 187 183)(12 179 188 184)(31 46 41 50)(32 47 42 51)(33 48 37 52)(34 43 38 53)(35 44 39 54)(36 45 40 49)(55 74 65 70)(56 75 66 71)(57 76 61 72)(58 77 62 67)(59 78 63 68)(60 73 64 69)(79 94 89 97)(80 95 90 98)(81 96 85 99)(82 91 86 100)(83 92 87 101)(84 93 88 102)(103 123 114 118)(104 124 109 119)(105 125 110 120)(106 126 111 115)(107 121 112 116)(108 122 113 117)(127 142 138 147)(128 143 133 148)(129 144 134 149)(130 139 135 150)(131 140 136 145)(132 141 137 146)(151 171 162 166)(152 172 157 167)(153 173 158 168)(154 174 159 163)(155 169 160 164)(156 170 161 165)
(1 37 16 33)(2 38 17 34)(3 39 18 35)(4 40 13 36)(5 41 14 31)(6 42 15 32)(7 173 189 168)(8 174 190 163)(9 169 191 164)(10 170 192 165)(11 171 187 166)(12 172 188 167)(19 50 29 46)(20 51 30 47)(21 52 25 48)(22 53 26 43)(23 54 27 44)(24 49 28 45)(55 86 65 82)(56 87 66 83)(57 88 61 84)(58 89 62 79)(59 90 63 80)(60 85 64 81)(67 97 77 94)(68 98 78 95)(69 99 73 96)(70 100 74 91)(71 101 75 92)(72 102 76 93)(103 135 114 130)(104 136 109 131)(105 137 110 132)(106 138 111 127)(107 133 112 128)(108 134 113 129)(115 147 126 142)(116 148 121 143)(117 149 122 144)(118 150 123 139)(119 145 124 140)(120 146 125 141)(151 183 162 178)(152 184 157 179)(153 185 158 180)(154 186 159 175)(155 181 160 176)(156 182 161 177)
(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)
(1 153 4 156)(2 152 5 155)(3 151 6 154)(7 49 10 52)(8 54 11 51)(9 53 12 50)(13 161 16 158)(14 160 17 157)(15 159 18 162)(19 164 22 167)(20 163 23 166)(21 168 24 165)(25 173 28 170)(26 172 29 169)(27 171 30 174)(31 176 34 179)(32 175 35 178)(33 180 36 177)(37 185 40 182)(38 184 41 181)(39 183 42 186)(43 188 46 191)(44 187 47 190)(45 192 48 189)(55 104 58 107)(56 103 59 106)(57 108 60 105)(61 113 64 110)(62 112 65 109)(63 111 66 114)(67 116 70 119)(68 115 71 118)(69 120 72 117)(73 125 76 122)(74 124 77 121)(75 123 78 126)(79 128 82 131)(80 127 83 130)(81 132 84 129)(85 137 88 134)(86 136 89 133)(87 135 90 138)(91 140 94 143)(92 139 95 142)(93 144 96 141)(97 148 100 145)(98 147 101 150)(99 146 102 149)
G:=sub<Sym(192)| (1,64)(2,65)(3,66)(4,61)(5,62)(6,63)(7,141)(8,142)(9,143)(10,144)(11,139)(12,140)(13,57)(14,58)(15,59)(16,60)(17,55)(18,56)(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)(43,100)(44,101)(45,102)(46,97)(47,98)(48,99)(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), (1,25,16,21)(2,26,17,22)(3,27,18,23)(4,28,13,24)(5,29,14,19)(6,30,15,20)(7,180,189,185)(8,175,190,186)(9,176,191,181)(10,177,192,182)(11,178,187,183)(12,179,188,184)(31,46,41,50)(32,47,42,51)(33,48,37,52)(34,43,38,53)(35,44,39,54)(36,45,40,49)(55,74,65,70)(56,75,66,71)(57,76,61,72)(58,77,62,67)(59,78,63,68)(60,73,64,69)(79,94,89,97)(80,95,90,98)(81,96,85,99)(82,91,86,100)(83,92,87,101)(84,93,88,102)(103,123,114,118)(104,124,109,119)(105,125,110,120)(106,126,111,115)(107,121,112,116)(108,122,113,117)(127,142,138,147)(128,143,133,148)(129,144,134,149)(130,139,135,150)(131,140,136,145)(132,141,137,146)(151,171,162,166)(152,172,157,167)(153,173,158,168)(154,174,159,163)(155,169,160,164)(156,170,161,165), (1,37,16,33)(2,38,17,34)(3,39,18,35)(4,40,13,36)(5,41,14,31)(6,42,15,32)(7,173,189,168)(8,174,190,163)(9,169,191,164)(10,170,192,165)(11,171,187,166)(12,172,188,167)(19,50,29,46)(20,51,30,47)(21,52,25,48)(22,53,26,43)(23,54,27,44)(24,49,28,45)(55,86,65,82)(56,87,66,83)(57,88,61,84)(58,89,62,79)(59,90,63,80)(60,85,64,81)(67,97,77,94)(68,98,78,95)(69,99,73,96)(70,100,74,91)(71,101,75,92)(72,102,76,93)(103,135,114,130)(104,136,109,131)(105,137,110,132)(106,138,111,127)(107,133,112,128)(108,134,113,129)(115,147,126,142)(116,148,121,143)(117,149,122,144)(118,150,123,139)(119,145,124,140)(120,146,125,141)(151,183,162,178)(152,184,157,179)(153,185,158,180)(154,186,159,175)(155,181,160,176)(156,182,161,177), (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), (1,153,4,156)(2,152,5,155)(3,151,6,154)(7,49,10,52)(8,54,11,51)(9,53,12,50)(13,161,16,158)(14,160,17,157)(15,159,18,162)(19,164,22,167)(20,163,23,166)(21,168,24,165)(25,173,28,170)(26,172,29,169)(27,171,30,174)(31,176,34,179)(32,175,35,178)(33,180,36,177)(37,185,40,182)(38,184,41,181)(39,183,42,186)(43,188,46,191)(44,187,47,190)(45,192,48,189)(55,104,58,107)(56,103,59,106)(57,108,60,105)(61,113,64,110)(62,112,65,109)(63,111,66,114)(67,116,70,119)(68,115,71,118)(69,120,72,117)(73,125,76,122)(74,124,77,121)(75,123,78,126)(79,128,82,131)(80,127,83,130)(81,132,84,129)(85,137,88,134)(86,136,89,133)(87,135,90,138)(91,140,94,143)(92,139,95,142)(93,144,96,141)(97,148,100,145)(98,147,101,150)(99,146,102,149)>;
G:=Group( (1,64)(2,65)(3,66)(4,61)(5,62)(6,63)(7,141)(8,142)(9,143)(10,144)(11,139)(12,140)(13,57)(14,58)(15,59)(16,60)(17,55)(18,56)(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)(43,100)(44,101)(45,102)(46,97)(47,98)(48,99)(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), (1,25,16,21)(2,26,17,22)(3,27,18,23)(4,28,13,24)(5,29,14,19)(6,30,15,20)(7,180,189,185)(8,175,190,186)(9,176,191,181)(10,177,192,182)(11,178,187,183)(12,179,188,184)(31,46,41,50)(32,47,42,51)(33,48,37,52)(34,43,38,53)(35,44,39,54)(36,45,40,49)(55,74,65,70)(56,75,66,71)(57,76,61,72)(58,77,62,67)(59,78,63,68)(60,73,64,69)(79,94,89,97)(80,95,90,98)(81,96,85,99)(82,91,86,100)(83,92,87,101)(84,93,88,102)(103,123,114,118)(104,124,109,119)(105,125,110,120)(106,126,111,115)(107,121,112,116)(108,122,113,117)(127,142,138,147)(128,143,133,148)(129,144,134,149)(130,139,135,150)(131,140,136,145)(132,141,137,146)(151,171,162,166)(152,172,157,167)(153,173,158,168)(154,174,159,163)(155,169,160,164)(156,170,161,165), (1,37,16,33)(2,38,17,34)(3,39,18,35)(4,40,13,36)(5,41,14,31)(6,42,15,32)(7,173,189,168)(8,174,190,163)(9,169,191,164)(10,170,192,165)(11,171,187,166)(12,172,188,167)(19,50,29,46)(20,51,30,47)(21,52,25,48)(22,53,26,43)(23,54,27,44)(24,49,28,45)(55,86,65,82)(56,87,66,83)(57,88,61,84)(58,89,62,79)(59,90,63,80)(60,85,64,81)(67,97,77,94)(68,98,78,95)(69,99,73,96)(70,100,74,91)(71,101,75,92)(72,102,76,93)(103,135,114,130)(104,136,109,131)(105,137,110,132)(106,138,111,127)(107,133,112,128)(108,134,113,129)(115,147,126,142)(116,148,121,143)(117,149,122,144)(118,150,123,139)(119,145,124,140)(120,146,125,141)(151,183,162,178)(152,184,157,179)(153,185,158,180)(154,186,159,175)(155,181,160,176)(156,182,161,177), (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), (1,153,4,156)(2,152,5,155)(3,151,6,154)(7,49,10,52)(8,54,11,51)(9,53,12,50)(13,161,16,158)(14,160,17,157)(15,159,18,162)(19,164,22,167)(20,163,23,166)(21,168,24,165)(25,173,28,170)(26,172,29,169)(27,171,30,174)(31,176,34,179)(32,175,35,178)(33,180,36,177)(37,185,40,182)(38,184,41,181)(39,183,42,186)(43,188,46,191)(44,187,47,190)(45,192,48,189)(55,104,58,107)(56,103,59,106)(57,108,60,105)(61,113,64,110)(62,112,65,109)(63,111,66,114)(67,116,70,119)(68,115,71,118)(69,120,72,117)(73,125,76,122)(74,124,77,121)(75,123,78,126)(79,128,82,131)(80,127,83,130)(81,132,84,129)(85,137,88,134)(86,136,89,133)(87,135,90,138)(91,140,94,143)(92,139,95,142)(93,144,96,141)(97,148,100,145)(98,147,101,150)(99,146,102,149) );
G=PermutationGroup([[(1,64),(2,65),(3,66),(4,61),(5,62),(6,63),(7,141),(8,142),(9,143),(10,144),(11,139),(12,140),(13,57),(14,58),(15,59),(16,60),(17,55),(18,56),(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),(43,100),(44,101),(45,102),(46,97),(47,98),(48,99),(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)], [(1,25,16,21),(2,26,17,22),(3,27,18,23),(4,28,13,24),(5,29,14,19),(6,30,15,20),(7,180,189,185),(8,175,190,186),(9,176,191,181),(10,177,192,182),(11,178,187,183),(12,179,188,184),(31,46,41,50),(32,47,42,51),(33,48,37,52),(34,43,38,53),(35,44,39,54),(36,45,40,49),(55,74,65,70),(56,75,66,71),(57,76,61,72),(58,77,62,67),(59,78,63,68),(60,73,64,69),(79,94,89,97),(80,95,90,98),(81,96,85,99),(82,91,86,100),(83,92,87,101),(84,93,88,102),(103,123,114,118),(104,124,109,119),(105,125,110,120),(106,126,111,115),(107,121,112,116),(108,122,113,117),(127,142,138,147),(128,143,133,148),(129,144,134,149),(130,139,135,150),(131,140,136,145),(132,141,137,146),(151,171,162,166),(152,172,157,167),(153,173,158,168),(154,174,159,163),(155,169,160,164),(156,170,161,165)], [(1,37,16,33),(2,38,17,34),(3,39,18,35),(4,40,13,36),(5,41,14,31),(6,42,15,32),(7,173,189,168),(8,174,190,163),(9,169,191,164),(10,170,192,165),(11,171,187,166),(12,172,188,167),(19,50,29,46),(20,51,30,47),(21,52,25,48),(22,53,26,43),(23,54,27,44),(24,49,28,45),(55,86,65,82),(56,87,66,83),(57,88,61,84),(58,89,62,79),(59,90,63,80),(60,85,64,81),(67,97,77,94),(68,98,78,95),(69,99,73,96),(70,100,74,91),(71,101,75,92),(72,102,76,93),(103,135,114,130),(104,136,109,131),(105,137,110,132),(106,138,111,127),(107,133,112,128),(108,134,113,129),(115,147,126,142),(116,148,121,143),(117,149,122,144),(118,150,123,139),(119,145,124,140),(120,146,125,141),(151,183,162,178),(152,184,157,179),(153,185,158,180),(154,186,159,175),(155,181,160,176),(156,182,161,177)], [(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)], [(1,153,4,156),(2,152,5,155),(3,151,6,154),(7,49,10,52),(8,54,11,51),(9,53,12,50),(13,161,16,158),(14,160,17,157),(15,159,18,162),(19,164,22,167),(20,163,23,166),(21,168,24,165),(25,173,28,170),(26,172,29,169),(27,171,30,174),(31,176,34,179),(32,175,35,178),(33,180,36,177),(37,185,40,182),(38,184,41,181),(39,183,42,186),(43,188,46,191),(44,187,47,190),(45,192,48,189),(55,104,58,107),(56,103,59,106),(57,108,60,105),(61,113,64,110),(62,112,65,109),(63,111,66,114),(67,116,70,119),(68,115,71,118),(69,120,72,117),(73,125,76,122),(74,124,77,121),(75,123,78,126),(79,128,82,131),(80,127,83,130),(81,132,84,129),(85,137,88,134),(86,136,89,133),(87,135,90,138),(91,140,94,143),(92,139,95,142),(93,144,96,141),(97,148,100,145),(98,147,101,150),(99,146,102,149)]])
60 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | ··· | 4L | 4M | ··· | 4T | 4U | ··· | 4AF | 6A | ··· | 6G | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | ··· | 2 | 3 | ··· | 3 | 6 | ··· | 6 | 2 | ··· | 2 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C4 | S3 | Q8 | D6 | Dic3 | D6 | C4○D4 | S3×Q8 | Q8⋊3S3 |
| kernel | C2×Q8×Dic3 | C2×C4×Dic3 | C2×C4⋊Dic3 | Q8×Dic3 | Q8×C2×C6 | C6×Q8 | C22×Q8 | C2×Dic3 | C22×C4 | C2×Q8 | C2×Q8 | C2×C6 | C22 | C22 |
| # reps | 1 | 3 | 3 | 8 | 1 | 16 | 1 | 4 | 3 | 8 | 4 | 4 | 2 | 2 |
Matrix representation of C2×Q8×Dic3 ►in GL5(𝔽13)
| 12 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 12 | 8 | 0 | 0 |
| 0 | 3 | 1 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 |
| 0 | 7 | 2 | 0 | 0 |
| 0 | 1 | 6 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 12 |
| 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 |
| 0 | 0 | 0 | 8 | 0 |
G:=sub<GL(5,GF(13))| [12,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,0,12],[1,0,0,0,0,0,12,3,0,0,0,8,1,0,0,0,0,0,12,0,0,0,0,0,12],[12,0,0,0,0,0,7,1,0,0,0,2,6,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,12,0],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,8,0,0,0,8,0] >;
C2×Q8×Dic3 in GAP, Magma, Sage, TeX
C_2\times Q_8\times {\rm Dic}_3 % in TeX
G:=Group("C2xQ8xDic3"); // GroupNames label
G:=SmallGroup(192,1370);
// by ID
G=gap.SmallGroup(192,1370);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,184,297,136,6278]);
// 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=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations