Copied to
clipboard

G = C22×C3⋊Q16order 192 = 26·3

Direct product of C22 and C3⋊Q16

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22×C3⋊Q16, C12.32C24, Dic6.28C23, C63(C2×Q16), (C2×C6)⋊9Q16, C33(C22×Q16), C3⋊C8.29C23, C12.256(C2×D4), (C2×C12).212D4, C4.32(S3×C23), (C2×Q8).209D6, C6.151(C22×D4), (C22×C6).211D4, (C22×C4).398D6, (C22×Q8).13S3, (C3×Q8).21C23, Q8.31(C22×S3), (C2×C12).549C23, (C6×Q8).230C22, C23.114(C3⋊D4), (C22×Dic6).18C2, (C22×C12).281C22, (C2×Dic6).306C22, (Q8×C2×C6).6C2, C4.26(C2×C3⋊D4), (C2×C6).586(C2×D4), (C22×C3⋊C8).14C2, (C2×C3⋊C8).287C22, C2.24(C22×C3⋊D4), (C2×C4).155(C3⋊D4), (C2×C4).630(C22×S3), C22.114(C2×C3⋊D4), SmallGroup(192,1368)

Series: Derived Chief Lower central Upper central

C1C12 — C22×C3⋊Q16
C1C3C6C12Dic6C2×Dic6C22×Dic6 — C22×C3⋊Q16
C3C6C12 — C22×C3⋊Q16
C1C23C22×C4C22×Q8

Generators and relations for C22×C3⋊Q16
 G = < a,b,c,d,e | a2=b2=c3=d8=1, e2=d4, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c-1, ce=ec, ede-1=d-1 >

Subgroups: 520 in 258 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2 [×6], C3, C4, C4 [×3], C4 [×8], C22 [×7], C6, C6 [×6], C8 [×4], C2×C4 [×6], C2×C4 [×12], Q8 [×4], Q8 [×16], C23, Dic3 [×4], C12, C12 [×3], C12 [×4], C2×C6 [×7], C2×C8 [×6], Q16 [×16], C22×C4, C22×C4 [×2], C2×Q8 [×6], C2×Q8 [×12], C3⋊C8 [×4], Dic6 [×4], Dic6 [×6], C2×Dic3 [×6], C2×C12 [×6], C2×C12 [×6], C3×Q8 [×4], C3×Q8 [×6], C22×C6, C22×C8, C2×Q16 [×12], C22×Q8, C22×Q8, C2×C3⋊C8 [×6], C3⋊Q16 [×16], C2×Dic6 [×6], C2×Dic6 [×3], C22×Dic3, C22×C12, C22×C12, C6×Q8 [×6], C6×Q8 [×3], C22×Q16, C22×C3⋊C8, C2×C3⋊Q16 [×12], C22×Dic6, Q8×C2×C6, C22×C3⋊Q16
Quotients: C1, C2 [×15], C22 [×35], S3, D4 [×4], C23 [×15], D6 [×7], Q16 [×4], C2×D4 [×6], C24, C3⋊D4 [×4], C22×S3 [×7], C2×Q16 [×6], C22×D4, C3⋊Q16 [×4], C2×C3⋊D4 [×6], S3×C23, C22×Q16, C2×C3⋊Q16 [×6], C22×C3⋊D4, C22×C3⋊Q16

Smallest permutation representation of C22×C3⋊Q16
Regular action on 192 points
Generators in S192
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 9)(8 10)(17 115)(18 116)(19 117)(20 118)(21 119)(22 120)(23 113)(24 114)(25 94)(26 95)(27 96)(28 89)(29 90)(30 91)(31 92)(32 93)(33 79)(34 80)(35 73)(36 74)(37 75)(38 76)(39 77)(40 78)(41 170)(42 171)(43 172)(44 173)(45 174)(46 175)(47 176)(48 169)(49 138)(50 139)(51 140)(52 141)(53 142)(54 143)(55 144)(56 137)(57 85)(58 86)(59 87)(60 88)(61 81)(62 82)(63 83)(64 84)(65 131)(66 132)(67 133)(68 134)(69 135)(70 136)(71 129)(72 130)(97 125)(98 126)(99 127)(100 128)(101 121)(102 122)(103 123)(104 124)(105 150)(106 151)(107 152)(108 145)(109 146)(110 147)(111 148)(112 149)(153 181)(154 182)(155 183)(156 184)(157 177)(158 178)(159 179)(160 180)(161 189)(162 190)(163 191)(164 192)(165 185)(166 186)(167 187)(168 188)
(1 81)(2 82)(3 83)(4 84)(5 85)(6 86)(7 87)(8 88)(9 59)(10 60)(11 61)(12 62)(13 63)(14 64)(15 57)(16 58)(17 146)(18 147)(19 148)(20 149)(21 150)(22 151)(23 152)(24 145)(25 41)(26 42)(27 43)(28 44)(29 45)(30 46)(31 47)(32 48)(33 101)(34 102)(35 103)(36 104)(37 97)(38 98)(39 99)(40 100)(49 163)(50 164)(51 165)(52 166)(53 167)(54 168)(55 161)(56 162)(65 153)(66 154)(67 155)(68 156)(69 157)(70 158)(71 159)(72 160)(73 123)(74 124)(75 125)(76 126)(77 127)(78 128)(79 121)(80 122)(89 173)(90 174)(91 175)(92 176)(93 169)(94 170)(95 171)(96 172)(105 119)(106 120)(107 113)(108 114)(109 115)(110 116)(111 117)(112 118)(129 179)(130 180)(131 181)(132 182)(133 183)(134 184)(135 177)(136 178)(137 190)(138 191)(139 192)(140 185)(141 186)(142 187)(143 188)(144 189)
(1 44 49)(2 50 45)(3 46 51)(4 52 47)(5 48 53)(6 54 41)(7 42 55)(8 56 43)(9 171 144)(10 137 172)(11 173 138)(12 139 174)(13 175 140)(14 141 176)(15 169 142)(16 143 170)(17 130 124)(18 125 131)(19 132 126)(20 127 133)(21 134 128)(22 121 135)(23 136 122)(24 123 129)(25 86 168)(26 161 87)(27 88 162)(28 163 81)(29 82 164)(30 165 83)(31 84 166)(32 167 85)(33 157 106)(34 107 158)(35 159 108)(36 109 160)(37 153 110)(38 111 154)(39 155 112)(40 105 156)(57 93 187)(58 188 94)(59 95 189)(60 190 96)(61 89 191)(62 192 90)(63 91 185)(64 186 92)(65 116 97)(66 98 117)(67 118 99)(68 100 119)(69 120 101)(70 102 113)(71 114 103)(72 104 115)(73 179 145)(74 146 180)(75 181 147)(76 148 182)(77 183 149)(78 150 184)(79 177 151)(80 152 178)
(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)
(1 152 5 148)(2 151 6 147)(3 150 7 146)(4 149 8 145)(9 109 13 105)(10 108 14 112)(11 107 15 111)(12 106 16 110)(17 83 21 87)(18 82 22 86)(19 81 23 85)(20 88 24 84)(25 131 29 135)(26 130 30 134)(27 129 31 133)(28 136 32 132)(33 143 37 139)(34 142 38 138)(35 141 39 137)(36 140 40 144)(41 181 45 177)(42 180 46 184)(43 179 47 183)(44 178 48 182)(49 80 53 76)(50 79 54 75)(51 78 55 74)(52 77 56 73)(57 117 61 113)(58 116 62 120)(59 115 63 119)(60 114 64 118)(65 90 69 94)(66 89 70 93)(67 96 71 92)(68 95 72 91)(97 192 101 188)(98 191 102 187)(99 190 103 186)(100 189 104 185)(121 168 125 164)(122 167 126 163)(123 166 127 162)(124 165 128 161)(153 174 157 170)(154 173 158 169)(155 172 159 176)(156 171 160 175)

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

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

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

48 conjugacy classes

class 1 2A···2G 3 4A4B4C4D4E4F4G4H4I4J4K4L6A···6G8A···8H12A···12L
order12···234444444444446···68···812···12
size11···1222224444121212122···26···64···4

48 irreducible representations

dim11111222222224
type++++++++++--
imageC1C2C2C2C2S3D4D4D6D6Q16C3⋊D4C3⋊D4C3⋊Q16
kernelC22×C3⋊Q16C22×C3⋊C8C2×C3⋊Q16C22×Dic6Q8×C2×C6C22×Q8C2×C12C22×C6C22×C4C2×Q8C2×C6C2×C4C23C22
# reps111211131168624

Matrix representation of C22×C3⋊Q16 in GL6(𝔽73)

7200000
0720000
0072000
0007200
0000720
0000072
,
7200000
0720000
001000
000100
0000720
0000072
,
0720000
1720000
0007200
0017200
000010
000001
,
1720000
0720000
0017200
0007200
0000032
00005732
,
7200000
0720000
0072000
0007200
00006759
0000606

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],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[0,1,0,0,0,0,72,72,0,0,0,0,0,0,0,1,0,0,0,0,72,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,72,72,0,0,0,0,0,0,1,0,0,0,0,0,72,72,0,0,0,0,0,0,0,57,0,0,0,0,32,32],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,67,60,0,0,0,0,59,6] >;

C22×C3⋊Q16 in GAP, Magma, Sage, TeX

C_2^2\times C_3\rtimes Q_{16}
% in TeX

G:=Group("C2^2xC3:Q16");
// GroupNames label

G:=SmallGroup(192,1368);
// by ID

G=gap.SmallGroup(192,1368);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,675,136,1684,235,102,6278]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^3=d^8=1,e^2=d^4,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽