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G = (C2×Dic3)⋊Q8order 192 = 26·3

2nd semidirect product of C2×Dic3 and Q8 acting via Q8/C2=C22

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(C232D6), 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), C32(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

C1C22×C6 — (C2×Dic3)⋊Q8
C1C3C6C2×C6C22×C6C22×Dic3C22×Dic6 — (C2×Dic3)⋊Q8
C3C22×C6 — (C2×Dic3)⋊Q8
C1C23C2×C4⋊C4

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 [×3], C2 [×4], C3, C4 [×13], C22 [×3], C22 [×4], C6 [×3], C6 [×4], C2×C4 [×4], C2×C4 [×23], Q8 [×8], C23, Dic3 [×8], C12 [×5], C2×C6 [×3], C2×C6 [×4], C4⋊C4 [×6], C22×C4 [×3], C22×C4 [×4], C2×Q8 [×6], Dic6 [×8], C2×Dic3 [×8], C2×Dic3 [×8], C2×C12 [×4], C2×C12 [×7], C22×C6, C2.C42 [×3], C2×C4⋊C4, C2×C4⋊C4 [×2], C22×Q8, Dic3⋊C4 [×4], C3×C4⋊C4 [×2], C2×Dic6 [×6], C22×Dic3 [×4], C22×C12 [×3], C23.78C23, C6.C42, C6.C42 [×2], C2×Dic3⋊C4 [×2], C6×C4⋊C4, C22×Dic6, (C2×Dic3)⋊Q8
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×6], Q8 [×6], C23, D6 [×3], C2×D4 [×3], C2×Q8 [×3], C4○D4, Dic6 [×2], C3⋊D4 [×2], C22×S3, C22≀C2, C22⋊Q8 [×3], C4⋊Q8 [×3], C2×Dic6, C4○D12, S3×D4 [×2], S3×Q8 [×2], C2×C3⋊D4, C23.78C23, C12⋊Q8 [×2], D6⋊Q8 [×2], C12.48D4, C232D6, Dic3⋊Q8, (C2×Dic3)⋊Q8

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

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

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

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

42 conjugacy classes

class 1 2A···2G 3 4A···4F4G···4N6A···6G12A···12L
order12···234···44···46···612···12
size11···124···412···122···24···4

42 irreducible representations

dim11111222222222244
type+++++++-+-+-+-
imageC1C2C2C2C2S3D4Q8D4Q8D6C4○D4Dic6C3⋊D4C4○D12S3×D4S3×Q8
kernel(C2×Dic3)⋊Q8C6.C42C2×Dic3⋊C4C6×C4⋊C4C22×Dic6C2×C4⋊C4C2×Dic3C2×Dic3C2×C12C2×C12C22×C4C2×C6C2×C4C2×C4C22C22C22
# reps13211144223244422

Matrix representation of (C2×Dic3)⋊Q8 in GL6(𝔽13)

1200000
0120000
0012000
0001200
0000120
0000012
,
1200000
0120000
000100
0012100
000010
000001
,
010000
1200000
000500
005000
000010
0000012
,
1200000
0120000
000800
008000
0000012
0000120
,
0120000
1200000
0010600
007300
000001
000010

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

׿
×
𝔽