direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C3×Q82, C6.1672+ 1+4, C4⋊Q8.14C6, C4.20(C6×Q8), (C4×Q8).16C6, C42.52(C2×C6), (Q8×C12).23C2, C12.126(C2×Q8), C6.66(C22×Q8), (C2×C6).378C24, (C2×C12).966C23, (C4×C12).293C22, C22.52(C23×C6), (C6×Q8).186C22, C2.19(C3×2+ 1+4), C2.12(Q8×C2×C6), C4⋊C4.78(C2×C6), (C3×C4⋊Q8).29C2, (C2×Q8).30(C2×C6), (C2×C4).39(C22×C6), (C3×C4⋊C4).403C22, SmallGroup(192,1447)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×Q82
G = < a,b,c,d,e | a3=b4=d4=1, c2=b2, e2=d2, 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: 266 in 212 conjugacy classes, 182 normal (8 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C2×C4, Q8, Q8, C12, C12, C2×C6, C42, C4⋊C4, C2×Q8, C2×C12, C3×Q8, C3×Q8, C4×Q8, C4⋊Q8, C4×C12, C3×C4⋊C4, C6×Q8, Q82, Q8×C12, C3×C4⋊Q8, C3×Q82
Quotients: C1, C2, C3, C22, C6, Q8, C23, C2×C6, C2×Q8, C24, C3×Q8, C22×C6, C22×Q8, 2+ 1+4, C6×Q8, C23×C6, Q82, Q8×C2×C6, C3×2+ 1+4, C3×Q82
►Regular action on 192 points
Generators in S192
(1 41 18)(2 42 19)(3 43 20)(4 44 17)(5 31 12)(6 32 9)(7 29 10)(8 30 11)(13 38 33)(14 39 34)(15 40 35)(16 37 36)(21 49 48)(22 50 45)(23 51 46)(24 52 47)(25 190 168)(26 191 165)(27 192 166)(28 189 167)(53 76 80)(54 73 77)(55 74 78)(56 75 79)(57 61 84)(58 62 81)(59 63 82)(60 64 83)(65 88 92)(66 85 89)(67 86 90)(68 87 91)(69 98 96)(70 99 93)(71 100 94)(72 97 95)(101 123 127)(102 124 128)(103 121 125)(104 122 126)(105 109 131)(106 110 132)(107 111 129)(108 112 130)(113 135 139)(114 136 140)(115 133 137)(116 134 138)(117 145 143)(118 146 144)(119 147 141)(120 148 142)(149 171 175)(150 172 176)(151 169 173)(152 170 174)(153 157 179)(154 158 180)(155 159 177)(156 160 178)(161 183 187)(162 184 188)(163 181 185)(164 182 186)
(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)
(1 108 3 106)(2 107 4 105)(5 141 7 143)(6 144 8 142)(9 146 11 148)(10 145 12 147)(13 123 15 121)(14 122 16 124)(17 131 19 129)(18 130 20 132)(21 136 23 134)(22 135 24 133)(25 92 27 90)(26 91 28 89)(29 117 31 119)(30 120 32 118)(33 101 35 103)(34 104 36 102)(37 128 39 126)(38 127 40 125)(41 112 43 110)(42 111 44 109)(45 113 47 115)(46 116 48 114)(49 140 51 138)(50 139 52 137)(53 180 55 178)(54 179 56 177)(57 181 59 183)(58 184 60 182)(61 185 63 187)(62 188 64 186)(65 192 67 190)(66 191 68 189)(69 171 71 169)(70 170 72 172)(73 153 75 155)(74 156 76 154)(77 157 79 159)(78 160 80 158)(81 162 83 164)(82 161 84 163)(85 165 87 167)(86 168 88 166)(93 152 95 150)(94 151 96 149)(97 176 99 174)(98 175 100 173)
(1 14 29 22)(2 15 30 23)(3 16 31 24)(4 13 32 21)(5 47 20 36)(6 48 17 33)(7 45 18 34)(8 46 19 35)(9 49 44 38)(10 50 41 39)(11 51 42 40)(12 52 43 37)(25 173 159 186)(26 174 160 187)(27 175 157 188)(28 176 158 185)(53 84 68 95)(54 81 65 96)(55 82 66 93)(56 83 67 94)(57 87 72 76)(58 88 69 73)(59 85 70 74)(60 86 71 75)(61 91 97 80)(62 92 98 77)(63 89 99 78)(64 90 100 79)(101 144 114 131)(102 141 115 132)(103 142 116 129)(104 143 113 130)(105 123 118 136)(106 124 119 133)(107 121 120 134)(108 122 117 135)(109 127 146 140)(110 128 147 137)(111 125 148 138)(112 126 145 139)(149 179 162 192)(150 180 163 189)(151 177 164 190)(152 178 161 191)(153 184 166 171)(154 181 167 172)(155 182 168 169)(156 183 165 170)
(1 74 29 85)(2 75 30 86)(3 76 31 87)(4 73 32 88)(5 68 20 53)(6 65 17 54)(7 66 18 55)(8 67 19 56)(9 92 44 77)(10 89 41 78)(11 90 42 79)(12 91 43 80)(13 69 21 58)(14 70 22 59)(15 71 23 60)(16 72 24 57)(25 111 159 148)(26 112 160 145)(27 109 157 146)(28 110 158 147)(33 96 48 81)(34 93 45 82)(35 94 46 83)(36 95 47 84)(37 97 52 61)(38 98 49 62)(39 99 50 63)(40 100 51 64)(101 149 114 162)(102 150 115 163)(103 151 116 164)(104 152 113 161)(105 153 118 166)(106 154 119 167)(107 155 120 168)(108 156 117 165)(121 169 134 182)(122 170 135 183)(123 171 136 184)(124 172 133 181)(125 173 138 186)(126 174 139 187)(127 175 140 188)(128 176 137 185)(129 177 142 190)(130 178 143 191)(131 179 144 192)(132 180 141 189)
G:=sub<Sym(192)| (1,41,18)(2,42,19)(3,43,20)(4,44,17)(5,31,12)(6,32,9)(7,29,10)(8,30,11)(13,38,33)(14,39,34)(15,40,35)(16,37,36)(21,49,48)(22,50,45)(23,51,46)(24,52,47)(25,190,168)(26,191,165)(27,192,166)(28,189,167)(53,76,80)(54,73,77)(55,74,78)(56,75,79)(57,61,84)(58,62,81)(59,63,82)(60,64,83)(65,88,92)(66,85,89)(67,86,90)(68,87,91)(69,98,96)(70,99,93)(71,100,94)(72,97,95)(101,123,127)(102,124,128)(103,121,125)(104,122,126)(105,109,131)(106,110,132)(107,111,129)(108,112,130)(113,135,139)(114,136,140)(115,133,137)(116,134,138)(117,145,143)(118,146,144)(119,147,141)(120,148,142)(149,171,175)(150,172,176)(151,169,173)(152,170,174)(153,157,179)(154,158,180)(155,159,177)(156,160,178)(161,183,187)(162,184,188)(163,181,185)(164,182,186), (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), (1,108,3,106)(2,107,4,105)(5,141,7,143)(6,144,8,142)(9,146,11,148)(10,145,12,147)(13,123,15,121)(14,122,16,124)(17,131,19,129)(18,130,20,132)(21,136,23,134)(22,135,24,133)(25,92,27,90)(26,91,28,89)(29,117,31,119)(30,120,32,118)(33,101,35,103)(34,104,36,102)(37,128,39,126)(38,127,40,125)(41,112,43,110)(42,111,44,109)(45,113,47,115)(46,116,48,114)(49,140,51,138)(50,139,52,137)(53,180,55,178)(54,179,56,177)(57,181,59,183)(58,184,60,182)(61,185,63,187)(62,188,64,186)(65,192,67,190)(66,191,68,189)(69,171,71,169)(70,170,72,172)(73,153,75,155)(74,156,76,154)(77,157,79,159)(78,160,80,158)(81,162,83,164)(82,161,84,163)(85,165,87,167)(86,168,88,166)(93,152,95,150)(94,151,96,149)(97,176,99,174)(98,175,100,173), (1,14,29,22)(2,15,30,23)(3,16,31,24)(4,13,32,21)(5,47,20,36)(6,48,17,33)(7,45,18,34)(8,46,19,35)(9,49,44,38)(10,50,41,39)(11,51,42,40)(12,52,43,37)(25,173,159,186)(26,174,160,187)(27,175,157,188)(28,176,158,185)(53,84,68,95)(54,81,65,96)(55,82,66,93)(56,83,67,94)(57,87,72,76)(58,88,69,73)(59,85,70,74)(60,86,71,75)(61,91,97,80)(62,92,98,77)(63,89,99,78)(64,90,100,79)(101,144,114,131)(102,141,115,132)(103,142,116,129)(104,143,113,130)(105,123,118,136)(106,124,119,133)(107,121,120,134)(108,122,117,135)(109,127,146,140)(110,128,147,137)(111,125,148,138)(112,126,145,139)(149,179,162,192)(150,180,163,189)(151,177,164,190)(152,178,161,191)(153,184,166,171)(154,181,167,172)(155,182,168,169)(156,183,165,170), (1,74,29,85)(2,75,30,86)(3,76,31,87)(4,73,32,88)(5,68,20,53)(6,65,17,54)(7,66,18,55)(8,67,19,56)(9,92,44,77)(10,89,41,78)(11,90,42,79)(12,91,43,80)(13,69,21,58)(14,70,22,59)(15,71,23,60)(16,72,24,57)(25,111,159,148)(26,112,160,145)(27,109,157,146)(28,110,158,147)(33,96,48,81)(34,93,45,82)(35,94,46,83)(36,95,47,84)(37,97,52,61)(38,98,49,62)(39,99,50,63)(40,100,51,64)(101,149,114,162)(102,150,115,163)(103,151,116,164)(104,152,113,161)(105,153,118,166)(106,154,119,167)(107,155,120,168)(108,156,117,165)(121,169,134,182)(122,170,135,183)(123,171,136,184)(124,172,133,181)(125,173,138,186)(126,174,139,187)(127,175,140,188)(128,176,137,185)(129,177,142,190)(130,178,143,191)(131,179,144,192)(132,180,141,189)>;
G:=Group( (1,41,18)(2,42,19)(3,43,20)(4,44,17)(5,31,12)(6,32,9)(7,29,10)(8,30,11)(13,38,33)(14,39,34)(15,40,35)(16,37,36)(21,49,48)(22,50,45)(23,51,46)(24,52,47)(25,190,168)(26,191,165)(27,192,166)(28,189,167)(53,76,80)(54,73,77)(55,74,78)(56,75,79)(57,61,84)(58,62,81)(59,63,82)(60,64,83)(65,88,92)(66,85,89)(67,86,90)(68,87,91)(69,98,96)(70,99,93)(71,100,94)(72,97,95)(101,123,127)(102,124,128)(103,121,125)(104,122,126)(105,109,131)(106,110,132)(107,111,129)(108,112,130)(113,135,139)(114,136,140)(115,133,137)(116,134,138)(117,145,143)(118,146,144)(119,147,141)(120,148,142)(149,171,175)(150,172,176)(151,169,173)(152,170,174)(153,157,179)(154,158,180)(155,159,177)(156,160,178)(161,183,187)(162,184,188)(163,181,185)(164,182,186), (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), (1,108,3,106)(2,107,4,105)(5,141,7,143)(6,144,8,142)(9,146,11,148)(10,145,12,147)(13,123,15,121)(14,122,16,124)(17,131,19,129)(18,130,20,132)(21,136,23,134)(22,135,24,133)(25,92,27,90)(26,91,28,89)(29,117,31,119)(30,120,32,118)(33,101,35,103)(34,104,36,102)(37,128,39,126)(38,127,40,125)(41,112,43,110)(42,111,44,109)(45,113,47,115)(46,116,48,114)(49,140,51,138)(50,139,52,137)(53,180,55,178)(54,179,56,177)(57,181,59,183)(58,184,60,182)(61,185,63,187)(62,188,64,186)(65,192,67,190)(66,191,68,189)(69,171,71,169)(70,170,72,172)(73,153,75,155)(74,156,76,154)(77,157,79,159)(78,160,80,158)(81,162,83,164)(82,161,84,163)(85,165,87,167)(86,168,88,166)(93,152,95,150)(94,151,96,149)(97,176,99,174)(98,175,100,173), (1,14,29,22)(2,15,30,23)(3,16,31,24)(4,13,32,21)(5,47,20,36)(6,48,17,33)(7,45,18,34)(8,46,19,35)(9,49,44,38)(10,50,41,39)(11,51,42,40)(12,52,43,37)(25,173,159,186)(26,174,160,187)(27,175,157,188)(28,176,158,185)(53,84,68,95)(54,81,65,96)(55,82,66,93)(56,83,67,94)(57,87,72,76)(58,88,69,73)(59,85,70,74)(60,86,71,75)(61,91,97,80)(62,92,98,77)(63,89,99,78)(64,90,100,79)(101,144,114,131)(102,141,115,132)(103,142,116,129)(104,143,113,130)(105,123,118,136)(106,124,119,133)(107,121,120,134)(108,122,117,135)(109,127,146,140)(110,128,147,137)(111,125,148,138)(112,126,145,139)(149,179,162,192)(150,180,163,189)(151,177,164,190)(152,178,161,191)(153,184,166,171)(154,181,167,172)(155,182,168,169)(156,183,165,170), (1,74,29,85)(2,75,30,86)(3,76,31,87)(4,73,32,88)(5,68,20,53)(6,65,17,54)(7,66,18,55)(8,67,19,56)(9,92,44,77)(10,89,41,78)(11,90,42,79)(12,91,43,80)(13,69,21,58)(14,70,22,59)(15,71,23,60)(16,72,24,57)(25,111,159,148)(26,112,160,145)(27,109,157,146)(28,110,158,147)(33,96,48,81)(34,93,45,82)(35,94,46,83)(36,95,47,84)(37,97,52,61)(38,98,49,62)(39,99,50,63)(40,100,51,64)(101,149,114,162)(102,150,115,163)(103,151,116,164)(104,152,113,161)(105,153,118,166)(106,154,119,167)(107,155,120,168)(108,156,117,165)(121,169,134,182)(122,170,135,183)(123,171,136,184)(124,172,133,181)(125,173,138,186)(126,174,139,187)(127,175,140,188)(128,176,137,185)(129,177,142,190)(130,178,143,191)(131,179,144,192)(132,180,141,189) );
G=PermutationGroup([[(1,41,18),(2,42,19),(3,43,20),(4,44,17),(5,31,12),(6,32,9),(7,29,10),(8,30,11),(13,38,33),(14,39,34),(15,40,35),(16,37,36),(21,49,48),(22,50,45),(23,51,46),(24,52,47),(25,190,168),(26,191,165),(27,192,166),(28,189,167),(53,76,80),(54,73,77),(55,74,78),(56,75,79),(57,61,84),(58,62,81),(59,63,82),(60,64,83),(65,88,92),(66,85,89),(67,86,90),(68,87,91),(69,98,96),(70,99,93),(71,100,94),(72,97,95),(101,123,127),(102,124,128),(103,121,125),(104,122,126),(105,109,131),(106,110,132),(107,111,129),(108,112,130),(113,135,139),(114,136,140),(115,133,137),(116,134,138),(117,145,143),(118,146,144),(119,147,141),(120,148,142),(149,171,175),(150,172,176),(151,169,173),(152,170,174),(153,157,179),(154,158,180),(155,159,177),(156,160,178),(161,183,187),(162,184,188),(163,181,185),(164,182,186)], [(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)], [(1,108,3,106),(2,107,4,105),(5,141,7,143),(6,144,8,142),(9,146,11,148),(10,145,12,147),(13,123,15,121),(14,122,16,124),(17,131,19,129),(18,130,20,132),(21,136,23,134),(22,135,24,133),(25,92,27,90),(26,91,28,89),(29,117,31,119),(30,120,32,118),(33,101,35,103),(34,104,36,102),(37,128,39,126),(38,127,40,125),(41,112,43,110),(42,111,44,109),(45,113,47,115),(46,116,48,114),(49,140,51,138),(50,139,52,137),(53,180,55,178),(54,179,56,177),(57,181,59,183),(58,184,60,182),(61,185,63,187),(62,188,64,186),(65,192,67,190),(66,191,68,189),(69,171,71,169),(70,170,72,172),(73,153,75,155),(74,156,76,154),(77,157,79,159),(78,160,80,158),(81,162,83,164),(82,161,84,163),(85,165,87,167),(86,168,88,166),(93,152,95,150),(94,151,96,149),(97,176,99,174),(98,175,100,173)], [(1,14,29,22),(2,15,30,23),(3,16,31,24),(4,13,32,21),(5,47,20,36),(6,48,17,33),(7,45,18,34),(8,46,19,35),(9,49,44,38),(10,50,41,39),(11,51,42,40),(12,52,43,37),(25,173,159,186),(26,174,160,187),(27,175,157,188),(28,176,158,185),(53,84,68,95),(54,81,65,96),(55,82,66,93),(56,83,67,94),(57,87,72,76),(58,88,69,73),(59,85,70,74),(60,86,71,75),(61,91,97,80),(62,92,98,77),(63,89,99,78),(64,90,100,79),(101,144,114,131),(102,141,115,132),(103,142,116,129),(104,143,113,130),(105,123,118,136),(106,124,119,133),(107,121,120,134),(108,122,117,135),(109,127,146,140),(110,128,147,137),(111,125,148,138),(112,126,145,139),(149,179,162,192),(150,180,163,189),(151,177,164,190),(152,178,161,191),(153,184,166,171),(154,181,167,172),(155,182,168,169),(156,183,165,170)], [(1,74,29,85),(2,75,30,86),(3,76,31,87),(4,73,32,88),(5,68,20,53),(6,65,17,54),(7,66,18,55),(8,67,19,56),(9,92,44,77),(10,89,41,78),(11,90,42,79),(12,91,43,80),(13,69,21,58),(14,70,22,59),(15,71,23,60),(16,72,24,57),(25,111,159,148),(26,112,160,145),(27,109,157,146),(28,110,158,147),(33,96,48,81),(34,93,45,82),(35,94,46,83),(36,95,47,84),(37,97,52,61),(38,98,49,62),(39,99,50,63),(40,100,51,64),(101,149,114,162),(102,150,115,163),(103,151,116,164),(104,152,113,161),(105,153,118,166),(106,154,119,167),(107,155,120,168),(108,156,117,165),(121,169,134,182),(122,170,135,183),(123,171,136,184),(124,172,133,181),(125,173,138,186),(126,174,139,187),(127,175,140,188),(128,176,137,185),(129,177,142,190),(130,178,143,191),(131,179,144,192),(132,180,141,189)]])
75 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | ··· | 4L | 4M | ··· | 4U | 6A | ··· | 6F | 12A | ··· | 12X | 12Y | ··· | 12AP |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 |
75 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 |
| type | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | Q8 | C3×Q8 | 2+ 1+4 | C3×2+ 1+4 |
| kernel | C3×Q82 | Q8×C12 | C3×C4⋊Q8 | Q82 | C4×Q8 | C4⋊Q8 | C3×Q8 | Q8 | C6 | C2 |
| # reps | 1 | 6 | 9 | 2 | 12 | 18 | 8 | 16 | 1 | 2 |
Matrix representation of C3×Q82 ►in GL4(𝔽13) generated by
| 3 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 2 | 0 | 0 |
| 12 | 12 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 12 | 6 | 0 | 0 |
| 4 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 8 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 12 | 0 |
G:=sub<GL(4,GF(13))| [3,0,0,0,0,3,0,0,0,0,1,0,0,0,0,1],[1,12,0,0,2,12,0,0,0,0,1,0,0,0,0,1],[12,4,0,0,6,1,0,0,0,0,12,0,0,0,0,12],[1,0,0,0,0,1,0,0,0,0,5,0,0,0,0,8],[1,0,0,0,0,1,0,0,0,0,0,12,0,0,1,0] >;
C3×Q82 in GAP, Magma, Sage, TeX
C_3\times Q_8^2
% in TeX
G:=Group("C3xQ8^2"); // GroupNames label
G:=SmallGroup(192,1447);
// by ID
G=gap.SmallGroup(192,1447);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,1008,701,344,2102,520,794,192]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^4=d^4=1,c^2=b^2,e^2=d^2,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