direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C3⋊Q16, C12.32C24, Dic6.28C23, C6⋊3(C2×Q16), (C2×C6)⋊9Q16, C3⋊3(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
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, C3, C4, C4, C4, C22, C6, C6, C8, C2×C4, C2×C4, Q8, Q8, C23, Dic3, C12, C12, C12, C2×C6, C2×C8, Q16, C22×C4, C22×C4, C2×Q8, C2×Q8, C3⋊C8, Dic6, Dic6, C2×Dic3, C2×C12, C2×C12, C3×Q8, C3×Q8, C22×C6, C22×C8, C2×Q16, C22×Q8, C22×Q8, C2×C3⋊C8, C3⋊Q16, C2×Dic6, C2×Dic6, C22×Dic3, C22×C12, C22×C12, C6×Q8, C6×Q8, C22×Q16, C22×C3⋊C8, C2×C3⋊Q16, C22×Dic6, Q8×C2×C6, C22×C3⋊Q16
Quotients: C1, C2, C22, S3, D4, C23, D6, Q16, C2×D4, C24, C3⋊D4, C22×S3, C2×Q16, C22×D4, C3⋊Q16, C2×C3⋊D4, S3×C23, C22×Q16, C2×C3⋊Q16, C22×C3⋊D4, C22×C3⋊Q16
►Regular action on 192 points
Generators in S192
(1 134)(2 135)(3 136)(4 129)(5 130)(6 131)(7 132)(8 133)(9 66)(10 67)(11 68)(12 69)(13 70)(14 71)(15 72)(16 65)(17 156)(18 157)(19 158)(20 159)(21 160)(22 153)(23 154)(24 155)(25 151)(26 152)(27 145)(28 146)(29 147)(30 148)(31 149)(32 150)(33 173)(34 174)(35 175)(36 176)(37 169)(38 170)(39 171)(40 172)(41 119)(42 120)(43 113)(44 114)(45 115)(46 116)(47 117)(48 118)(49 77)(50 78)(51 79)(52 80)(53 73)(54 74)(55 75)(56 76)(57 85)(58 86)(59 87)(60 88)(61 81)(62 82)(63 83)(64 84)(89 109)(90 110)(91 111)(92 112)(93 105)(94 106)(95 107)(96 108)(97 125)(98 126)(99 127)(100 128)(101 121)(102 122)(103 123)(104 124)(137 177)(138 178)(139 179)(140 180)(141 181)(142 182)(143 183)(144 184)(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 53)(10 54)(11 55)(12 56)(13 49)(14 50)(15 51)(16 52)(17 97)(18 98)(19 99)(20 100)(21 101)(22 102)(23 103)(24 104)(25 40)(26 33)(27 34)(28 35)(29 36)(30 37)(31 38)(32 39)(41 106)(42 107)(43 108)(44 109)(45 110)(46 111)(47 112)(48 105)(57 130)(58 131)(59 132)(60 133)(61 134)(62 135)(63 136)(64 129)(65 80)(66 73)(67 74)(68 75)(69 76)(70 77)(71 78)(72 79)(89 114)(90 115)(91 116)(92 117)(93 118)(94 119)(95 120)(96 113)(121 160)(122 153)(123 154)(124 155)(125 156)(126 157)(127 158)(128 159)(137 190)(138 191)(139 192)(140 185)(141 186)(142 187)(143 188)(144 189)(145 174)(146 175)(147 176)(148 169)(149 170)(150 171)(151 172)(152 173)(161 184)(162 177)(163 178)(164 179)(165 180)(166 181)(167 182)(168 183)
(1 44 178)(2 179 45)(3 46 180)(4 181 47)(5 48 182)(6 183 41)(7 42 184)(8 177 43)(9 126 169)(10 170 127)(11 128 171)(12 172 121)(13 122 173)(14 174 123)(15 124 175)(16 176 125)(17 80 29)(18 30 73)(19 74 31)(20 32 75)(21 76 25)(22 26 77)(23 78 27)(24 28 79)(33 70 102)(34 103 71)(35 72 104)(36 97 65)(37 66 98)(38 99 67)(39 68 100)(40 101 69)(49 153 152)(50 145 154)(51 155 146)(52 147 156)(53 157 148)(54 149 158)(55 159 150)(56 151 160)(57 93 187)(58 188 94)(59 95 189)(60 190 96)(61 89 191)(62 192 90)(63 91 185)(64 186 92)(81 109 163)(82 164 110)(83 111 165)(84 166 112)(85 105 167)(86 168 106)(87 107 161)(88 162 108)(113 133 137)(114 138 134)(115 135 139)(116 140 136)(117 129 141)(118 142 130)(119 131 143)(120 144 132)
(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)(17 139 21 143)(18 138 22 142)(19 137 23 141)(20 144 24 140)(25 131 29 135)(26 130 30 134)(27 129 31 133)(28 136 32 132)(33 57 37 61)(34 64 38 60)(35 63 39 59)(36 62 40 58)(41 52 45 56)(42 51 46 55)(43 50 47 54)(44 49 48 53)(65 90 69 94)(66 89 70 93)(67 96 71 92)(68 95 72 91)(73 114 77 118)(74 113 78 117)(75 120 79 116)(76 119 80 115)(81 173 85 169)(82 172 86 176)(83 171 87 175)(84 170 88 174)(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)(153 182 157 178)(154 181 158 177)(155 180 159 184)(156 179 160 183)
G:=sub<Sym(192)| (1,134)(2,135)(3,136)(4,129)(5,130)(6,131)(7,132)(8,133)(9,66)(10,67)(11,68)(12,69)(13,70)(14,71)(15,72)(16,65)(17,156)(18,157)(19,158)(20,159)(21,160)(22,153)(23,154)(24,155)(25,151)(26,152)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,173)(34,174)(35,175)(36,176)(37,169)(38,170)(39,171)(40,172)(41,119)(42,120)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,77)(50,78)(51,79)(52,80)(53,73)(54,74)(55,75)(56,76)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(89,109)(90,110)(91,111)(92,112)(93,105)(94,106)(95,107)(96,108)(97,125)(98,126)(99,127)(100,128)(101,121)(102,122)(103,123)(104,124)(137,177)(138,178)(139,179)(140,180)(141,181)(142,182)(143,183)(144,184)(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)(9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,40)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(32,39)(41,106)(42,107)(43,108)(44,109)(45,110)(46,111)(47,112)(48,105)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,129)(65,80)(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79)(89,114)(90,115)(91,116)(92,117)(93,118)(94,119)(95,120)(96,113)(121,160)(122,153)(123,154)(124,155)(125,156)(126,157)(127,158)(128,159)(137,190)(138,191)(139,192)(140,185)(141,186)(142,187)(143,188)(144,189)(145,174)(146,175)(147,176)(148,169)(149,170)(150,171)(151,172)(152,173)(161,184)(162,177)(163,178)(164,179)(165,180)(166,181)(167,182)(168,183), (1,44,178)(2,179,45)(3,46,180)(4,181,47)(5,48,182)(6,183,41)(7,42,184)(8,177,43)(9,126,169)(10,170,127)(11,128,171)(12,172,121)(13,122,173)(14,174,123)(15,124,175)(16,176,125)(17,80,29)(18,30,73)(19,74,31)(20,32,75)(21,76,25)(22,26,77)(23,78,27)(24,28,79)(33,70,102)(34,103,71)(35,72,104)(36,97,65)(37,66,98)(38,99,67)(39,68,100)(40,101,69)(49,153,152)(50,145,154)(51,155,146)(52,147,156)(53,157,148)(54,149,158)(55,159,150)(56,151,160)(57,93,187)(58,188,94)(59,95,189)(60,190,96)(61,89,191)(62,192,90)(63,91,185)(64,186,92)(81,109,163)(82,164,110)(83,111,165)(84,166,112)(85,105,167)(86,168,106)(87,107,161)(88,162,108)(113,133,137)(114,138,134)(115,135,139)(116,140,136)(117,129,141)(118,142,130)(119,131,143)(120,144,132), (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)(17,139,21,143)(18,138,22,142)(19,137,23,141)(20,144,24,140)(25,131,29,135)(26,130,30,134)(27,129,31,133)(28,136,32,132)(33,57,37,61)(34,64,38,60)(35,63,39,59)(36,62,40,58)(41,52,45,56)(42,51,46,55)(43,50,47,54)(44,49,48,53)(65,90,69,94)(66,89,70,93)(67,96,71,92)(68,95,72,91)(73,114,77,118)(74,113,78,117)(75,120,79,116)(76,119,80,115)(81,173,85,169)(82,172,86,176)(83,171,87,175)(84,170,88,174)(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)(153,182,157,178)(154,181,158,177)(155,180,159,184)(156,179,160,183)>;
G:=Group( (1,134)(2,135)(3,136)(4,129)(5,130)(6,131)(7,132)(8,133)(9,66)(10,67)(11,68)(12,69)(13,70)(14,71)(15,72)(16,65)(17,156)(18,157)(19,158)(20,159)(21,160)(22,153)(23,154)(24,155)(25,151)(26,152)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,173)(34,174)(35,175)(36,176)(37,169)(38,170)(39,171)(40,172)(41,119)(42,120)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,77)(50,78)(51,79)(52,80)(53,73)(54,74)(55,75)(56,76)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(89,109)(90,110)(91,111)(92,112)(93,105)(94,106)(95,107)(96,108)(97,125)(98,126)(99,127)(100,128)(101,121)(102,122)(103,123)(104,124)(137,177)(138,178)(139,179)(140,180)(141,181)(142,182)(143,183)(144,184)(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)(9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,40)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(32,39)(41,106)(42,107)(43,108)(44,109)(45,110)(46,111)(47,112)(48,105)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,129)(65,80)(66,73)(67,74)(68,75)(69,76)(70,77)(71,78)(72,79)(89,114)(90,115)(91,116)(92,117)(93,118)(94,119)(95,120)(96,113)(121,160)(122,153)(123,154)(124,155)(125,156)(126,157)(127,158)(128,159)(137,190)(138,191)(139,192)(140,185)(141,186)(142,187)(143,188)(144,189)(145,174)(146,175)(147,176)(148,169)(149,170)(150,171)(151,172)(152,173)(161,184)(162,177)(163,178)(164,179)(165,180)(166,181)(167,182)(168,183), (1,44,178)(2,179,45)(3,46,180)(4,181,47)(5,48,182)(6,183,41)(7,42,184)(8,177,43)(9,126,169)(10,170,127)(11,128,171)(12,172,121)(13,122,173)(14,174,123)(15,124,175)(16,176,125)(17,80,29)(18,30,73)(19,74,31)(20,32,75)(21,76,25)(22,26,77)(23,78,27)(24,28,79)(33,70,102)(34,103,71)(35,72,104)(36,97,65)(37,66,98)(38,99,67)(39,68,100)(40,101,69)(49,153,152)(50,145,154)(51,155,146)(52,147,156)(53,157,148)(54,149,158)(55,159,150)(56,151,160)(57,93,187)(58,188,94)(59,95,189)(60,190,96)(61,89,191)(62,192,90)(63,91,185)(64,186,92)(81,109,163)(82,164,110)(83,111,165)(84,166,112)(85,105,167)(86,168,106)(87,107,161)(88,162,108)(113,133,137)(114,138,134)(115,135,139)(116,140,136)(117,129,141)(118,142,130)(119,131,143)(120,144,132), (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)(17,139,21,143)(18,138,22,142)(19,137,23,141)(20,144,24,140)(25,131,29,135)(26,130,30,134)(27,129,31,133)(28,136,32,132)(33,57,37,61)(34,64,38,60)(35,63,39,59)(36,62,40,58)(41,52,45,56)(42,51,46,55)(43,50,47,54)(44,49,48,53)(65,90,69,94)(66,89,70,93)(67,96,71,92)(68,95,72,91)(73,114,77,118)(74,113,78,117)(75,120,79,116)(76,119,80,115)(81,173,85,169)(82,172,86,176)(83,171,87,175)(84,170,88,174)(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)(153,182,157,178)(154,181,158,177)(155,180,159,184)(156,179,160,183) );
G=PermutationGroup([[(1,134),(2,135),(3,136),(4,129),(5,130),(6,131),(7,132),(8,133),(9,66),(10,67),(11,68),(12,69),(13,70),(14,71),(15,72),(16,65),(17,156),(18,157),(19,158),(20,159),(21,160),(22,153),(23,154),(24,155),(25,151),(26,152),(27,145),(28,146),(29,147),(30,148),(31,149),(32,150),(33,173),(34,174),(35,175),(36,176),(37,169),(38,170),(39,171),(40,172),(41,119),(42,120),(43,113),(44,114),(45,115),(46,116),(47,117),(48,118),(49,77),(50,78),(51,79),(52,80),(53,73),(54,74),(55,75),(56,76),(57,85),(58,86),(59,87),(60,88),(61,81),(62,82),(63,83),(64,84),(89,109),(90,110),(91,111),(92,112),(93,105),(94,106),(95,107),(96,108),(97,125),(98,126),(99,127),(100,128),(101,121),(102,122),(103,123),(104,124),(137,177),(138,178),(139,179),(140,180),(141,181),(142,182),(143,183),(144,184),(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),(9,53),(10,54),(11,55),(12,56),(13,49),(14,50),(15,51),(16,52),(17,97),(18,98),(19,99),(20,100),(21,101),(22,102),(23,103),(24,104),(25,40),(26,33),(27,34),(28,35),(29,36),(30,37),(31,38),(32,39),(41,106),(42,107),(43,108),(44,109),(45,110),(46,111),(47,112),(48,105),(57,130),(58,131),(59,132),(60,133),(61,134),(62,135),(63,136),(64,129),(65,80),(66,73),(67,74),(68,75),(69,76),(70,77),(71,78),(72,79),(89,114),(90,115),(91,116),(92,117),(93,118),(94,119),(95,120),(96,113),(121,160),(122,153),(123,154),(124,155),(125,156),(126,157),(127,158),(128,159),(137,190),(138,191),(139,192),(140,185),(141,186),(142,187),(143,188),(144,189),(145,174),(146,175),(147,176),(148,169),(149,170),(150,171),(151,172),(152,173),(161,184),(162,177),(163,178),(164,179),(165,180),(166,181),(167,182),(168,183)], [(1,44,178),(2,179,45),(3,46,180),(4,181,47),(5,48,182),(6,183,41),(7,42,184),(8,177,43),(9,126,169),(10,170,127),(11,128,171),(12,172,121),(13,122,173),(14,174,123),(15,124,175),(16,176,125),(17,80,29),(18,30,73),(19,74,31),(20,32,75),(21,76,25),(22,26,77),(23,78,27),(24,28,79),(33,70,102),(34,103,71),(35,72,104),(36,97,65),(37,66,98),(38,99,67),(39,68,100),(40,101,69),(49,153,152),(50,145,154),(51,155,146),(52,147,156),(53,157,148),(54,149,158),(55,159,150),(56,151,160),(57,93,187),(58,188,94),(59,95,189),(60,190,96),(61,89,191),(62,192,90),(63,91,185),(64,186,92),(81,109,163),(82,164,110),(83,111,165),(84,166,112),(85,105,167),(86,168,106),(87,107,161),(88,162,108),(113,133,137),(114,138,134),(115,135,139),(116,140,136),(117,129,141),(118,142,130),(119,131,143),(120,144,132)], [(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),(17,139,21,143),(18,138,22,142),(19,137,23,141),(20,144,24,140),(25,131,29,135),(26,130,30,134),(27,129,31,133),(28,136,32,132),(33,57,37,61),(34,64,38,60),(35,63,39,59),(36,62,40,58),(41,52,45,56),(42,51,46,55),(43,50,47,54),(44,49,48,53),(65,90,69,94),(66,89,70,93),(67,96,71,92),(68,95,72,91),(73,114,77,118),(74,113,78,117),(75,120,79,116),(76,119,80,115),(81,173,85,169),(82,172,86,176),(83,171,87,175),(84,170,88,174),(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),(153,182,157,178),(154,181,158,177),(155,180,159,184),(156,179,160,183)]])
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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D6 | D6 | Q16 | C3⋊D4 | C3⋊D4 | C3⋊Q16 |
| kernel | C22×C3⋊Q16 | C22×C3⋊C8 | C2×C3⋊Q16 | C22×Dic6 | Q8×C2×C6 | C22×Q8 | C2×C12 | C22×C6 | C22×C4 | C2×Q8 | C2×C6 | C2×C4 | C23 | C22 |
| # reps | 1 | 1 | 12 | 1 | 1 | 1 | 3 | 1 | 1 | 6 | 8 | 6 | 2 | 4 |
Matrix representation of C22×C3⋊Q16 ►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 |
| 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 | 72 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 32 |
| 0 | 0 | 0 | 0 | 57 | 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 | 59 |
| 0 | 0 | 0 | 0 | 60 | 6 |
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