direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C3×Q16⋊C4, Q16⋊3C12, C8.5(C2×C12), (C3×Q16)⋊9C4, (C4×Q8).9C6, C4.Q8.2C6, C8⋊C4.1C6, C24.40(C2×C4), C2.16(D4×C12), C6.118(C4×D4), C42.9(C2×C6), (C2×Q16).6C6, Q8.7(C2×C12), (C2×C12).457D4, Q8⋊C4.6C6, (Q8×C12).16C2, (C6×Q16).13C2, C22.55(C6×D4), C4.13(C22×C12), C12.260(C4○D4), (C2×C24).330C22, (C4×C12).250C22, C12.158(C22×C4), (C2×C12).908C23, (C6×Q8).257C22, C6.130(C8.C22), C4.5(C3×C4○D4), C4⋊C4.49(C2×C6), (C2×C8).19(C2×C6), (C3×C4.Q8).7C2, (C3×C8⋊C4).3C2, (C2×C6).631(C2×D4), (C2×C4).103(C3×D4), (C2×Q8).54(C2×C6), (C3×Q8).20(C2×C4), C2.5(C3×C8.C22), (C2×C4).83(C22×C6), (C3×C4⋊C4).370C22, (C3×Q8⋊C4).15C2, SmallGroup(192,874)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×Q16⋊C4
G = < a,b,c,d | a3=b8=d4=1, c2=b4, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b5, cd=dc >
Subgroups: 154 in 108 conjugacy classes, 70 normal (26 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C8, C8, C2×C4, C2×C4, C2×C4, Q8, Q8, C12, C12, C2×C6, C42, C42, C4⋊C4, C4⋊C4, C2×C8, Q16, C2×Q8, C24, C24, C2×C12, C2×C12, C2×C12, C3×Q8, C3×Q8, C8⋊C4, Q8⋊C4, C4.Q8, C4×Q8, C2×Q16, C4×C12, C4×C12, C3×C4⋊C4, C3×C4⋊C4, C2×C24, C3×Q16, C6×Q8, Q16⋊C4, C3×C8⋊C4, C3×Q8⋊C4, C3×C4.Q8, Q8×C12, C6×Q16, C3×Q16⋊C4
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D4, C23, C12, C2×C6, C22×C4, C2×D4, C4○D4, C2×C12, C3×D4, C22×C6, C4×D4, C8.C22, C22×C12, C6×D4, C3×C4○D4, Q16⋊C4, D4×C12, C3×C8.C22, C3×Q16⋊C4
►Regular action on 192 points
Generators in S192
(1 79 101)(2 80 102)(3 73 103)(4 74 104)(5 75 97)(6 76 98)(7 77 99)(8 78 100)(9 161 177)(10 162 178)(11 163 179)(12 164 180)(13 165 181)(14 166 182)(15 167 183)(16 168 184)(17 174 185)(18 175 186)(19 176 187)(20 169 188)(21 170 189)(22 171 190)(23 172 191)(24 173 192)(25 139 147)(26 140 148)(27 141 149)(28 142 150)(29 143 151)(30 144 152)(31 137 145)(32 138 146)(33 41 155)(34 42 156)(35 43 157)(36 44 158)(37 45 159)(38 46 160)(39 47 153)(40 48 154)(49 114 123)(50 115 124)(51 116 125)(52 117 126)(53 118 127)(54 119 128)(55 120 121)(56 113 122)(57 65 130)(58 66 131)(59 67 132)(60 68 133)(61 69 134)(62 70 135)(63 71 136)(64 72 129)(81 89 108)(82 90 109)(83 91 110)(84 92 111)(85 93 112)(86 94 105)(87 95 106)(88 96 107)
(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 37 5 33)(2 36 6 40)(3 35 7 39)(4 34 8 38)(9 132 13 136)(10 131 14 135)(11 130 15 134)(12 129 16 133)(17 125 21 121)(18 124 22 128)(19 123 23 127)(20 122 24 126)(25 106 29 110)(26 105 30 109)(27 112 31 108)(28 111 32 107)(41 79 45 75)(42 78 46 74)(43 77 47 73)(44 76 48 80)(49 172 53 176)(50 171 54 175)(51 170 55 174)(52 169 56 173)(57 167 61 163)(58 166 62 162)(59 165 63 161)(60 164 64 168)(65 183 69 179)(66 182 70 178)(67 181 71 177)(68 180 72 184)(81 141 85 137)(82 140 86 144)(83 139 87 143)(84 138 88 142)(89 149 93 145)(90 148 94 152)(91 147 95 151)(92 146 96 150)(97 155 101 159)(98 154 102 158)(99 153 103 157)(100 160 104 156)(113 192 117 188)(114 191 118 187)(115 190 119 186)(116 189 120 185)
(1 87 19 163)(2 84 20 168)(3 81 21 165)(4 86 22 162)(5 83 23 167)(6 88 24 164)(7 85 17 161)(8 82 18 166)(9 99 112 185)(10 104 105 190)(11 101 106 187)(12 98 107 192)(13 103 108 189)(14 100 109 186)(15 97 110 191)(16 102 111 188)(25 118 134 155)(26 115 135 160)(27 120 136 157)(28 117 129 154)(29 114 130 159)(30 119 131 156)(31 116 132 153)(32 113 133 158)(33 139 127 61)(34 144 128 58)(35 141 121 63)(36 138 122 60)(37 143 123 57)(38 140 124 62)(39 137 125 59)(40 142 126 64)(41 147 53 69)(42 152 54 66)(43 149 55 71)(44 146 56 68)(45 151 49 65)(46 148 50 70)(47 145 51 67)(48 150 52 72)(73 89 170 181)(74 94 171 178)(75 91 172 183)(76 96 173 180)(77 93 174 177)(78 90 175 182)(79 95 176 179)(80 92 169 184)
G:=sub<Sym(192)| (1,79,101)(2,80,102)(3,73,103)(4,74,104)(5,75,97)(6,76,98)(7,77,99)(8,78,100)(9,161,177)(10,162,178)(11,163,179)(12,164,180)(13,165,181)(14,166,182)(15,167,183)(16,168,184)(17,174,185)(18,175,186)(19,176,187)(20,169,188)(21,170,189)(22,171,190)(23,172,191)(24,173,192)(25,139,147)(26,140,148)(27,141,149)(28,142,150)(29,143,151)(30,144,152)(31,137,145)(32,138,146)(33,41,155)(34,42,156)(35,43,157)(36,44,158)(37,45,159)(38,46,160)(39,47,153)(40,48,154)(49,114,123)(50,115,124)(51,116,125)(52,117,126)(53,118,127)(54,119,128)(55,120,121)(56,113,122)(57,65,130)(58,66,131)(59,67,132)(60,68,133)(61,69,134)(62,70,135)(63,71,136)(64,72,129)(81,89,108)(82,90,109)(83,91,110)(84,92,111)(85,93,112)(86,94,105)(87,95,106)(88,96,107), (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), (1,37,5,33)(2,36,6,40)(3,35,7,39)(4,34,8,38)(9,132,13,136)(10,131,14,135)(11,130,15,134)(12,129,16,133)(17,125,21,121)(18,124,22,128)(19,123,23,127)(20,122,24,126)(25,106,29,110)(26,105,30,109)(27,112,31,108)(28,111,32,107)(41,79,45,75)(42,78,46,74)(43,77,47,73)(44,76,48,80)(49,172,53,176)(50,171,54,175)(51,170,55,174)(52,169,56,173)(57,167,61,163)(58,166,62,162)(59,165,63,161)(60,164,64,168)(65,183,69,179)(66,182,70,178)(67,181,71,177)(68,180,72,184)(81,141,85,137)(82,140,86,144)(83,139,87,143)(84,138,88,142)(89,149,93,145)(90,148,94,152)(91,147,95,151)(92,146,96,150)(97,155,101,159)(98,154,102,158)(99,153,103,157)(100,160,104,156)(113,192,117,188)(114,191,118,187)(115,190,119,186)(116,189,120,185), (1,87,19,163)(2,84,20,168)(3,81,21,165)(4,86,22,162)(5,83,23,167)(6,88,24,164)(7,85,17,161)(8,82,18,166)(9,99,112,185)(10,104,105,190)(11,101,106,187)(12,98,107,192)(13,103,108,189)(14,100,109,186)(15,97,110,191)(16,102,111,188)(25,118,134,155)(26,115,135,160)(27,120,136,157)(28,117,129,154)(29,114,130,159)(30,119,131,156)(31,116,132,153)(32,113,133,158)(33,139,127,61)(34,144,128,58)(35,141,121,63)(36,138,122,60)(37,143,123,57)(38,140,124,62)(39,137,125,59)(40,142,126,64)(41,147,53,69)(42,152,54,66)(43,149,55,71)(44,146,56,68)(45,151,49,65)(46,148,50,70)(47,145,51,67)(48,150,52,72)(73,89,170,181)(74,94,171,178)(75,91,172,183)(76,96,173,180)(77,93,174,177)(78,90,175,182)(79,95,176,179)(80,92,169,184)>;
G:=Group( (1,79,101)(2,80,102)(3,73,103)(4,74,104)(5,75,97)(6,76,98)(7,77,99)(8,78,100)(9,161,177)(10,162,178)(11,163,179)(12,164,180)(13,165,181)(14,166,182)(15,167,183)(16,168,184)(17,174,185)(18,175,186)(19,176,187)(20,169,188)(21,170,189)(22,171,190)(23,172,191)(24,173,192)(25,139,147)(26,140,148)(27,141,149)(28,142,150)(29,143,151)(30,144,152)(31,137,145)(32,138,146)(33,41,155)(34,42,156)(35,43,157)(36,44,158)(37,45,159)(38,46,160)(39,47,153)(40,48,154)(49,114,123)(50,115,124)(51,116,125)(52,117,126)(53,118,127)(54,119,128)(55,120,121)(56,113,122)(57,65,130)(58,66,131)(59,67,132)(60,68,133)(61,69,134)(62,70,135)(63,71,136)(64,72,129)(81,89,108)(82,90,109)(83,91,110)(84,92,111)(85,93,112)(86,94,105)(87,95,106)(88,96,107), (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), (1,37,5,33)(2,36,6,40)(3,35,7,39)(4,34,8,38)(9,132,13,136)(10,131,14,135)(11,130,15,134)(12,129,16,133)(17,125,21,121)(18,124,22,128)(19,123,23,127)(20,122,24,126)(25,106,29,110)(26,105,30,109)(27,112,31,108)(28,111,32,107)(41,79,45,75)(42,78,46,74)(43,77,47,73)(44,76,48,80)(49,172,53,176)(50,171,54,175)(51,170,55,174)(52,169,56,173)(57,167,61,163)(58,166,62,162)(59,165,63,161)(60,164,64,168)(65,183,69,179)(66,182,70,178)(67,181,71,177)(68,180,72,184)(81,141,85,137)(82,140,86,144)(83,139,87,143)(84,138,88,142)(89,149,93,145)(90,148,94,152)(91,147,95,151)(92,146,96,150)(97,155,101,159)(98,154,102,158)(99,153,103,157)(100,160,104,156)(113,192,117,188)(114,191,118,187)(115,190,119,186)(116,189,120,185), (1,87,19,163)(2,84,20,168)(3,81,21,165)(4,86,22,162)(5,83,23,167)(6,88,24,164)(7,85,17,161)(8,82,18,166)(9,99,112,185)(10,104,105,190)(11,101,106,187)(12,98,107,192)(13,103,108,189)(14,100,109,186)(15,97,110,191)(16,102,111,188)(25,118,134,155)(26,115,135,160)(27,120,136,157)(28,117,129,154)(29,114,130,159)(30,119,131,156)(31,116,132,153)(32,113,133,158)(33,139,127,61)(34,144,128,58)(35,141,121,63)(36,138,122,60)(37,143,123,57)(38,140,124,62)(39,137,125,59)(40,142,126,64)(41,147,53,69)(42,152,54,66)(43,149,55,71)(44,146,56,68)(45,151,49,65)(46,148,50,70)(47,145,51,67)(48,150,52,72)(73,89,170,181)(74,94,171,178)(75,91,172,183)(76,96,173,180)(77,93,174,177)(78,90,175,182)(79,95,176,179)(80,92,169,184) );
G=PermutationGroup([[(1,79,101),(2,80,102),(3,73,103),(4,74,104),(5,75,97),(6,76,98),(7,77,99),(8,78,100),(9,161,177),(10,162,178),(11,163,179),(12,164,180),(13,165,181),(14,166,182),(15,167,183),(16,168,184),(17,174,185),(18,175,186),(19,176,187),(20,169,188),(21,170,189),(22,171,190),(23,172,191),(24,173,192),(25,139,147),(26,140,148),(27,141,149),(28,142,150),(29,143,151),(30,144,152),(31,137,145),(32,138,146),(33,41,155),(34,42,156),(35,43,157),(36,44,158),(37,45,159),(38,46,160),(39,47,153),(40,48,154),(49,114,123),(50,115,124),(51,116,125),(52,117,126),(53,118,127),(54,119,128),(55,120,121),(56,113,122),(57,65,130),(58,66,131),(59,67,132),(60,68,133),(61,69,134),(62,70,135),(63,71,136),(64,72,129),(81,89,108),(82,90,109),(83,91,110),(84,92,111),(85,93,112),(86,94,105),(87,95,106),(88,96,107)], [(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)], [(1,37,5,33),(2,36,6,40),(3,35,7,39),(4,34,8,38),(9,132,13,136),(10,131,14,135),(11,130,15,134),(12,129,16,133),(17,125,21,121),(18,124,22,128),(19,123,23,127),(20,122,24,126),(25,106,29,110),(26,105,30,109),(27,112,31,108),(28,111,32,107),(41,79,45,75),(42,78,46,74),(43,77,47,73),(44,76,48,80),(49,172,53,176),(50,171,54,175),(51,170,55,174),(52,169,56,173),(57,167,61,163),(58,166,62,162),(59,165,63,161),(60,164,64,168),(65,183,69,179),(66,182,70,178),(67,181,71,177),(68,180,72,184),(81,141,85,137),(82,140,86,144),(83,139,87,143),(84,138,88,142),(89,149,93,145),(90,148,94,152),(91,147,95,151),(92,146,96,150),(97,155,101,159),(98,154,102,158),(99,153,103,157),(100,160,104,156),(113,192,117,188),(114,191,118,187),(115,190,119,186),(116,189,120,185)], [(1,87,19,163),(2,84,20,168),(3,81,21,165),(4,86,22,162),(5,83,23,167),(6,88,24,164),(7,85,17,161),(8,82,18,166),(9,99,112,185),(10,104,105,190),(11,101,106,187),(12,98,107,192),(13,103,108,189),(14,100,109,186),(15,97,110,191),(16,102,111,188),(25,118,134,155),(26,115,135,160),(27,120,136,157),(28,117,129,154),(29,114,130,159),(30,119,131,156),(31,116,132,153),(32,113,133,158),(33,139,127,61),(34,144,128,58),(35,141,121,63),(36,138,122,60),(37,143,123,57),(38,140,124,62),(39,137,125,59),(40,142,126,64),(41,147,53,69),(42,152,54,66),(43,149,55,71),(44,146,56,68),(45,151,49,65),(46,148,50,70),(47,145,51,67),(48,150,52,72),(73,89,170,181),(74,94,171,178),(75,91,172,183),(76,96,173,180),(77,93,174,177),(78,90,175,182),(79,95,176,179),(80,92,169,184)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | ··· | 4F | 4G | ··· | 4N | 6A | ··· | 6F | 8A | 8B | 8C | 8D | 12A | ··· | 12L | 12M | ··· | 12AB | 24A | ··· | 24H |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 12 | ··· | 12 | 12 | ··· | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C3 | C4 | C6 | C6 | C6 | C6 | C6 | C12 | D4 | C4○D4 | C3×D4 | C3×C4○D4 | C8.C22 | C3×C8.C22 |
| kernel | C3×Q16⋊C4 | C3×C8⋊C4 | C3×Q8⋊C4 | C3×C4.Q8 | Q8×C12 | C6×Q16 | Q16⋊C4 | C3×Q16 | C8⋊C4 | Q8⋊C4 | C4.Q8 | C4×Q8 | C2×Q16 | Q16 | C2×C12 | C12 | C2×C4 | C4 | C6 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 8 | 2 | 4 | 2 | 4 | 2 | 16 | 2 | 2 | 4 | 4 | 2 | 4 |
Matrix representation of C3×Q16⋊C4 ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 64 | 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 |
| 61 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
| 12 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 46 | 71 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 37 | 8 | 46 | 32 |
| 0 | 0 | 0 | 0 | 60 | 10 | 5 | 22 |
| 0 | 0 | 0 | 0 | 35 | 65 | 28 | 48 |
| 0 | 0 | 0 | 0 | 63 | 2 | 65 | 71 |
| 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 8 | 8 | 57 |
| 0 | 0 | 0 | 0 | 0 | 64 | 8 | 0 |
| 0 | 0 | 0 | 0 | 0 | 8 | 9 | 0 |
| 0 | 0 | 0 | 0 | 64 | 0 | 9 | 72 |
| 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 27 | 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 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 72 | 1 | 1 | 71 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 72 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[61,12,0,0,0,0,0,0,67,12,0,0,0,0,0,0,0,0,46,0,0,0,0,0,0,0,71,27,0,0,0,0,0,0,0,0,37,60,35,63,0,0,0,0,8,10,65,2,0,0,0,0,46,5,28,65,0,0,0,0,32,22,48,71],[1,0,0,0,0,0,0,0,2,72,0,0,0,0,0,0,0,0,72,27,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,64,0,0,0,0,8,64,8,0,0,0,0,0,8,8,9,9,0,0,0,0,57,0,0,72],[27,0,0,0,0,0,0,0,0,27,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,71,0,72] >;
C3×Q16⋊C4 in GAP, Magma, Sage, TeX
C_3\times Q_{16}\rtimes C_4 % in TeX
G:=Group("C3xQ16:C4"); // GroupNames label
G:=SmallGroup(192,874);
// by ID
G=gap.SmallGroup(192,874);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-2,336,365,680,2102,268,4204,2111,172]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=d^4=1,c^2=b^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^5,c*d=d*c>;
// generators/relations