metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊Q16⋊1C4, C6.35(C4×D4), Q8.6(C4×S3), C4⋊C4.143D6, (C2×C8).172D6, C24⋊C4.6C2, C3⋊2(Q16⋊C4), Q8⋊C4.7S3, (C2×Q8).121D6, Dic6.2(C2×C4), (Q8×Dic3).1C2, C22.74(S3×D4), C12.10(C22×C4), C2.3(D4.D6), C2.1(Q16⋊S3), C12.Q8.1C2, C2.Dic12.9C2, C12.155(C4○D4), (C6×Q8).12C22, C4.52(D4⋊2S3), (C2×C24).233C22, (C2×C12).229C23, Dic6⋊C4.1C2, (C2×Dic3).146D4, C6.52(C8.C22), C4⋊Dic3.79C22, (C4×Dic3).15C22, (C2×Dic6).62C22, C2.19(Dic3⋊4D4), C3⋊C8.1(C2×C4), C4.10(S3×C2×C4), (C3×Q8).1(C2×C4), (C2×C6).242(C2×D4), (C2×C3⋊C8).26C22, (C2×C3⋊Q16).1C2, (C3×C4⋊C4).30C22, (C3×Q8⋊C4).9C2, (C2×C4).336(C22×S3), SmallGroup(192,348)
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, bab-1=a-1, ac=ca, ad=da, cbc-1=b-1, dbd-1=b3, dcd-1=b6c >
Subgroups: 248 in 108 conjugacy classes, 49 normal (37 characteristic)
C1, C2, C3, C4, C4, C22, C6, C8, C2×C4, C2×C4, Q8, Q8, Dic3, C12, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, Q16, C2×Q8, C2×Q8, C3⋊C8, C24, Dic6, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C3×Q8, C3×Q8, C8⋊C4, Q8⋊C4, Q8⋊C4, C4.Q8, C4×Q8, C2×Q16, C2×C3⋊C8, C4×Dic3, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C4⋊Dic3, C3⋊Q16, C3×C4⋊C4, C2×C24, C2×Dic6, C6×Q8, Q16⋊C4, C12.Q8, C24⋊C4, C2.Dic12, C3×Q8⋊C4, Dic6⋊C4, C2×C3⋊Q16, Q8×Dic3, C3⋊Q16⋊C4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D6, C22×C4, C2×D4, C4○D4, C4×S3, C22×S3, C4×D4, C8.C22, S3×C2×C4, S3×D4, D4⋊2S3, Q16⋊C4, Dic3⋊4D4, D4.D6, Q16⋊S3, C3⋊Q16⋊C4
►Regular action on 192 points
Generators in S192
(1 102 174)(2 175 103)(3 104 176)(4 169 97)(5 98 170)(6 171 99)(7 100 172)(8 173 101)(9 89 180)(10 181 90)(11 91 182)(12 183 92)(13 93 184)(14 177 94)(15 95 178)(16 179 96)(17 108 74)(18 75 109)(19 110 76)(20 77 111)(21 112 78)(22 79 105)(23 106 80)(24 73 107)(25 56 65)(26 66 49)(27 50 67)(28 68 51)(29 52 69)(30 70 53)(31 54 71)(32 72 55)(33 127 47)(34 48 128)(35 121 41)(36 42 122)(37 123 43)(38 44 124)(39 125 45)(40 46 126)(57 157 120)(58 113 158)(59 159 114)(60 115 160)(61 153 116)(62 117 154)(63 155 118)(64 119 156)(81 165 191)(82 192 166)(83 167 185)(84 186 168)(85 161 187)(86 188 162)(87 163 189)(88 190 164)(129 148 138)(130 139 149)(131 150 140)(132 141 151)(133 152 142)(134 143 145)(135 146 144)(136 137 147)
(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 19 5 23)(2 18 6 22)(3 17 7 21)(4 24 8 20)(9 164 13 168)(10 163 14 167)(11 162 15 166)(12 161 16 165)(25 156 29 160)(26 155 30 159)(27 154 31 158)(28 153 32 157)(33 140 37 144)(34 139 38 143)(35 138 39 142)(36 137 40 141)(41 148 45 152)(42 147 46 151)(43 146 47 150)(44 145 48 149)(49 63 53 59)(50 62 54 58)(51 61 55 57)(52 60 56 64)(65 119 69 115)(66 118 70 114)(67 117 71 113)(68 116 72 120)(73 173 77 169)(74 172 78 176)(75 171 79 175)(76 170 80 174)(81 92 85 96)(82 91 86 95)(83 90 87 94)(84 89 88 93)(97 107 101 111)(98 106 102 110)(99 105 103 109)(100 112 104 108)(121 129 125 133)(122 136 126 132)(123 135 127 131)(124 134 128 130)(177 185 181 189)(178 192 182 188)(179 191 183 187)(180 190 184 186)
(1 153 96 126)(2 156 89 121)(3 159 90 124)(4 154 91 127)(5 157 92 122)(6 160 93 125)(7 155 94 128)(8 158 95 123)(9 35 103 119)(10 38 104 114)(11 33 97 117)(12 36 98 120)(13 39 99 115)(14 34 100 118)(15 37 101 113)(16 40 102 116)(17 28 87 136)(18 31 88 131)(19 26 81 134)(20 29 82 129)(21 32 83 132)(22 27 84 135)(23 30 85 130)(24 25 86 133)(41 175 64 180)(42 170 57 183)(43 173 58 178)(44 176 59 181)(45 171 60 184)(46 174 61 179)(47 169 62 182)(48 172 63 177)(49 191 145 76)(50 186 146 79)(51 189 147 74)(52 192 148 77)(53 187 149 80)(54 190 150 75)(55 185 151 78)(56 188 152 73)(65 162 142 107)(66 165 143 110)(67 168 144 105)(68 163 137 108)(69 166 138 111)(70 161 139 106)(71 164 140 109)(72 167 141 112)
G:=sub<Sym(192)| (1,102,174)(2,175,103)(3,104,176)(4,169,97)(5,98,170)(6,171,99)(7,100,172)(8,173,101)(9,89,180)(10,181,90)(11,91,182)(12,183,92)(13,93,184)(14,177,94)(15,95,178)(16,179,96)(17,108,74)(18,75,109)(19,110,76)(20,77,111)(21,112,78)(22,79,105)(23,106,80)(24,73,107)(25,56,65)(26,66,49)(27,50,67)(28,68,51)(29,52,69)(30,70,53)(31,54,71)(32,72,55)(33,127,47)(34,48,128)(35,121,41)(36,42,122)(37,123,43)(38,44,124)(39,125,45)(40,46,126)(57,157,120)(58,113,158)(59,159,114)(60,115,160)(61,153,116)(62,117,154)(63,155,118)(64,119,156)(81,165,191)(82,192,166)(83,167,185)(84,186,168)(85,161,187)(86,188,162)(87,163,189)(88,190,164)(129,148,138)(130,139,149)(131,150,140)(132,141,151)(133,152,142)(134,143,145)(135,146,144)(136,137,147), (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), (1,19,5,23)(2,18,6,22)(3,17,7,21)(4,24,8,20)(9,164,13,168)(10,163,14,167)(11,162,15,166)(12,161,16,165)(25,156,29,160)(26,155,30,159)(27,154,31,158)(28,153,32,157)(33,140,37,144)(34,139,38,143)(35,138,39,142)(36,137,40,141)(41,148,45,152)(42,147,46,151)(43,146,47,150)(44,145,48,149)(49,63,53,59)(50,62,54,58)(51,61,55,57)(52,60,56,64)(65,119,69,115)(66,118,70,114)(67,117,71,113)(68,116,72,120)(73,173,77,169)(74,172,78,176)(75,171,79,175)(76,170,80,174)(81,92,85,96)(82,91,86,95)(83,90,87,94)(84,89,88,93)(97,107,101,111)(98,106,102,110)(99,105,103,109)(100,112,104,108)(121,129,125,133)(122,136,126,132)(123,135,127,131)(124,134,128,130)(177,185,181,189)(178,192,182,188)(179,191,183,187)(180,190,184,186), (1,153,96,126)(2,156,89,121)(3,159,90,124)(4,154,91,127)(5,157,92,122)(6,160,93,125)(7,155,94,128)(8,158,95,123)(9,35,103,119)(10,38,104,114)(11,33,97,117)(12,36,98,120)(13,39,99,115)(14,34,100,118)(15,37,101,113)(16,40,102,116)(17,28,87,136)(18,31,88,131)(19,26,81,134)(20,29,82,129)(21,32,83,132)(22,27,84,135)(23,30,85,130)(24,25,86,133)(41,175,64,180)(42,170,57,183)(43,173,58,178)(44,176,59,181)(45,171,60,184)(46,174,61,179)(47,169,62,182)(48,172,63,177)(49,191,145,76)(50,186,146,79)(51,189,147,74)(52,192,148,77)(53,187,149,80)(54,190,150,75)(55,185,151,78)(56,188,152,73)(65,162,142,107)(66,165,143,110)(67,168,144,105)(68,163,137,108)(69,166,138,111)(70,161,139,106)(71,164,140,109)(72,167,141,112)>;
G:=Group( (1,102,174)(2,175,103)(3,104,176)(4,169,97)(5,98,170)(6,171,99)(7,100,172)(8,173,101)(9,89,180)(10,181,90)(11,91,182)(12,183,92)(13,93,184)(14,177,94)(15,95,178)(16,179,96)(17,108,74)(18,75,109)(19,110,76)(20,77,111)(21,112,78)(22,79,105)(23,106,80)(24,73,107)(25,56,65)(26,66,49)(27,50,67)(28,68,51)(29,52,69)(30,70,53)(31,54,71)(32,72,55)(33,127,47)(34,48,128)(35,121,41)(36,42,122)(37,123,43)(38,44,124)(39,125,45)(40,46,126)(57,157,120)(58,113,158)(59,159,114)(60,115,160)(61,153,116)(62,117,154)(63,155,118)(64,119,156)(81,165,191)(82,192,166)(83,167,185)(84,186,168)(85,161,187)(86,188,162)(87,163,189)(88,190,164)(129,148,138)(130,139,149)(131,150,140)(132,141,151)(133,152,142)(134,143,145)(135,146,144)(136,137,147), (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), (1,19,5,23)(2,18,6,22)(3,17,7,21)(4,24,8,20)(9,164,13,168)(10,163,14,167)(11,162,15,166)(12,161,16,165)(25,156,29,160)(26,155,30,159)(27,154,31,158)(28,153,32,157)(33,140,37,144)(34,139,38,143)(35,138,39,142)(36,137,40,141)(41,148,45,152)(42,147,46,151)(43,146,47,150)(44,145,48,149)(49,63,53,59)(50,62,54,58)(51,61,55,57)(52,60,56,64)(65,119,69,115)(66,118,70,114)(67,117,71,113)(68,116,72,120)(73,173,77,169)(74,172,78,176)(75,171,79,175)(76,170,80,174)(81,92,85,96)(82,91,86,95)(83,90,87,94)(84,89,88,93)(97,107,101,111)(98,106,102,110)(99,105,103,109)(100,112,104,108)(121,129,125,133)(122,136,126,132)(123,135,127,131)(124,134,128,130)(177,185,181,189)(178,192,182,188)(179,191,183,187)(180,190,184,186), (1,153,96,126)(2,156,89,121)(3,159,90,124)(4,154,91,127)(5,157,92,122)(6,160,93,125)(7,155,94,128)(8,158,95,123)(9,35,103,119)(10,38,104,114)(11,33,97,117)(12,36,98,120)(13,39,99,115)(14,34,100,118)(15,37,101,113)(16,40,102,116)(17,28,87,136)(18,31,88,131)(19,26,81,134)(20,29,82,129)(21,32,83,132)(22,27,84,135)(23,30,85,130)(24,25,86,133)(41,175,64,180)(42,170,57,183)(43,173,58,178)(44,176,59,181)(45,171,60,184)(46,174,61,179)(47,169,62,182)(48,172,63,177)(49,191,145,76)(50,186,146,79)(51,189,147,74)(52,192,148,77)(53,187,149,80)(54,190,150,75)(55,185,151,78)(56,188,152,73)(65,162,142,107)(66,165,143,110)(67,168,144,105)(68,163,137,108)(69,166,138,111)(70,161,139,106)(71,164,140,109)(72,167,141,112) );
G=PermutationGroup([[(1,102,174),(2,175,103),(3,104,176),(4,169,97),(5,98,170),(6,171,99),(7,100,172),(8,173,101),(9,89,180),(10,181,90),(11,91,182),(12,183,92),(13,93,184),(14,177,94),(15,95,178),(16,179,96),(17,108,74),(18,75,109),(19,110,76),(20,77,111),(21,112,78),(22,79,105),(23,106,80),(24,73,107),(25,56,65),(26,66,49),(27,50,67),(28,68,51),(29,52,69),(30,70,53),(31,54,71),(32,72,55),(33,127,47),(34,48,128),(35,121,41),(36,42,122),(37,123,43),(38,44,124),(39,125,45),(40,46,126),(57,157,120),(58,113,158),(59,159,114),(60,115,160),(61,153,116),(62,117,154),(63,155,118),(64,119,156),(81,165,191),(82,192,166),(83,167,185),(84,186,168),(85,161,187),(86,188,162),(87,163,189),(88,190,164),(129,148,138),(130,139,149),(131,150,140),(132,141,151),(133,152,142),(134,143,145),(135,146,144),(136,137,147)], [(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)], [(1,19,5,23),(2,18,6,22),(3,17,7,21),(4,24,8,20),(9,164,13,168),(10,163,14,167),(11,162,15,166),(12,161,16,165),(25,156,29,160),(26,155,30,159),(27,154,31,158),(28,153,32,157),(33,140,37,144),(34,139,38,143),(35,138,39,142),(36,137,40,141),(41,148,45,152),(42,147,46,151),(43,146,47,150),(44,145,48,149),(49,63,53,59),(50,62,54,58),(51,61,55,57),(52,60,56,64),(65,119,69,115),(66,118,70,114),(67,117,71,113),(68,116,72,120),(73,173,77,169),(74,172,78,176),(75,171,79,175),(76,170,80,174),(81,92,85,96),(82,91,86,95),(83,90,87,94),(84,89,88,93),(97,107,101,111),(98,106,102,110),(99,105,103,109),(100,112,104,108),(121,129,125,133),(122,136,126,132),(123,135,127,131),(124,134,128,130),(177,185,181,189),(178,192,182,188),(179,191,183,187),(180,190,184,186)], [(1,153,96,126),(2,156,89,121),(3,159,90,124),(4,154,91,127),(5,157,92,122),(6,160,93,125),(7,155,94,128),(8,158,95,123),(9,35,103,119),(10,38,104,114),(11,33,97,117),(12,36,98,120),(13,39,99,115),(14,34,100,118),(15,37,101,113),(16,40,102,116),(17,28,87,136),(18,31,88,131),(19,26,81,134),(20,29,82,129),(21,32,83,132),(22,27,84,135),(23,30,85,130),(24,25,86,133),(41,175,64,180),(42,170,57,183),(43,173,58,178),(44,176,59,181),(45,171,60,184),(46,174,61,179),(47,169,62,182),(48,172,63,177),(49,191,145,76),(50,186,146,79),(51,189,147,74),(52,192,148,77),(53,187,149,80),(54,190,150,75),(55,185,151,78),(56,188,152,73),(65,162,142,107),(66,165,143,110),(67,168,144,105),(68,163,137,108),(69,166,138,111),(70,161,139,106),(71,164,140,109),(72,167,141,112)]])
36 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 24A | 24B | 24C | 24D |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 12 | 12 | 24 | 24 | 24 | 24 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 12 | 12 | 12 | 12 | 2 | 2 | 2 | 4 | 4 | 12 | 12 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 |
36 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D6 | D6 | D6 | C4○D4 | C4×S3 | C8.C22 | D4⋊2S3 | S3×D4 | D4.D6 | Q16⋊S3 |
| kernel | C3⋊Q16⋊C4 | C12.Q8 | C24⋊C4 | C2.Dic12 | C3×Q8⋊C4 | Dic6⋊C4 | C2×C3⋊Q16 | Q8×Dic3 | C3⋊Q16 | Q8⋊C4 | C2×Dic3 | C4⋊C4 | C2×C8 | C2×Q8 | C12 | Q8 | C6 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 1 | 1 | 1 | 2 | 4 | 2 | 1 | 1 | 2 | 2 |
Matrix representation of C3⋊Q16⋊C4 ►in GL6(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 1 | 72 |
| 25 | 35 | 0 | 0 | 0 | 0 |
| 28 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 51 | 59 | 0 | 2 |
| 0 | 0 | 8 | 22 | 2 | 71 |
| 0 | 0 | 70 | 70 | 16 | 47 |
| 0 | 0 | 70 | 0 | 63 | 57 |
| 40 | 3 | 0 | 0 | 0 | 0 |
| 51 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 52 | 54 | 45 | 48 |
| 0 | 0 | 19 | 71 | 53 | 45 |
| 0 | 0 | 39 | 59 | 2 | 19 |
| 0 | 0 | 53 | 39 | 54 | 21 |
| 5 | 68 | 0 | 0 | 0 | 0 |
| 49 | 68 | 0 | 0 | 0 | 0 |
| 0 | 0 | 49 | 38 | 43 | 7 |
| 0 | 0 | 35 | 11 | 23 | 43 |
| 0 | 0 | 33 | 18 | 62 | 35 |
| 0 | 0 | 15 | 33 | 38 | 24 |
G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,1,0,0,0,0,72,0,0,0,0,0,0,0,0,1,0,0,0,0,72,72],[25,28,0,0,0,0,35,48,0,0,0,0,0,0,51,8,70,70,0,0,59,22,70,0,0,0,0,2,16,63,0,0,2,71,47,57],[40,51,0,0,0,0,3,33,0,0,0,0,0,0,52,19,39,53,0,0,54,71,59,39,0,0,45,53,2,54,0,0,48,45,19,21],[5,49,0,0,0,0,68,68,0,0,0,0,0,0,49,35,33,15,0,0,38,11,18,33,0,0,43,23,62,38,0,0,7,43,35,24] >;
C3⋊Q16⋊C4 in GAP, Magma, Sage, TeX
C_3\rtimes Q_{16}\rtimes C_4 % in TeX
G:=Group("C3:Q16:C4"); // GroupNames label
G:=SmallGroup(192,348);
// by ID
G=gap.SmallGroup(192,348);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,344,758,135,184,570,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=d^4=1,c^2=b^4,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^3,d*c*d^-1=b^6*c>;
// generators/relations