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## G = (C2×C42).6S3order 192 = 26·3

### 5th non-split extension by C2×C42 of S3 acting via S3/C3=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C6 — (C2×C42).6S3
 Chief series C1 — C3 — C6 — C2×C6 — C22×C6 — C22×Dic3 — C2×Dic3⋊C4 — (C2×C42).6S3
 Lower central C3 — C2×C6 — (C2×C42).6S3
 Upper central C1 — C23 — C2×C42

Generators and relations for (C2×C42).6S3
G = < a,b,c,d,e | a2=b4=c4=d3=1, e2=b2, ebe-1=ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, cd=dc, ece-1=b2c, ede-1=d-1 >

Subgroups: 344 in 154 conjugacy classes, 71 normal (51 characteristic)
C1, C2 [×7], C3, C4 [×12], C22 [×7], C6 [×7], C2×C4 [×6], C2×C4 [×20], C23, Dic3 [×6], C12 [×6], C2×C6 [×7], C42 [×2], C4⋊C4 [×6], C22×C4 [×3], C22×C4 [×4], C2×Dic3 [×4], C2×Dic3 [×10], C2×C12 [×6], C2×C12 [×6], C22×C6, C2.C42 [×4], C2×C42, C2×C4⋊C4 [×2], Dic3⋊C4 [×4], Dic3⋊C4 [×2], C4×C12 [×2], C22×Dic3 [×4], C22×C12 [×3], C23.63C23, C6.C42 [×4], C2×Dic3⋊C4 [×2], C2×C4×C12, (C2×C42).6S3
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×2], Q8 [×2], C23, D6 [×3], C22×C4, C2×D4, C2×Q8, C4○D4 [×4], Dic6 [×2], C4×S3 [×2], C3⋊D4 [×2], C22×S3, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C422C2, C2×Dic6, S3×C2×C4, C4○D12 [×4], C2×C3⋊D4, C23.63C23, C4×Dic6, C12.6Q8, C422S3, C423S3, C12.48D4, C4×C3⋊D4, C23.28D6, (C2×C42).6S3

Smallest permutation representation of (C2×C42).6S3
Regular action on 192 points
Generators in S192
(1 53)(2 54)(3 55)(4 56)(5 79)(6 80)(7 77)(8 78)(9 29)(10 30)(11 31)(12 32)(13 35)(14 36)(15 33)(16 34)(17 91)(18 92)(19 89)(20 90)(21 41)(22 42)(23 43)(24 44)(25 47)(26 48)(27 45)(28 46)(37 59)(38 60)(39 57)(40 58)(49 130)(50 131)(51 132)(52 129)(61 81)(62 82)(63 83)(64 84)(65 87)(66 88)(67 85)(68 86)(69 105)(70 106)(71 107)(72 108)(73 93)(74 94)(75 95)(76 96)(97 122)(98 123)(99 124)(100 121)(101 126)(102 127)(103 128)(104 125)(109 134)(110 135)(111 136)(112 133)(113 138)(114 139)(115 140)(116 137)(117 142)(118 143)(119 144)(120 141)(145 170)(146 171)(147 172)(148 169)(149 174)(150 175)(151 176)(152 173)(153 178)(154 179)(155 180)(156 177)(157 182)(158 183)(159 184)(160 181)(161 186)(162 187)(163 188)(164 185)(165 190)(166 191)(167 192)(168 189)
(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 47 35 87)(2 48 36 88)(3 45 33 85)(4 46 34 86)(5 69 57 17)(6 70 58 18)(7 71 59 19)(8 72 60 20)(9 73 61 21)(10 74 62 22)(11 75 63 23)(12 76 64 24)(13 65 53 25)(14 66 54 26)(15 67 55 27)(16 68 56 28)(29 93 81 41)(30 94 82 42)(31 95 83 43)(32 96 84 44)(37 89 77 107)(38 90 78 108)(39 91 79 105)(40 92 80 106)(49 141 136 122)(50 142 133 123)(51 143 134 124)(52 144 135 121)(97 130 120 111)(98 131 117 112)(99 132 118 109)(100 129 119 110)(101 157 147 115)(102 158 148 116)(103 159 145 113)(104 160 146 114)(125 181 171 139)(126 182 172 140)(127 183 169 137)(128 184 170 138)(149 167 153 163)(150 168 154 164)(151 165 155 161)(152 166 156 162)(173 191 177 187)(174 192 178 188)(175 189 179 185)(176 190 180 186)
(1 9 5)(2 10 6)(3 11 7)(4 12 8)(13 81 39)(14 82 40)(15 83 37)(16 84 38)(17 87 21)(18 88 22)(19 85 23)(20 86 24)(25 93 105)(26 94 106)(27 95 107)(28 96 108)(29 79 53)(30 80 54)(31 77 55)(32 78 56)(33 63 59)(34 64 60)(35 61 57)(36 62 58)(41 91 65)(42 92 66)(43 89 67)(44 90 68)(45 75 71)(46 76 72)(47 73 69)(48 74 70)(49 191 114)(50 192 115)(51 189 116)(52 190 113)(97 152 171)(98 149 172)(99 150 169)(100 151 170)(101 142 178)(102 143 179)(103 144 180)(104 141 177)(109 164 183)(110 161 184)(111 162 181)(112 163 182)(117 153 126)(118 154 127)(119 155 128)(120 156 125)(121 176 145)(122 173 146)(123 174 147)(124 175 148)(129 165 138)(130 166 139)(131 167 140)(132 168 137)(133 188 157)(134 185 158)(135 186 159)(136 187 160)
(1 148 3 146)(2 170 4 172)(5 124 7 122)(6 100 8 98)(9 175 11 173)(10 151 12 149)(13 127 15 125)(14 103 16 101)(17 136 19 134)(18 112 20 110)(21 187 23 185)(22 163 24 161)(25 139 27 137)(26 115 28 113)(29 150 31 152)(30 176 32 174)(33 104 35 102)(34 126 36 128)(37 120 39 118)(38 142 40 144)(41 162 43 164)(42 188 44 186)(45 116 47 114)(46 138 48 140)(49 71 51 69)(50 108 52 106)(53 169 55 171)(54 145 56 147)(57 143 59 141)(58 119 60 117)(61 179 63 177)(62 155 64 153)(65 181 67 183)(66 157 68 159)(70 131 72 129)(73 191 75 189)(74 167 76 165)(77 97 79 99)(78 123 80 121)(81 154 83 156)(82 180 84 178)(85 158 87 160)(86 184 88 182)(89 109 91 111)(90 135 92 133)(93 166 95 168)(94 192 96 190)(105 130 107 132)

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

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

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

60 conjugacy classes

 class 1 2A ··· 2G 3 4A ··· 4L 4M ··· 4T 6A ··· 6G 12A ··· 12X order 1 2 ··· 2 3 4 ··· 4 4 ··· 4 6 ··· 6 12 ··· 12 size 1 1 ··· 1 2 2 ··· 2 12 ··· 12 2 ··· 2 2 ··· 2

60 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 2 type + + + + + + - + - image C1 C2 C2 C2 C4 S3 D4 Q8 D6 C4○D4 Dic6 C4×S3 C3⋊D4 C4○D12 kernel (C2×C42).6S3 C6.C42 C2×Dic3⋊C4 C2×C4×C12 Dic3⋊C4 C2×C42 C2×C12 C2×C12 C22×C4 C2×C6 C2×C4 C2×C4 C2×C4 C22 # reps 1 4 2 1 8 1 2 2 3 8 4 4 4 16

Matrix representation of (C2×C42).6S3 in GL8(𝔽13)

 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
,
 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 8 11 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12
,
 8 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 8 11 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12
,
 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 1 12
,
 7 3 0 0 0 0 0 0 10 6 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 9 7 0 0 0 0 0 0 0 0 11 9 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 6 10 0 0 0 0 0 0 3 7

G:=sub<GL(8,GF(13))| [12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,11,5,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12],[8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,11,5,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[7,10,0,0,0,0,0,0,3,6,0,0,0,0,0,0,0,0,6,9,0,0,0,0,0,0,6,7,0,0,0,0,0,0,0,0,11,4,0,0,0,0,0,0,9,2,0,0,0,0,0,0,0,0,6,3,0,0,0,0,0,0,10,7] >;

(C2×C42).6S3 in GAP, Magma, Sage, TeX

(C_2\times C_4^2)._6S_3
% in TeX

G:=Group("(C2xC4^2).6S3");
// GroupNames label

G:=SmallGroup(192,492);
// by ID

G=gap.SmallGroup(192,492);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,253,232,758,58,6278]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=c^4=d^3=1,e^2=b^2,e*b*e^-1=a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,c*d=d*c,e*c*e^-1=b^2*c,e*d*e^-1=d^-1>;
// generators/relations

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