direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C6.SD16, C4⋊C4.229D6, C4.8(D6⋊C4), (C2×Dic6)⋊9C4, C4.61(C2×D12), C6.32(C2×Q16), (C2×C6).16Q16, C6⋊1(Q8⋊C4), Dic6⋊19(C2×C4), (C2×C4).140D12, C12.141(C2×D4), (C2×C12).135D4, C6.49(C2×SD16), (C2×C6).32SD16, C12.61(C22×C4), (C22×C6).187D4, (C22×C4).346D6, C12.21(C22⋊C4), (C2×C12).322C23, C22.46(D6⋊C4), C22.8(C3⋊Q16), C23.105(C3⋊D4), C22.11(D4.S3), (C22×Dic6).10C2, (C22×C12).137C22, (C2×Dic6).261C22, C4.50(S3×C2×C4), (C6×C4⋊C4).6C2, (C2×C4⋊C4).7S3, C3⋊2(C2×Q8⋊C4), (C2×C4).76(C4×S3), C2.13(C2×D6⋊C4), (C22×C3⋊C8).5C2, C2.2(C2×D4.S3), C2.2(C2×C3⋊Q16), (C2×C12).79(C2×C4), (C2×C6).442(C2×D4), C6.40(C2×C22⋊C4), (C2×C3⋊C8).241C22, C22.59(C2×C3⋊D4), (C2×C4).125(C3⋊D4), (C3×C4⋊C4).260C22, (C2×C6).59(C22⋊C4), (C2×C4).422(C22×S3), SmallGroup(192,528)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C6.SD16
G = < a,b,c,d | a2=b6=c8=1, d2=b3c4, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=b3c-1 >
Subgroups: 376 in 162 conjugacy classes, 79 normal (27 characteristic)
C1, C2, C2, C3, C4, C4, C4, C22, C22, C6, C6, C8, C2×C4, C2×C4, C2×C4, Q8, C23, Dic3, C12, C12, C12, C2×C6, C2×C6, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×Q8, C3⋊C8, Dic6, Dic6, C2×Dic3, C2×C12, C2×C12, C2×C12, C22×C6, Q8⋊C4, C2×C4⋊C4, C22×C8, C22×Q8, C2×C3⋊C8, C2×C3⋊C8, C3×C4⋊C4, C3×C4⋊C4, C2×Dic6, C2×Dic6, C22×Dic3, C22×C12, C22×C12, C2×Q8⋊C4, C6.SD16, C22×C3⋊C8, C6×C4⋊C4, C22×Dic6, C2×C6.SD16
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D6, C22⋊C4, SD16, Q16, C22×C4, C2×D4, C4×S3, D12, C3⋊D4, C22×S3, Q8⋊C4, C2×C22⋊C4, C2×SD16, C2×Q16, D6⋊C4, D4.S3, C3⋊Q16, S3×C2×C4, C2×D12, C2×C3⋊D4, C2×Q8⋊C4, C6.SD16, C2×D6⋊C4, C2×D4.S3, C2×C3⋊Q16, C2×C6.SD16
►Regular action on 192 points
Generators in S192
(1 58)(2 59)(3 60)(4 61)(5 62)(6 63)(7 64)(8 57)(9 25)(10 26)(11 27)(12 28)(13 29)(14 30)(15 31)(16 32)(17 146)(18 147)(19 148)(20 149)(21 150)(22 151)(23 152)(24 145)(33 191)(34 192)(35 185)(36 186)(37 187)(38 188)(39 189)(40 190)(41 175)(42 176)(43 169)(44 170)(45 171)(46 172)(47 173)(48 174)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(65 81)(66 82)(67 83)(68 84)(69 85)(70 86)(71 87)(72 88)(73 120)(74 113)(75 114)(76 115)(77 116)(78 117)(79 118)(80 119)(97 128)(98 121)(99 122)(100 123)(101 124)(102 125)(103 126)(104 127)(105 133)(106 134)(107 135)(108 136)(109 129)(110 130)(111 131)(112 132)(137 165)(138 166)(139 167)(140 168)(141 161)(142 162)(143 163)(144 164)(153 181)(154 182)(155 183)(156 184)(157 177)(158 178)(159 179)(160 180)
(1 109 75 23 189 171)(2 172 190 24 76 110)(3 111 77 17 191 173)(4 174 192 18 78 112)(5 105 79 19 185 175)(6 176 186 20 80 106)(7 107 73 21 187 169)(8 170 188 22 74 108)(9 179 163 103 82 96)(10 89 83 104 164 180)(11 181 165 97 84 90)(12 91 85 98 166 182)(13 183 167 99 86 92)(14 93 87 100 168 184)(15 177 161 101 88 94)(16 95 81 102 162 178)(25 159 143 126 66 56)(26 49 67 127 144 160)(27 153 137 128 68 50)(28 51 69 121 138 154)(29 155 139 122 70 52)(30 53 71 123 140 156)(31 157 141 124 72 54)(32 55 65 125 142 158)(33 47 60 131 116 146)(34 147 117 132 61 48)(35 41 62 133 118 148)(36 149 119 134 63 42)(37 43 64 135 120 150)(38 151 113 136 57 44)(39 45 58 129 114 152)(40 145 115 130 59 46)
(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)
(1 122 19 25)(2 28 20 125)(3 128 21 31)(4 26 22 123)(5 126 23 29)(6 32 24 121)(7 124 17 27)(8 30 18 127)(9 58 99 148)(10 151 100 61)(11 64 101 146)(12 149 102 59)(13 62 103 152)(14 147 104 57)(15 60 97 150)(16 145 98 63)(33 181 135 88)(34 83 136 184)(35 179 129 86)(36 81 130 182)(37 177 131 84)(38 87 132 180)(39 183 133 82)(40 85 134 178)(41 163 114 92)(42 95 115 166)(43 161 116 90)(44 93 117 164)(45 167 118 96)(46 91 119 162)(47 165 120 94)(48 89 113 168)(49 74 140 174)(50 169 141 77)(51 80 142 172)(52 175 143 75)(53 78 144 170)(54 173 137 73)(55 76 138 176)(56 171 139 79)(65 110 154 186)(66 189 155 105)(67 108 156 192)(68 187 157 111)(69 106 158 190)(70 185 159 109)(71 112 160 188)(72 191 153 107)
G:=sub<Sym(192)| (1,58)(2,59)(3,60)(4,61)(5,62)(6,63)(7,64)(8,57)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,145)(33,191)(34,192)(35,185)(36,186)(37,187)(38,188)(39,189)(40,190)(41,175)(42,176)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(65,81)(66,82)(67,83)(68,84)(69,85)(70,86)(71,87)(72,88)(73,120)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119)(97,128)(98,121)(99,122)(100,123)(101,124)(102,125)(103,126)(104,127)(105,133)(106,134)(107,135)(108,136)(109,129)(110,130)(111,131)(112,132)(137,165)(138,166)(139,167)(140,168)(141,161)(142,162)(143,163)(144,164)(153,181)(154,182)(155,183)(156,184)(157,177)(158,178)(159,179)(160,180), (1,109,75,23,189,171)(2,172,190,24,76,110)(3,111,77,17,191,173)(4,174,192,18,78,112)(5,105,79,19,185,175)(6,176,186,20,80,106)(7,107,73,21,187,169)(8,170,188,22,74,108)(9,179,163,103,82,96)(10,89,83,104,164,180)(11,181,165,97,84,90)(12,91,85,98,166,182)(13,183,167,99,86,92)(14,93,87,100,168,184)(15,177,161,101,88,94)(16,95,81,102,162,178)(25,159,143,126,66,56)(26,49,67,127,144,160)(27,153,137,128,68,50)(28,51,69,121,138,154)(29,155,139,122,70,52)(30,53,71,123,140,156)(31,157,141,124,72,54)(32,55,65,125,142,158)(33,47,60,131,116,146)(34,147,117,132,61,48)(35,41,62,133,118,148)(36,149,119,134,63,42)(37,43,64,135,120,150)(38,151,113,136,57,44)(39,45,58,129,114,152)(40,145,115,130,59,46), (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), (1,122,19,25)(2,28,20,125)(3,128,21,31)(4,26,22,123)(5,126,23,29)(6,32,24,121)(7,124,17,27)(8,30,18,127)(9,58,99,148)(10,151,100,61)(11,64,101,146)(12,149,102,59)(13,62,103,152)(14,147,104,57)(15,60,97,150)(16,145,98,63)(33,181,135,88)(34,83,136,184)(35,179,129,86)(36,81,130,182)(37,177,131,84)(38,87,132,180)(39,183,133,82)(40,85,134,178)(41,163,114,92)(42,95,115,166)(43,161,116,90)(44,93,117,164)(45,167,118,96)(46,91,119,162)(47,165,120,94)(48,89,113,168)(49,74,140,174)(50,169,141,77)(51,80,142,172)(52,175,143,75)(53,78,144,170)(54,173,137,73)(55,76,138,176)(56,171,139,79)(65,110,154,186)(66,189,155,105)(67,108,156,192)(68,187,157,111)(69,106,158,190)(70,185,159,109)(71,112,160,188)(72,191,153,107)>;
G:=Group( (1,58)(2,59)(3,60)(4,61)(5,62)(6,63)(7,64)(8,57)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,145)(33,191)(34,192)(35,185)(36,186)(37,187)(38,188)(39,189)(40,190)(41,175)(42,176)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(65,81)(66,82)(67,83)(68,84)(69,85)(70,86)(71,87)(72,88)(73,120)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119)(97,128)(98,121)(99,122)(100,123)(101,124)(102,125)(103,126)(104,127)(105,133)(106,134)(107,135)(108,136)(109,129)(110,130)(111,131)(112,132)(137,165)(138,166)(139,167)(140,168)(141,161)(142,162)(143,163)(144,164)(153,181)(154,182)(155,183)(156,184)(157,177)(158,178)(159,179)(160,180), (1,109,75,23,189,171)(2,172,190,24,76,110)(3,111,77,17,191,173)(4,174,192,18,78,112)(5,105,79,19,185,175)(6,176,186,20,80,106)(7,107,73,21,187,169)(8,170,188,22,74,108)(9,179,163,103,82,96)(10,89,83,104,164,180)(11,181,165,97,84,90)(12,91,85,98,166,182)(13,183,167,99,86,92)(14,93,87,100,168,184)(15,177,161,101,88,94)(16,95,81,102,162,178)(25,159,143,126,66,56)(26,49,67,127,144,160)(27,153,137,128,68,50)(28,51,69,121,138,154)(29,155,139,122,70,52)(30,53,71,123,140,156)(31,157,141,124,72,54)(32,55,65,125,142,158)(33,47,60,131,116,146)(34,147,117,132,61,48)(35,41,62,133,118,148)(36,149,119,134,63,42)(37,43,64,135,120,150)(38,151,113,136,57,44)(39,45,58,129,114,152)(40,145,115,130,59,46), (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), (1,122,19,25)(2,28,20,125)(3,128,21,31)(4,26,22,123)(5,126,23,29)(6,32,24,121)(7,124,17,27)(8,30,18,127)(9,58,99,148)(10,151,100,61)(11,64,101,146)(12,149,102,59)(13,62,103,152)(14,147,104,57)(15,60,97,150)(16,145,98,63)(33,181,135,88)(34,83,136,184)(35,179,129,86)(36,81,130,182)(37,177,131,84)(38,87,132,180)(39,183,133,82)(40,85,134,178)(41,163,114,92)(42,95,115,166)(43,161,116,90)(44,93,117,164)(45,167,118,96)(46,91,119,162)(47,165,120,94)(48,89,113,168)(49,74,140,174)(50,169,141,77)(51,80,142,172)(52,175,143,75)(53,78,144,170)(54,173,137,73)(55,76,138,176)(56,171,139,79)(65,110,154,186)(66,189,155,105)(67,108,156,192)(68,187,157,111)(69,106,158,190)(70,185,159,109)(71,112,160,188)(72,191,153,107) );
G=PermutationGroup([[(1,58),(2,59),(3,60),(4,61),(5,62),(6,63),(7,64),(8,57),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31),(16,32),(17,146),(18,147),(19,148),(20,149),(21,150),(22,151),(23,152),(24,145),(33,191),(34,192),(35,185),(36,186),(37,187),(38,188),(39,189),(40,190),(41,175),(42,176),(43,169),(44,170),(45,171),(46,172),(47,173),(48,174),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96),(65,81),(66,82),(67,83),(68,84),(69,85),(70,86),(71,87),(72,88),(73,120),(74,113),(75,114),(76,115),(77,116),(78,117),(79,118),(80,119),(97,128),(98,121),(99,122),(100,123),(101,124),(102,125),(103,126),(104,127),(105,133),(106,134),(107,135),(108,136),(109,129),(110,130),(111,131),(112,132),(137,165),(138,166),(139,167),(140,168),(141,161),(142,162),(143,163),(144,164),(153,181),(154,182),(155,183),(156,184),(157,177),(158,178),(159,179),(160,180)], [(1,109,75,23,189,171),(2,172,190,24,76,110),(3,111,77,17,191,173),(4,174,192,18,78,112),(5,105,79,19,185,175),(6,176,186,20,80,106),(7,107,73,21,187,169),(8,170,188,22,74,108),(9,179,163,103,82,96),(10,89,83,104,164,180),(11,181,165,97,84,90),(12,91,85,98,166,182),(13,183,167,99,86,92),(14,93,87,100,168,184),(15,177,161,101,88,94),(16,95,81,102,162,178),(25,159,143,126,66,56),(26,49,67,127,144,160),(27,153,137,128,68,50),(28,51,69,121,138,154),(29,155,139,122,70,52),(30,53,71,123,140,156),(31,157,141,124,72,54),(32,55,65,125,142,158),(33,47,60,131,116,146),(34,147,117,132,61,48),(35,41,62,133,118,148),(36,149,119,134,63,42),(37,43,64,135,120,150),(38,151,113,136,57,44),(39,45,58,129,114,152),(40,145,115,130,59,46)], [(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)], [(1,122,19,25),(2,28,20,125),(3,128,21,31),(4,26,22,123),(5,126,23,29),(6,32,24,121),(7,124,17,27),(8,30,18,127),(9,58,99,148),(10,151,100,61),(11,64,101,146),(12,149,102,59),(13,62,103,152),(14,147,104,57),(15,60,97,150),(16,145,98,63),(33,181,135,88),(34,83,136,184),(35,179,129,86),(36,81,130,182),(37,177,131,84),(38,87,132,180),(39,183,133,82),(40,85,134,178),(41,163,114,92),(42,95,115,166),(43,161,116,90),(44,93,117,164),(45,167,118,96),(46,91,119,162),(47,165,120,94),(48,89,113,168),(49,74,140,174),(50,169,141,77),(51,80,142,172),(52,175,143,75),(53,78,144,170),(54,173,137,73),(55,76,138,176),(56,171,139,79),(65,110,154,186),(66,189,155,105),(67,108,156,192),(68,187,157,111),(69,106,158,190),(70,185,159,109),(71,112,160,188),(72,191,153,107)]])
48 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 6A | ··· | 6G | 8A | ··· | 8H | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | - | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D4 | D6 | D6 | SD16 | Q16 | C4×S3 | D12 | C3⋊D4 | C3⋊D4 | D4.S3 | C3⋊Q16 |
| kernel | C2×C6.SD16 | C6.SD16 | C22×C3⋊C8 | C6×C4⋊C4 | C22×Dic6 | C2×Dic6 | C2×C4⋊C4 | C2×C12 | C22×C6 | C4⋊C4 | C22×C4 | C2×C6 | C2×C6 | C2×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 1 | 3 | 1 | 2 | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 |
Matrix representation of C2×C6.SD16 ►in GL6(𝔽73)
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 72 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 5 | 23 | 0 | 0 | 0 | 0 |
| 18 | 68 | 0 | 0 | 0 | 0 |
| 0 | 0 | 54 | 14 | 0 | 0 |
| 0 | 0 | 68 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 67 | 6 |
| 0 | 0 | 0 | 0 | 67 | 67 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 0 | 0 | 0 |
| 0 | 0 | 0 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 70 | 24 |
| 0 | 0 | 0 | 0 | 24 | 3 |
G:=sub<GL(6,GF(73))| [72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,1,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[5,18,0,0,0,0,23,68,0,0,0,0,0,0,54,68,0,0,0,0,14,19,0,0,0,0,0,0,67,67,0,0,0,0,6,67],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,27,0,0,0,0,0,0,27,0,0,0,0,0,0,70,24,0,0,0,0,24,3] >;
C2×C6.SD16 in GAP, Magma, Sage, TeX
C_2\times C_6.{\rm SD}_{16} % in TeX
G:=Group("C2xC6.SD16"); // GroupNames label
G:=SmallGroup(192,528);
// by ID
G=gap.SmallGroup(192,528);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,422,58,1684,438,102,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^6=c^8=1,d^2=b^3*c^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^3*c^-1>;
// generators/relations