metabelian, supersoluble, monomial
Aliases: (S3×C12)⋊5S3, C12.57(S32), (S3×C6).41D6, C12⋊S3⋊14S3, C33⋊6D4⋊6C2, C33⋊8Q8⋊8C2, (C3×C12).145D6, C33⋊17(C4○D4), C3⋊3(D12⋊5S3), (C3×Dic3).42D6, C3⋊3(C12.59D6), C32⋊11(C4○D12), (C32×C6).46C23, C32⋊22(D4⋊2S3), (C32×C12).47C22, C33⋊5C4.10C22, (C32×Dic3).28C22, (S3×C3×C12)⋊6C2, C6.56(C2×S32), C4.6(S3×C3⋊S3), D6.6(C2×C3⋊S3), (C4×S3)⋊1(C3⋊S3), C12.25(C2×C3⋊S3), (Dic3×C3⋊S3)⋊9C2, (C2×C3⋊S3).35D6, (C3×C12⋊S3)⋊9C2, C6.9(C22×C3⋊S3), (S3×C3×C6).25C22, (C6×C3⋊S3).27C22, Dic3.11(C2×C3⋊S3), (C3×C6).104(C22×S3), C2.13(C2×S3×C3⋊S3), SmallGroup(432,668)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊6D4⋊C2
G = < a,b,c,d,e,f | a3=b3=c3=d4=e2=f2=1, ab=ba, ac=ca, dad-1=faf=a-1, ae=ea, bc=cb, dbd-1=fbf=b-1, be=eb, dcd-1=ece=c-1, cf=fc, ede=d-1, df=fd, fef=d2e >
Subgroups: 1504 in 288 conjugacy classes, 68 normal (22 characteristic)
C1, C2, C2 [×3], C3, C3 [×4], C3 [×4], C4, C4 [×3], C22 [×3], S3 [×9], C6, C6 [×4], C6 [×10], C2×C4 [×3], D4 [×3], Q8, C32, C32 [×4], C32 [×4], Dic3, Dic3 [×18], C12, C12 [×4], C12 [×8], D6, D6 [×8], C2×C6 [×6], C4○D4, C3×S3 [×12], C3⋊S3 [×2], C3×C6, C3×C6 [×4], C3×C6 [×5], Dic6 [×9], C4×S3, C4×S3 [×8], D12 [×4], C2×Dic3 [×2], C3⋊D4 [×10], C2×C12 [×4], C3×D4, C33, C3×Dic3 [×4], C3⋊Dic3 [×18], C3×C12, C3×C12 [×4], C3×C12 [×5], S3×C6 [×4], S3×C6 [×8], C2×C3⋊S3 [×2], C62, C4○D12 [×4], D4⋊2S3, S3×C32, C3×C3⋊S3 [×2], C32×C6, S3×Dic3 [×8], D6⋊S3 [×8], S3×C12 [×4], C3×D12 [×4], C32⋊4Q8 [×9], C4×C3⋊S3 [×2], C12⋊S3, C32⋊7D4 [×2], C6×C12, C32×Dic3, C33⋊5C4 [×2], C32×C12, S3×C3×C6, C6×C3⋊S3 [×2], D12⋊5S3 [×4], C12.59D6, Dic3×C3⋊S3 [×2], C33⋊6D4 [×2], S3×C3×C12, C3×C12⋊S3, C33⋊8Q8, C33⋊6D4⋊C2
Quotients: C1, C2 [×7], C22 [×7], S3 [×5], C23, D6 [×15], C4○D4, C3⋊S3, C22×S3 [×5], S32 [×4], C2×C3⋊S3 [×3], C4○D12 [×4], D4⋊2S3, C2×S32 [×4], C22×C3⋊S3, S3×C3⋊S3, D12⋊5S3 [×4], C12.59D6, C2×S3×C3⋊S3, C33⋊6D4⋊C2
►On 144 points
Generators in S144
(1 29 134)(2 135 30)(3 31 136)(4 133 32)(5 95 104)(6 101 96)(7 93 102)(8 103 94)(9 80 33)(10 34 77)(11 78 35)(12 36 79)(13 107 60)(14 57 108)(15 105 58)(16 59 106)(17 131 99)(18 100 132)(19 129 97)(20 98 130)(21 63 124)(22 121 64)(23 61 122)(24 123 62)(25 39 82)(26 83 40)(27 37 84)(28 81 38)(41 46 140)(42 137 47)(43 48 138)(44 139 45)(49 143 119)(50 120 144)(51 141 117)(52 118 142)(53 67 114)(54 115 68)(55 65 116)(56 113 66)(69 128 90)(70 91 125)(71 126 92)(72 89 127)(73 112 87)(74 88 109)(75 110 85)(76 86 111)
(1 47 26)(2 27 48)(3 45 28)(4 25 46)(5 54 16)(6 13 55)(7 56 14)(8 15 53)(9 141 87)(10 88 142)(11 143 85)(12 86 144)(17 72 23)(18 24 69)(19 70 21)(20 22 71)(29 42 83)(30 84 43)(31 44 81)(32 82 41)(33 51 112)(34 109 52)(35 49 110)(36 111 50)(37 138 135)(38 136 139)(39 140 133)(40 134 137)(57 93 113)(58 114 94)(59 95 115)(60 116 96)(61 131 89)(62 90 132)(63 129 91)(64 92 130)(65 101 107)(66 108 102)(67 103 105)(68 106 104)(73 80 117)(74 118 77)(75 78 119)(76 120 79)(97 125 124)(98 121 126)(99 127 122)(100 123 128)
(1 26 47)(2 48 27)(3 28 45)(4 46 25)(5 54 16)(6 13 55)(7 56 14)(8 15 53)(9 87 141)(10 142 88)(11 85 143)(12 144 86)(17 72 23)(18 24 69)(19 70 21)(20 22 71)(29 83 42)(30 43 84)(31 81 44)(32 41 82)(33 112 51)(34 52 109)(35 110 49)(36 50 111)(37 135 138)(38 139 136)(39 133 140)(40 137 134)(57 93 113)(58 114 94)(59 95 115)(60 116 96)(61 131 89)(62 90 132)(63 129 91)(64 92 130)(65 101 107)(66 108 102)(67 103 105)(68 106 104)(73 117 80)(74 77 118)(75 119 78)(76 79 120)(97 125 124)(98 121 126)(99 127 122)(100 123 128)
(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)
(1 57)(2 60)(3 59)(4 58)(5 139)(6 138)(7 137)(8 140)(9 21)(10 24)(11 23)(12 22)(13 135)(14 134)(15 133)(16 136)(17 143)(18 142)(19 141)(20 144)(25 114)(26 113)(27 116)(28 115)(29 108)(30 107)(31 106)(32 105)(33 124)(34 123)(35 122)(36 121)(37 55)(38 54)(39 53)(40 56)(41 103)(42 102)(43 101)(44 104)(45 95)(46 94)(47 93)(48 96)(49 99)(50 98)(51 97)(52 100)(61 78)(62 77)(63 80)(64 79)(65 84)(66 83)(67 82)(68 81)(69 88)(70 87)(71 86)(72 85)(73 91)(74 90)(75 89)(76 92)(109 128)(110 127)(111 126)(112 125)(117 129)(118 132)(119 131)(120 130)
(1 126)(2 127)(3 128)(4 125)(5 79)(6 80)(7 77)(8 78)(9 101)(10 102)(11 103)(12 104)(13 73)(14 74)(15 75)(16 76)(17 84)(18 81)(19 82)(20 83)(21 41)(22 42)(23 43)(24 44)(25 97)(26 98)(27 99)(28 100)(29 71)(30 72)(31 69)(32 70)(33 96)(34 93)(35 94)(36 95)(37 131)(38 132)(39 129)(40 130)(45 123)(46 124)(47 121)(48 122)(49 114)(50 115)(51 116)(52 113)(53 119)(54 120)(55 117)(56 118)(57 109)(58 110)(59 111)(60 112)(61 138)(62 139)(63 140)(64 137)(65 141)(66 142)(67 143)(68 144)(85 105)(86 106)(87 107)(88 108)(89 135)(90 136)(91 133)(92 134)
G:=sub<Sym(144)| (1,29,134)(2,135,30)(3,31,136)(4,133,32)(5,95,104)(6,101,96)(7,93,102)(8,103,94)(9,80,33)(10,34,77)(11,78,35)(12,36,79)(13,107,60)(14,57,108)(15,105,58)(16,59,106)(17,131,99)(18,100,132)(19,129,97)(20,98,130)(21,63,124)(22,121,64)(23,61,122)(24,123,62)(25,39,82)(26,83,40)(27,37,84)(28,81,38)(41,46,140)(42,137,47)(43,48,138)(44,139,45)(49,143,119)(50,120,144)(51,141,117)(52,118,142)(53,67,114)(54,115,68)(55,65,116)(56,113,66)(69,128,90)(70,91,125)(71,126,92)(72,89,127)(73,112,87)(74,88,109)(75,110,85)(76,86,111), (1,47,26)(2,27,48)(3,45,28)(4,25,46)(5,54,16)(6,13,55)(7,56,14)(8,15,53)(9,141,87)(10,88,142)(11,143,85)(12,86,144)(17,72,23)(18,24,69)(19,70,21)(20,22,71)(29,42,83)(30,84,43)(31,44,81)(32,82,41)(33,51,112)(34,109,52)(35,49,110)(36,111,50)(37,138,135)(38,136,139)(39,140,133)(40,134,137)(57,93,113)(58,114,94)(59,95,115)(60,116,96)(61,131,89)(62,90,132)(63,129,91)(64,92,130)(65,101,107)(66,108,102)(67,103,105)(68,106,104)(73,80,117)(74,118,77)(75,78,119)(76,120,79)(97,125,124)(98,121,126)(99,127,122)(100,123,128), (1,26,47)(2,48,27)(3,28,45)(4,46,25)(5,54,16)(6,13,55)(7,56,14)(8,15,53)(9,87,141)(10,142,88)(11,85,143)(12,144,86)(17,72,23)(18,24,69)(19,70,21)(20,22,71)(29,83,42)(30,43,84)(31,81,44)(32,41,82)(33,112,51)(34,52,109)(35,110,49)(36,50,111)(37,135,138)(38,139,136)(39,133,140)(40,137,134)(57,93,113)(58,114,94)(59,95,115)(60,116,96)(61,131,89)(62,90,132)(63,129,91)(64,92,130)(65,101,107)(66,108,102)(67,103,105)(68,106,104)(73,117,80)(74,77,118)(75,119,78)(76,79,120)(97,125,124)(98,121,126)(99,127,122)(100,123,128), (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), (1,57)(2,60)(3,59)(4,58)(5,139)(6,138)(7,137)(8,140)(9,21)(10,24)(11,23)(12,22)(13,135)(14,134)(15,133)(16,136)(17,143)(18,142)(19,141)(20,144)(25,114)(26,113)(27,116)(28,115)(29,108)(30,107)(31,106)(32,105)(33,124)(34,123)(35,122)(36,121)(37,55)(38,54)(39,53)(40,56)(41,103)(42,102)(43,101)(44,104)(45,95)(46,94)(47,93)(48,96)(49,99)(50,98)(51,97)(52,100)(61,78)(62,77)(63,80)(64,79)(65,84)(66,83)(67,82)(68,81)(69,88)(70,87)(71,86)(72,85)(73,91)(74,90)(75,89)(76,92)(109,128)(110,127)(111,126)(112,125)(117,129)(118,132)(119,131)(120,130), (1,126)(2,127)(3,128)(4,125)(5,79)(6,80)(7,77)(8,78)(9,101)(10,102)(11,103)(12,104)(13,73)(14,74)(15,75)(16,76)(17,84)(18,81)(19,82)(20,83)(21,41)(22,42)(23,43)(24,44)(25,97)(26,98)(27,99)(28,100)(29,71)(30,72)(31,69)(32,70)(33,96)(34,93)(35,94)(36,95)(37,131)(38,132)(39,129)(40,130)(45,123)(46,124)(47,121)(48,122)(49,114)(50,115)(51,116)(52,113)(53,119)(54,120)(55,117)(56,118)(57,109)(58,110)(59,111)(60,112)(61,138)(62,139)(63,140)(64,137)(65,141)(66,142)(67,143)(68,144)(85,105)(86,106)(87,107)(88,108)(89,135)(90,136)(91,133)(92,134)>;
G:=Group( (1,29,134)(2,135,30)(3,31,136)(4,133,32)(5,95,104)(6,101,96)(7,93,102)(8,103,94)(9,80,33)(10,34,77)(11,78,35)(12,36,79)(13,107,60)(14,57,108)(15,105,58)(16,59,106)(17,131,99)(18,100,132)(19,129,97)(20,98,130)(21,63,124)(22,121,64)(23,61,122)(24,123,62)(25,39,82)(26,83,40)(27,37,84)(28,81,38)(41,46,140)(42,137,47)(43,48,138)(44,139,45)(49,143,119)(50,120,144)(51,141,117)(52,118,142)(53,67,114)(54,115,68)(55,65,116)(56,113,66)(69,128,90)(70,91,125)(71,126,92)(72,89,127)(73,112,87)(74,88,109)(75,110,85)(76,86,111), (1,47,26)(2,27,48)(3,45,28)(4,25,46)(5,54,16)(6,13,55)(7,56,14)(8,15,53)(9,141,87)(10,88,142)(11,143,85)(12,86,144)(17,72,23)(18,24,69)(19,70,21)(20,22,71)(29,42,83)(30,84,43)(31,44,81)(32,82,41)(33,51,112)(34,109,52)(35,49,110)(36,111,50)(37,138,135)(38,136,139)(39,140,133)(40,134,137)(57,93,113)(58,114,94)(59,95,115)(60,116,96)(61,131,89)(62,90,132)(63,129,91)(64,92,130)(65,101,107)(66,108,102)(67,103,105)(68,106,104)(73,80,117)(74,118,77)(75,78,119)(76,120,79)(97,125,124)(98,121,126)(99,127,122)(100,123,128), (1,26,47)(2,48,27)(3,28,45)(4,46,25)(5,54,16)(6,13,55)(7,56,14)(8,15,53)(9,87,141)(10,142,88)(11,85,143)(12,144,86)(17,72,23)(18,24,69)(19,70,21)(20,22,71)(29,83,42)(30,43,84)(31,81,44)(32,41,82)(33,112,51)(34,52,109)(35,110,49)(36,50,111)(37,135,138)(38,139,136)(39,133,140)(40,137,134)(57,93,113)(58,114,94)(59,95,115)(60,116,96)(61,131,89)(62,90,132)(63,129,91)(64,92,130)(65,101,107)(66,108,102)(67,103,105)(68,106,104)(73,117,80)(74,77,118)(75,119,78)(76,79,120)(97,125,124)(98,121,126)(99,127,122)(100,123,128), (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), (1,57)(2,60)(3,59)(4,58)(5,139)(6,138)(7,137)(8,140)(9,21)(10,24)(11,23)(12,22)(13,135)(14,134)(15,133)(16,136)(17,143)(18,142)(19,141)(20,144)(25,114)(26,113)(27,116)(28,115)(29,108)(30,107)(31,106)(32,105)(33,124)(34,123)(35,122)(36,121)(37,55)(38,54)(39,53)(40,56)(41,103)(42,102)(43,101)(44,104)(45,95)(46,94)(47,93)(48,96)(49,99)(50,98)(51,97)(52,100)(61,78)(62,77)(63,80)(64,79)(65,84)(66,83)(67,82)(68,81)(69,88)(70,87)(71,86)(72,85)(73,91)(74,90)(75,89)(76,92)(109,128)(110,127)(111,126)(112,125)(117,129)(118,132)(119,131)(120,130), (1,126)(2,127)(3,128)(4,125)(5,79)(6,80)(7,77)(8,78)(9,101)(10,102)(11,103)(12,104)(13,73)(14,74)(15,75)(16,76)(17,84)(18,81)(19,82)(20,83)(21,41)(22,42)(23,43)(24,44)(25,97)(26,98)(27,99)(28,100)(29,71)(30,72)(31,69)(32,70)(33,96)(34,93)(35,94)(36,95)(37,131)(38,132)(39,129)(40,130)(45,123)(46,124)(47,121)(48,122)(49,114)(50,115)(51,116)(52,113)(53,119)(54,120)(55,117)(56,118)(57,109)(58,110)(59,111)(60,112)(61,138)(62,139)(63,140)(64,137)(65,141)(66,142)(67,143)(68,144)(85,105)(86,106)(87,107)(88,108)(89,135)(90,136)(91,133)(92,134) );
G=PermutationGroup([(1,29,134),(2,135,30),(3,31,136),(4,133,32),(5,95,104),(6,101,96),(7,93,102),(8,103,94),(9,80,33),(10,34,77),(11,78,35),(12,36,79),(13,107,60),(14,57,108),(15,105,58),(16,59,106),(17,131,99),(18,100,132),(19,129,97),(20,98,130),(21,63,124),(22,121,64),(23,61,122),(24,123,62),(25,39,82),(26,83,40),(27,37,84),(28,81,38),(41,46,140),(42,137,47),(43,48,138),(44,139,45),(49,143,119),(50,120,144),(51,141,117),(52,118,142),(53,67,114),(54,115,68),(55,65,116),(56,113,66),(69,128,90),(70,91,125),(71,126,92),(72,89,127),(73,112,87),(74,88,109),(75,110,85),(76,86,111)], [(1,47,26),(2,27,48),(3,45,28),(4,25,46),(5,54,16),(6,13,55),(7,56,14),(8,15,53),(9,141,87),(10,88,142),(11,143,85),(12,86,144),(17,72,23),(18,24,69),(19,70,21),(20,22,71),(29,42,83),(30,84,43),(31,44,81),(32,82,41),(33,51,112),(34,109,52),(35,49,110),(36,111,50),(37,138,135),(38,136,139),(39,140,133),(40,134,137),(57,93,113),(58,114,94),(59,95,115),(60,116,96),(61,131,89),(62,90,132),(63,129,91),(64,92,130),(65,101,107),(66,108,102),(67,103,105),(68,106,104),(73,80,117),(74,118,77),(75,78,119),(76,120,79),(97,125,124),(98,121,126),(99,127,122),(100,123,128)], [(1,26,47),(2,48,27),(3,28,45),(4,46,25),(5,54,16),(6,13,55),(7,56,14),(8,15,53),(9,87,141),(10,142,88),(11,85,143),(12,144,86),(17,72,23),(18,24,69),(19,70,21),(20,22,71),(29,83,42),(30,43,84),(31,81,44),(32,41,82),(33,112,51),(34,52,109),(35,110,49),(36,50,111),(37,135,138),(38,139,136),(39,133,140),(40,137,134),(57,93,113),(58,114,94),(59,95,115),(60,116,96),(61,131,89),(62,90,132),(63,129,91),(64,92,130),(65,101,107),(66,108,102),(67,103,105),(68,106,104),(73,117,80),(74,77,118),(75,119,78),(76,79,120),(97,125,124),(98,121,126),(99,127,122),(100,123,128)], [(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)], [(1,57),(2,60),(3,59),(4,58),(5,139),(6,138),(7,137),(8,140),(9,21),(10,24),(11,23),(12,22),(13,135),(14,134),(15,133),(16,136),(17,143),(18,142),(19,141),(20,144),(25,114),(26,113),(27,116),(28,115),(29,108),(30,107),(31,106),(32,105),(33,124),(34,123),(35,122),(36,121),(37,55),(38,54),(39,53),(40,56),(41,103),(42,102),(43,101),(44,104),(45,95),(46,94),(47,93),(48,96),(49,99),(50,98),(51,97),(52,100),(61,78),(62,77),(63,80),(64,79),(65,84),(66,83),(67,82),(68,81),(69,88),(70,87),(71,86),(72,85),(73,91),(74,90),(75,89),(76,92),(109,128),(110,127),(111,126),(112,125),(117,129),(118,132),(119,131),(120,130)], [(1,126),(2,127),(3,128),(4,125),(5,79),(6,80),(7,77),(8,78),(9,101),(10,102),(11,103),(12,104),(13,73),(14,74),(15,75),(16,76),(17,84),(18,81),(19,82),(20,83),(21,41),(22,42),(23,43),(24,44),(25,97),(26,98),(27,99),(28,100),(29,71),(30,72),(31,69),(32,70),(33,96),(34,93),(35,94),(36,95),(37,131),(38,132),(39,129),(40,130),(45,123),(46,124),(47,121),(48,122),(49,114),(50,115),(51,116),(52,113),(53,119),(54,120),(55,117),(56,118),(57,109),(58,110),(59,111),(60,112),(61,138),(62,139),(63,140),(64,137),(65,141),(66,142),(67,143),(68,144),(85,105),(86,106),(87,107),(88,108),(89,135),(90,136),(91,133),(92,134)])
63 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 4D | 4E | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | ··· | 6Q | 6R | 6S | 12A | ··· | 12H | 12I | ··· | 12Q | 12R | ··· | 12Y |
| order | 1 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 6 | 6 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 6 | 18 | 18 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 3 | 3 | 54 | 54 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 36 | 36 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 |
63 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | S3 | D6 | D6 | D6 | D6 | C4○D4 | C4○D12 | S32 | D4⋊2S3 | C2×S32 | D12⋊5S3 |
| kernel | C33⋊6D4⋊C2 | Dic3×C3⋊S3 | C33⋊6D4 | S3×C3×C12 | C3×C12⋊S3 | C33⋊8Q8 | S3×C12 | C12⋊S3 | C3×Dic3 | C3×C12 | S3×C6 | C2×C3⋊S3 | C33 | C32 | C12 | C32 | C6 | C3 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 4 | 1 | 4 | 5 | 4 | 2 | 2 | 16 | 4 | 1 | 4 | 8 |
Matrix representation of C33⋊6D4⋊C2 ►in GL8(𝔽13)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 12 | 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 |
| 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 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 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 | 12 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 12 |
| 3 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 2 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(8,GF(13))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[3,4,0,0,0,0,0,0,4,10,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[0,8,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[2,7,0,0,0,0,0,0,7,11,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1] >;
C33⋊6D4⋊C2 in GAP, Magma, Sage, TeX
C_3^3\rtimes_6D_4\rtimes C_2
% in TeX
G:=Group("C3^3:6D4:C2"); // GroupNames label
G:=SmallGroup(432,668);
// by ID
G=gap.SmallGroup(432,668);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,141,135,58,571,2028,14118]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^3=b^3=c^3=d^4=e^2=f^2=1,a*b=b*a,a*c=c*a,d*a*d^-1=f*a*f=a^-1,a*e=e*a,b*c=c*b,d*b*d^-1=f*b*f=b^-1,b*e=e*b,d*c*d^-1=e*c*e=c^-1,c*f=f*c,e*d*e=d^-1,d*f=f*d,f*e*f=d^2*e>;
// generators/relations