metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C12)⋊7Q8, (C2×C4)⋊2Dic6, (C2×Dic3)⋊2Q8, (C2×C12).52D4, C6.21(C4⋊Q8), C6.40C22≀C2, C2.14(C12⋊Q8), C2.9(C23⋊2D6), C22.45(S3×Q8), (C2×Dic3).58D4, C22.244(S3×D4), (C22×C4).114D6, C6.58(C22⋊Q8), C2.20(D6⋊Q8), (C22×Dic6).5C2, C22.47(C2×Dic6), C2.5(Dic3⋊Q8), C2.9(C12.48D4), C6.C42.37C2, (C22×C12).63C22, C23.384(C22×S3), (C22×C6).343C23, C22.102(C4○D12), C3⋊2(C23.78C23), (C22×Dic3).52C22, (C6×C4⋊C4).21C2, (C2×C4⋊C4).16S3, (C2×C6).78(C2×Q8), (C2×C6).330(C2×D4), (C2×C6).82(C4○D4), (C2×C4).35(C3⋊D4), (C2×Dic3⋊C4).13C2, C22.134(C2×C3⋊D4), SmallGroup(192,538)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×Dic3)⋊Q8
G = < a,b,c,d,e | a2=b6=d4=1, c2=b3, e2=d2, ab=ba, ece-1=ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, dcd-1=ab3c, ede-1=d-1 >
Subgroups: 456 in 182 conjugacy classes, 67 normal (27 characteristic)
C1, C2, C2, C3, C4, C22, C22, C6, C6, C2×C4, C2×C4, Q8, C23, Dic3, C12, C2×C6, C2×C6, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×C6, C2.C42, C2×C4⋊C4, C2×C4⋊C4, C22×Q8, Dic3⋊C4, C3×C4⋊C4, C2×Dic6, C22×Dic3, C22×C12, C23.78C23, C6.C42, C6.C42, C2×Dic3⋊C4, C6×C4⋊C4, C22×Dic6, (C2×Dic3)⋊Q8
Quotients: C1, C2, C22, S3, D4, Q8, C23, D6, C2×D4, C2×Q8, C4○D4, Dic6, C3⋊D4, C22×S3, C22≀C2, C22⋊Q8, C4⋊Q8, C2×Dic6, C4○D12, S3×D4, S3×Q8, C2×C3⋊D4, C23.78C23, C12⋊Q8, D6⋊Q8, C12.48D4, C23⋊2D6, Dic3⋊Q8, (C2×Dic3)⋊Q8
►Regular action on 192 points
Generators in S192
(1 13)(2 14)(3 15)(4 16)(5 17)(6 18)(7 32)(8 33)(9 34)(10 35)(11 36)(12 31)(19 173)(20 174)(21 169)(22 170)(23 171)(24 172)(25 56)(26 57)(27 58)(28 59)(29 60)(30 55)(37 44)(38 45)(39 46)(40 47)(41 48)(42 43)(49 80)(50 81)(51 82)(52 83)(53 84)(54 79)(61 68)(62 69)(63 70)(64 71)(65 72)(66 67)(73 105)(74 106)(75 107)(76 108)(77 103)(78 104)(85 92)(86 93)(87 94)(88 95)(89 96)(90 91)(97 132)(98 127)(99 128)(100 129)(101 130)(102 131)(109 120)(110 115)(111 116)(112 117)(113 118)(114 119)(121 156)(122 151)(123 152)(124 153)(125 154)(126 155)(133 144)(134 139)(135 140)(136 141)(137 142)(138 143)(145 180)(146 175)(147 176)(148 177)(149 178)(150 179)(157 168)(158 163)(159 164)(160 165)(161 166)(162 167)(181 192)(182 187)(183 188)(184 189)(185 190)(186 191)
(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)
(1 183 4 186)(2 182 5 185)(3 181 6 184)(7 173 10 170)(8 172 11 169)(9 171 12 174)(13 188 16 191)(14 187 17 190)(15 192 18 189)(19 35 22 32)(20 34 23 31)(21 33 24 36)(25 167 28 164)(26 166 29 163)(27 165 30 168)(37 180 40 177)(38 179 41 176)(39 178 42 175)(43 146 46 149)(44 145 47 148)(45 150 48 147)(49 154 52 151)(50 153 53 156)(51 152 54 155)(55 157 58 160)(56 162 59 159)(57 161 60 158)(61 139 64 142)(62 144 65 141)(63 143 66 140)(67 135 70 138)(68 134 71 137)(69 133 72 136)(73 114 76 111)(74 113 77 110)(75 112 78 109)(79 126 82 123)(80 125 83 122)(81 124 84 121)(85 97 88 100)(86 102 89 99)(87 101 90 98)(91 127 94 130)(92 132 95 129)(93 131 96 128)(103 115 106 118)(104 120 107 117)(105 119 108 116)
(1 167 10 178)(2 166 11 177)(3 165 12 176)(4 164 7 175)(5 163 8 180)(6 168 9 179)(13 162 35 149)(14 161 36 148)(15 160 31 147)(16 159 32 146)(17 158 33 145)(18 157 34 150)(19 42 191 28)(20 41 192 27)(21 40 187 26)(22 39 188 25)(23 38 189 30)(24 37 190 29)(43 186 59 173)(44 185 60 172)(45 184 55 171)(46 183 56 170)(47 182 57 169)(48 181 58 174)(49 116 63 127)(50 115 64 132)(51 120 65 131)(52 119 66 130)(53 118 61 129)(54 117 62 128)(67 101 83 114)(68 100 84 113)(69 99 79 112)(70 98 80 111)(71 97 81 110)(72 102 82 109)(73 140 87 151)(74 139 88 156)(75 144 89 155)(76 143 90 154)(77 142 85 153)(78 141 86 152)(91 125 108 138)(92 124 103 137)(93 123 104 136)(94 122 105 135)(95 121 106 134)(96 126 107 133)
(1 52 10 66)(2 53 11 61)(3 54 12 62)(4 49 7 63)(5 50 8 64)(6 51 9 65)(13 83 35 67)(14 84 36 68)(15 79 31 69)(16 80 32 70)(17 81 33 71)(18 82 34 72)(19 143 191 154)(20 144 192 155)(21 139 187 156)(22 140 188 151)(23 141 189 152)(24 142 190 153)(25 87 39 73)(26 88 40 74)(27 89 41 75)(28 90 42 76)(29 85 37 77)(30 86 38 78)(43 108 59 91)(44 103 60 92)(45 104 55 93)(46 105 56 94)(47 106 57 95)(48 107 58 96)(97 145 110 158)(98 146 111 159)(99 147 112 160)(100 148 113 161)(101 149 114 162)(102 150 109 157)(115 163 132 180)(116 164 127 175)(117 165 128 176)(118 166 129 177)(119 167 130 178)(120 168 131 179)(121 169 134 182)(122 170 135 183)(123 171 136 184)(124 172 137 185)(125 173 138 186)(126 174 133 181)
G:=sub<Sym(192)| (1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,32)(8,33)(9,34)(10,35)(11,36)(12,31)(19,173)(20,174)(21,169)(22,170)(23,171)(24,172)(25,56)(26,57)(27,58)(28,59)(29,60)(30,55)(37,44)(38,45)(39,46)(40,47)(41,48)(42,43)(49,80)(50,81)(51,82)(52,83)(53,84)(54,79)(61,68)(62,69)(63,70)(64,71)(65,72)(66,67)(73,105)(74,106)(75,107)(76,108)(77,103)(78,104)(85,92)(86,93)(87,94)(88,95)(89,96)(90,91)(97,132)(98,127)(99,128)(100,129)(101,130)(102,131)(109,120)(110,115)(111,116)(112,117)(113,118)(114,119)(121,156)(122,151)(123,152)(124,153)(125,154)(126,155)(133,144)(134,139)(135,140)(136,141)(137,142)(138,143)(145,180)(146,175)(147,176)(148,177)(149,178)(150,179)(157,168)(158,163)(159,164)(160,165)(161,166)(162,167)(181,192)(182,187)(183,188)(184,189)(185,190)(186,191), (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), (1,183,4,186)(2,182,5,185)(3,181,6,184)(7,173,10,170)(8,172,11,169)(9,171,12,174)(13,188,16,191)(14,187,17,190)(15,192,18,189)(19,35,22,32)(20,34,23,31)(21,33,24,36)(25,167,28,164)(26,166,29,163)(27,165,30,168)(37,180,40,177)(38,179,41,176)(39,178,42,175)(43,146,46,149)(44,145,47,148)(45,150,48,147)(49,154,52,151)(50,153,53,156)(51,152,54,155)(55,157,58,160)(56,162,59,159)(57,161,60,158)(61,139,64,142)(62,144,65,141)(63,143,66,140)(67,135,70,138)(68,134,71,137)(69,133,72,136)(73,114,76,111)(74,113,77,110)(75,112,78,109)(79,126,82,123)(80,125,83,122)(81,124,84,121)(85,97,88,100)(86,102,89,99)(87,101,90,98)(91,127,94,130)(92,132,95,129)(93,131,96,128)(103,115,106,118)(104,120,107,117)(105,119,108,116), (1,167,10,178)(2,166,11,177)(3,165,12,176)(4,164,7,175)(5,163,8,180)(6,168,9,179)(13,162,35,149)(14,161,36,148)(15,160,31,147)(16,159,32,146)(17,158,33,145)(18,157,34,150)(19,42,191,28)(20,41,192,27)(21,40,187,26)(22,39,188,25)(23,38,189,30)(24,37,190,29)(43,186,59,173)(44,185,60,172)(45,184,55,171)(46,183,56,170)(47,182,57,169)(48,181,58,174)(49,116,63,127)(50,115,64,132)(51,120,65,131)(52,119,66,130)(53,118,61,129)(54,117,62,128)(67,101,83,114)(68,100,84,113)(69,99,79,112)(70,98,80,111)(71,97,81,110)(72,102,82,109)(73,140,87,151)(74,139,88,156)(75,144,89,155)(76,143,90,154)(77,142,85,153)(78,141,86,152)(91,125,108,138)(92,124,103,137)(93,123,104,136)(94,122,105,135)(95,121,106,134)(96,126,107,133), (1,52,10,66)(2,53,11,61)(3,54,12,62)(4,49,7,63)(5,50,8,64)(6,51,9,65)(13,83,35,67)(14,84,36,68)(15,79,31,69)(16,80,32,70)(17,81,33,71)(18,82,34,72)(19,143,191,154)(20,144,192,155)(21,139,187,156)(22,140,188,151)(23,141,189,152)(24,142,190,153)(25,87,39,73)(26,88,40,74)(27,89,41,75)(28,90,42,76)(29,85,37,77)(30,86,38,78)(43,108,59,91)(44,103,60,92)(45,104,55,93)(46,105,56,94)(47,106,57,95)(48,107,58,96)(97,145,110,158)(98,146,111,159)(99,147,112,160)(100,148,113,161)(101,149,114,162)(102,150,109,157)(115,163,132,180)(116,164,127,175)(117,165,128,176)(118,166,129,177)(119,167,130,178)(120,168,131,179)(121,169,134,182)(122,170,135,183)(123,171,136,184)(124,172,137,185)(125,173,138,186)(126,174,133,181)>;
G:=Group( (1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,32)(8,33)(9,34)(10,35)(11,36)(12,31)(19,173)(20,174)(21,169)(22,170)(23,171)(24,172)(25,56)(26,57)(27,58)(28,59)(29,60)(30,55)(37,44)(38,45)(39,46)(40,47)(41,48)(42,43)(49,80)(50,81)(51,82)(52,83)(53,84)(54,79)(61,68)(62,69)(63,70)(64,71)(65,72)(66,67)(73,105)(74,106)(75,107)(76,108)(77,103)(78,104)(85,92)(86,93)(87,94)(88,95)(89,96)(90,91)(97,132)(98,127)(99,128)(100,129)(101,130)(102,131)(109,120)(110,115)(111,116)(112,117)(113,118)(114,119)(121,156)(122,151)(123,152)(124,153)(125,154)(126,155)(133,144)(134,139)(135,140)(136,141)(137,142)(138,143)(145,180)(146,175)(147,176)(148,177)(149,178)(150,179)(157,168)(158,163)(159,164)(160,165)(161,166)(162,167)(181,192)(182,187)(183,188)(184,189)(185,190)(186,191), (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), (1,183,4,186)(2,182,5,185)(3,181,6,184)(7,173,10,170)(8,172,11,169)(9,171,12,174)(13,188,16,191)(14,187,17,190)(15,192,18,189)(19,35,22,32)(20,34,23,31)(21,33,24,36)(25,167,28,164)(26,166,29,163)(27,165,30,168)(37,180,40,177)(38,179,41,176)(39,178,42,175)(43,146,46,149)(44,145,47,148)(45,150,48,147)(49,154,52,151)(50,153,53,156)(51,152,54,155)(55,157,58,160)(56,162,59,159)(57,161,60,158)(61,139,64,142)(62,144,65,141)(63,143,66,140)(67,135,70,138)(68,134,71,137)(69,133,72,136)(73,114,76,111)(74,113,77,110)(75,112,78,109)(79,126,82,123)(80,125,83,122)(81,124,84,121)(85,97,88,100)(86,102,89,99)(87,101,90,98)(91,127,94,130)(92,132,95,129)(93,131,96,128)(103,115,106,118)(104,120,107,117)(105,119,108,116), (1,167,10,178)(2,166,11,177)(3,165,12,176)(4,164,7,175)(5,163,8,180)(6,168,9,179)(13,162,35,149)(14,161,36,148)(15,160,31,147)(16,159,32,146)(17,158,33,145)(18,157,34,150)(19,42,191,28)(20,41,192,27)(21,40,187,26)(22,39,188,25)(23,38,189,30)(24,37,190,29)(43,186,59,173)(44,185,60,172)(45,184,55,171)(46,183,56,170)(47,182,57,169)(48,181,58,174)(49,116,63,127)(50,115,64,132)(51,120,65,131)(52,119,66,130)(53,118,61,129)(54,117,62,128)(67,101,83,114)(68,100,84,113)(69,99,79,112)(70,98,80,111)(71,97,81,110)(72,102,82,109)(73,140,87,151)(74,139,88,156)(75,144,89,155)(76,143,90,154)(77,142,85,153)(78,141,86,152)(91,125,108,138)(92,124,103,137)(93,123,104,136)(94,122,105,135)(95,121,106,134)(96,126,107,133), (1,52,10,66)(2,53,11,61)(3,54,12,62)(4,49,7,63)(5,50,8,64)(6,51,9,65)(13,83,35,67)(14,84,36,68)(15,79,31,69)(16,80,32,70)(17,81,33,71)(18,82,34,72)(19,143,191,154)(20,144,192,155)(21,139,187,156)(22,140,188,151)(23,141,189,152)(24,142,190,153)(25,87,39,73)(26,88,40,74)(27,89,41,75)(28,90,42,76)(29,85,37,77)(30,86,38,78)(43,108,59,91)(44,103,60,92)(45,104,55,93)(46,105,56,94)(47,106,57,95)(48,107,58,96)(97,145,110,158)(98,146,111,159)(99,147,112,160)(100,148,113,161)(101,149,114,162)(102,150,109,157)(115,163,132,180)(116,164,127,175)(117,165,128,176)(118,166,129,177)(119,167,130,178)(120,168,131,179)(121,169,134,182)(122,170,135,183)(123,171,136,184)(124,172,137,185)(125,173,138,186)(126,174,133,181) );
G=PermutationGroup([[(1,13),(2,14),(3,15),(4,16),(5,17),(6,18),(7,32),(8,33),(9,34),(10,35),(11,36),(12,31),(19,173),(20,174),(21,169),(22,170),(23,171),(24,172),(25,56),(26,57),(27,58),(28,59),(29,60),(30,55),(37,44),(38,45),(39,46),(40,47),(41,48),(42,43),(49,80),(50,81),(51,82),(52,83),(53,84),(54,79),(61,68),(62,69),(63,70),(64,71),(65,72),(66,67),(73,105),(74,106),(75,107),(76,108),(77,103),(78,104),(85,92),(86,93),(87,94),(88,95),(89,96),(90,91),(97,132),(98,127),(99,128),(100,129),(101,130),(102,131),(109,120),(110,115),(111,116),(112,117),(113,118),(114,119),(121,156),(122,151),(123,152),(124,153),(125,154),(126,155),(133,144),(134,139),(135,140),(136,141),(137,142),(138,143),(145,180),(146,175),(147,176),(148,177),(149,178),(150,179),(157,168),(158,163),(159,164),(160,165),(161,166),(162,167),(181,192),(182,187),(183,188),(184,189),(185,190),(186,191)], [(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)], [(1,183,4,186),(2,182,5,185),(3,181,6,184),(7,173,10,170),(8,172,11,169),(9,171,12,174),(13,188,16,191),(14,187,17,190),(15,192,18,189),(19,35,22,32),(20,34,23,31),(21,33,24,36),(25,167,28,164),(26,166,29,163),(27,165,30,168),(37,180,40,177),(38,179,41,176),(39,178,42,175),(43,146,46,149),(44,145,47,148),(45,150,48,147),(49,154,52,151),(50,153,53,156),(51,152,54,155),(55,157,58,160),(56,162,59,159),(57,161,60,158),(61,139,64,142),(62,144,65,141),(63,143,66,140),(67,135,70,138),(68,134,71,137),(69,133,72,136),(73,114,76,111),(74,113,77,110),(75,112,78,109),(79,126,82,123),(80,125,83,122),(81,124,84,121),(85,97,88,100),(86,102,89,99),(87,101,90,98),(91,127,94,130),(92,132,95,129),(93,131,96,128),(103,115,106,118),(104,120,107,117),(105,119,108,116)], [(1,167,10,178),(2,166,11,177),(3,165,12,176),(4,164,7,175),(5,163,8,180),(6,168,9,179),(13,162,35,149),(14,161,36,148),(15,160,31,147),(16,159,32,146),(17,158,33,145),(18,157,34,150),(19,42,191,28),(20,41,192,27),(21,40,187,26),(22,39,188,25),(23,38,189,30),(24,37,190,29),(43,186,59,173),(44,185,60,172),(45,184,55,171),(46,183,56,170),(47,182,57,169),(48,181,58,174),(49,116,63,127),(50,115,64,132),(51,120,65,131),(52,119,66,130),(53,118,61,129),(54,117,62,128),(67,101,83,114),(68,100,84,113),(69,99,79,112),(70,98,80,111),(71,97,81,110),(72,102,82,109),(73,140,87,151),(74,139,88,156),(75,144,89,155),(76,143,90,154),(77,142,85,153),(78,141,86,152),(91,125,108,138),(92,124,103,137),(93,123,104,136),(94,122,105,135),(95,121,106,134),(96,126,107,133)], [(1,52,10,66),(2,53,11,61),(3,54,12,62),(4,49,7,63),(5,50,8,64),(6,51,9,65),(13,83,35,67),(14,84,36,68),(15,79,31,69),(16,80,32,70),(17,81,33,71),(18,82,34,72),(19,143,191,154),(20,144,192,155),(21,139,187,156),(22,140,188,151),(23,141,189,152),(24,142,190,153),(25,87,39,73),(26,88,40,74),(27,89,41,75),(28,90,42,76),(29,85,37,77),(30,86,38,78),(43,108,59,91),(44,103,60,92),(45,104,55,93),(46,105,56,94),(47,106,57,95),(48,107,58,96),(97,145,110,158),(98,146,111,159),(99,147,112,160),(100,148,113,161),(101,149,114,162),(102,150,109,157),(115,163,132,180),(116,164,127,175),(117,165,128,176),(118,166,129,177),(119,167,130,178),(120,168,131,179),(121,169,134,182),(122,170,135,183),(123,171,136,184),(124,172,137,185),(125,173,138,186),(126,174,133,181)]])
42 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | ··· | 4F | 4G | ··· | 4N | 6A | ··· | 6G | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 4 | ··· | 4 | 12 | ··· | 12 | 2 | ··· | 2 | 4 | ··· | 4 |
42 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | - | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | S3 | D4 | Q8 | D4 | Q8 | D6 | C4○D4 | Dic6 | C3⋊D4 | C4○D12 | S3×D4 | S3×Q8 |
| kernel | (C2×Dic3)⋊Q8 | C6.C42 | C2×Dic3⋊C4 | C6×C4⋊C4 | C22×Dic6 | C2×C4⋊C4 | C2×Dic3 | C2×Dic3 | C2×C12 | C2×C12 | C22×C4 | C2×C6 | C2×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 3 | 2 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 3 | 2 | 4 | 4 | 4 | 2 | 2 |
Matrix representation of (C2×Dic3)⋊Q8 ►in GL6(𝔽13)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 5 | 0 | 0 |
| 0 | 0 | 5 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 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 | 0 | 12 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 6 | 0 | 0 |
| 0 | 0 | 7 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(13))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,12,0,0,0,0,1,0,0,0,0,0,0,0,0,5,0,0,0,0,5,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,8,0,0,0,0,8,0,0,0,0,0,0,0,0,12,0,0,0,0,12,0],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,10,7,0,0,0,0,6,3,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
(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(192,538);
// by ID
G=gap.SmallGroup(192,538);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,253,120,254,387,184,6278]);
// 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,e*c*e^-1=a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=a*b^3*c,e*d*e^-1=d^-1>;
// generators/relations