direct product, metabelian, supersoluble, monomial
Aliases: C2×C33⋊4Q8, C62.116D6, (C3×C6)⋊5Dic6, (C32×C6)⋊4Q8, C33⋊14(C2×Q8), C6⋊1(C32⋊2Q8), C3⋊Dic3.46D6, C6⋊1(C32⋊4Q8), (C6×Dic3).12S3, (C3×Dic3).36D6, C32⋊10(C2×Dic6), (C3×C62).32C22, (C32×C6).61C23, C33⋊5C4.18C22, (C32×Dic3).23C22, C6.71(C2×S32), (C2×C6).45S32, C3⋊2(C2×C32⋊2Q8), (Dic3×C3×C6).8C2, C3⋊2(C2×C32⋊4Q8), C22.17(S3×C3⋊S3), C6.24(C22×C3⋊S3), (C6×C3⋊Dic3).9C2, Dic3.10(C2×C3⋊S3), (C2×C3⋊Dic3).12S3, (C2×C33⋊5C4).7C2, (C2×Dic3).4(C3⋊S3), (C3×C6).150(C22×S3), (C3×C3⋊Dic3).45C22, C2.24(C2×S3×C3⋊S3), (C2×C6).26(C2×C3⋊S3), SmallGroup(432,683)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C33⋊4Q8
G = < a,b,c,d,e,f | a2=b3=c3=d3=e4=1, f2=e2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, ebe-1=b-1, bf=fb, cd=dc, ece-1=c-1, cf=fc, de=ed, fdf-1=d-1, fef-1=e-1 >
Subgroups: 1336 in 292 conjugacy classes, 92 normal (18 characteristic)
C1, C2, C2, C3, C3, C3, C4, C22, C6, C6, C6, C2×C4, Q8, C32, C32, C32, Dic3, Dic3, C12, C2×C6, C2×C6, C2×C6, C2×Q8, C3×C6, C3×C6, C3×C6, Dic6, C2×Dic3, C2×Dic3, C2×C12, C33, C3×Dic3, C3×Dic3, C3⋊Dic3, C3⋊Dic3, C3×C12, C62, C62, C62, C2×Dic6, C32×C6, C32×C6, C32⋊2Q8, C6×Dic3, C6×Dic3, C32⋊4Q8, C2×C3⋊Dic3, C2×C3⋊Dic3, C6×C12, C32×Dic3, C3×C3⋊Dic3, C33⋊5C4, C3×C62, C2×C32⋊2Q8, C2×C32⋊4Q8, C33⋊4Q8, Dic3×C3×C6, C6×C3⋊Dic3, C2×C33⋊5C4, C2×C33⋊4Q8
Quotients: C1, C2, C22, S3, Q8, C23, D6, C2×Q8, C3⋊S3, Dic6, C22×S3, S32, C2×C3⋊S3, C2×Dic6, C32⋊2Q8, C32⋊4Q8, C2×S32, C22×C3⋊S3, S3×C3⋊S3, C2×C32⋊2Q8, C2×C32⋊4Q8, C33⋊4Q8, C2×S3×C3⋊S3, C2×C33⋊4Q8
►On 144 points
Generators in S144
(1 83)(2 84)(3 81)(4 82)(5 73)(6 74)(7 75)(8 76)(9 130)(10 131)(11 132)(12 129)(13 35)(14 36)(15 33)(16 34)(17 109)(18 110)(19 111)(20 112)(21 25)(22 26)(23 27)(24 28)(29 58)(30 59)(31 60)(32 57)(37 86)(38 87)(39 88)(40 85)(41 61)(42 62)(43 63)(44 64)(45 80)(46 77)(47 78)(48 79)(49 71)(50 72)(51 69)(52 70)(53 66)(54 67)(55 68)(56 65)(89 108)(90 105)(91 106)(92 107)(93 124)(94 121)(95 122)(96 123)(97 125)(98 126)(99 127)(100 128)(101 134)(102 135)(103 136)(104 133)(113 143)(114 144)(115 141)(116 142)(117 137)(118 138)(119 139)(120 140)
(1 65 51)(2 52 66)(3 67 49)(4 50 68)(5 14 32)(6 29 15)(7 16 30)(8 31 13)(9 92 101)(10 102 89)(11 90 103)(12 104 91)(17 61 25)(18 26 62)(19 63 27)(20 28 64)(21 109 41)(22 42 110)(23 111 43)(24 44 112)(33 74 58)(34 59 75)(35 76 60)(36 57 73)(37 142 118)(38 119 143)(39 144 120)(40 117 141)(45 123 100)(46 97 124)(47 121 98)(48 99 122)(53 84 70)(54 71 81)(55 82 72)(56 69 83)(77 125 93)(78 94 126)(79 127 95)(80 96 128)(85 137 115)(86 116 138)(87 139 113)(88 114 140)(105 136 132)(106 129 133)(107 134 130)(108 131 135)
(1 62 29)(2 30 63)(3 64 31)(4 32 61)(5 25 50)(6 51 26)(7 27 52)(8 49 28)(9 100 117)(10 118 97)(11 98 119)(12 120 99)(13 67 20)(14 17 68)(15 65 18)(16 19 66)(21 72 73)(22 74 69)(23 70 75)(24 76 71)(33 56 110)(34 111 53)(35 54 112)(36 109 55)(37 124 102)(38 103 121)(39 122 104)(40 101 123)(41 82 57)(42 58 83)(43 84 59)(44 60 81)(45 141 92)(46 89 142)(47 143 90)(48 91 144)(77 108 116)(78 113 105)(79 106 114)(80 115 107)(85 134 96)(86 93 135)(87 136 94)(88 95 133)(125 131 138)(126 139 132)(127 129 140)(128 137 130)
(1 26 15)(2 27 16)(3 28 13)(4 25 14)(5 68 61)(6 65 62)(7 66 63)(8 67 64)(9 141 123)(10 142 124)(11 143 121)(12 144 122)(17 32 50)(18 29 51)(19 30 52)(20 31 49)(21 36 82)(22 33 83)(23 34 84)(24 35 81)(37 97 89)(38 98 90)(39 99 91)(40 100 92)(41 73 55)(42 74 56)(43 75 53)(44 76 54)(45 101 117)(46 102 118)(47 103 119)(48 104 120)(57 72 109)(58 69 110)(59 70 111)(60 71 112)(77 135 138)(78 136 139)(79 133 140)(80 134 137)(85 128 107)(86 125 108)(87 126 105)(88 127 106)(93 131 116)(94 132 113)(95 129 114)(96 130 115)
(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 85 3 87)(2 88 4 86)(5 77 7 79)(6 80 8 78)(9 112 11 110)(10 111 12 109)(13 126 15 128)(14 125 16 127)(17 131 19 129)(18 130 20 132)(21 89 23 91)(22 92 24 90)(25 108 27 106)(26 107 28 105)(29 96 31 94)(30 95 32 93)(33 100 35 98)(34 99 36 97)(37 84 39 82)(38 83 40 81)(41 102 43 104)(42 101 44 103)(45 76 47 74)(46 75 48 73)(49 113 51 115)(50 116 52 114)(53 120 55 118)(54 119 56 117)(57 124 59 122)(58 123 60 121)(61 135 63 133)(62 134 64 136)(65 137 67 139)(66 140 68 138)(69 141 71 143)(70 144 72 142)
G:=sub<Sym(144)| (1,83)(2,84)(3,81)(4,82)(5,73)(6,74)(7,75)(8,76)(9,130)(10,131)(11,132)(12,129)(13,35)(14,36)(15,33)(16,34)(17,109)(18,110)(19,111)(20,112)(21,25)(22,26)(23,27)(24,28)(29,58)(30,59)(31,60)(32,57)(37,86)(38,87)(39,88)(40,85)(41,61)(42,62)(43,63)(44,64)(45,80)(46,77)(47,78)(48,79)(49,71)(50,72)(51,69)(52,70)(53,66)(54,67)(55,68)(56,65)(89,108)(90,105)(91,106)(92,107)(93,124)(94,121)(95,122)(96,123)(97,125)(98,126)(99,127)(100,128)(101,134)(102,135)(103,136)(104,133)(113,143)(114,144)(115,141)(116,142)(117,137)(118,138)(119,139)(120,140), (1,65,51)(2,52,66)(3,67,49)(4,50,68)(5,14,32)(6,29,15)(7,16,30)(8,31,13)(9,92,101)(10,102,89)(11,90,103)(12,104,91)(17,61,25)(18,26,62)(19,63,27)(20,28,64)(21,109,41)(22,42,110)(23,111,43)(24,44,112)(33,74,58)(34,59,75)(35,76,60)(36,57,73)(37,142,118)(38,119,143)(39,144,120)(40,117,141)(45,123,100)(46,97,124)(47,121,98)(48,99,122)(53,84,70)(54,71,81)(55,82,72)(56,69,83)(77,125,93)(78,94,126)(79,127,95)(80,96,128)(85,137,115)(86,116,138)(87,139,113)(88,114,140)(105,136,132)(106,129,133)(107,134,130)(108,131,135), (1,62,29)(2,30,63)(3,64,31)(4,32,61)(5,25,50)(6,51,26)(7,27,52)(8,49,28)(9,100,117)(10,118,97)(11,98,119)(12,120,99)(13,67,20)(14,17,68)(15,65,18)(16,19,66)(21,72,73)(22,74,69)(23,70,75)(24,76,71)(33,56,110)(34,111,53)(35,54,112)(36,109,55)(37,124,102)(38,103,121)(39,122,104)(40,101,123)(41,82,57)(42,58,83)(43,84,59)(44,60,81)(45,141,92)(46,89,142)(47,143,90)(48,91,144)(77,108,116)(78,113,105)(79,106,114)(80,115,107)(85,134,96)(86,93,135)(87,136,94)(88,95,133)(125,131,138)(126,139,132)(127,129,140)(128,137,130), (1,26,15)(2,27,16)(3,28,13)(4,25,14)(5,68,61)(6,65,62)(7,66,63)(8,67,64)(9,141,123)(10,142,124)(11,143,121)(12,144,122)(17,32,50)(18,29,51)(19,30,52)(20,31,49)(21,36,82)(22,33,83)(23,34,84)(24,35,81)(37,97,89)(38,98,90)(39,99,91)(40,100,92)(41,73,55)(42,74,56)(43,75,53)(44,76,54)(45,101,117)(46,102,118)(47,103,119)(48,104,120)(57,72,109)(58,69,110)(59,70,111)(60,71,112)(77,135,138)(78,136,139)(79,133,140)(80,134,137)(85,128,107)(86,125,108)(87,126,105)(88,127,106)(93,131,116)(94,132,113)(95,129,114)(96,130,115), (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), (1,85,3,87)(2,88,4,86)(5,77,7,79)(6,80,8,78)(9,112,11,110)(10,111,12,109)(13,126,15,128)(14,125,16,127)(17,131,19,129)(18,130,20,132)(21,89,23,91)(22,92,24,90)(25,108,27,106)(26,107,28,105)(29,96,31,94)(30,95,32,93)(33,100,35,98)(34,99,36,97)(37,84,39,82)(38,83,40,81)(41,102,43,104)(42,101,44,103)(45,76,47,74)(46,75,48,73)(49,113,51,115)(50,116,52,114)(53,120,55,118)(54,119,56,117)(57,124,59,122)(58,123,60,121)(61,135,63,133)(62,134,64,136)(65,137,67,139)(66,140,68,138)(69,141,71,143)(70,144,72,142)>;
G:=Group( (1,83)(2,84)(3,81)(4,82)(5,73)(6,74)(7,75)(8,76)(9,130)(10,131)(11,132)(12,129)(13,35)(14,36)(15,33)(16,34)(17,109)(18,110)(19,111)(20,112)(21,25)(22,26)(23,27)(24,28)(29,58)(30,59)(31,60)(32,57)(37,86)(38,87)(39,88)(40,85)(41,61)(42,62)(43,63)(44,64)(45,80)(46,77)(47,78)(48,79)(49,71)(50,72)(51,69)(52,70)(53,66)(54,67)(55,68)(56,65)(89,108)(90,105)(91,106)(92,107)(93,124)(94,121)(95,122)(96,123)(97,125)(98,126)(99,127)(100,128)(101,134)(102,135)(103,136)(104,133)(113,143)(114,144)(115,141)(116,142)(117,137)(118,138)(119,139)(120,140), (1,65,51)(2,52,66)(3,67,49)(4,50,68)(5,14,32)(6,29,15)(7,16,30)(8,31,13)(9,92,101)(10,102,89)(11,90,103)(12,104,91)(17,61,25)(18,26,62)(19,63,27)(20,28,64)(21,109,41)(22,42,110)(23,111,43)(24,44,112)(33,74,58)(34,59,75)(35,76,60)(36,57,73)(37,142,118)(38,119,143)(39,144,120)(40,117,141)(45,123,100)(46,97,124)(47,121,98)(48,99,122)(53,84,70)(54,71,81)(55,82,72)(56,69,83)(77,125,93)(78,94,126)(79,127,95)(80,96,128)(85,137,115)(86,116,138)(87,139,113)(88,114,140)(105,136,132)(106,129,133)(107,134,130)(108,131,135), (1,62,29)(2,30,63)(3,64,31)(4,32,61)(5,25,50)(6,51,26)(7,27,52)(8,49,28)(9,100,117)(10,118,97)(11,98,119)(12,120,99)(13,67,20)(14,17,68)(15,65,18)(16,19,66)(21,72,73)(22,74,69)(23,70,75)(24,76,71)(33,56,110)(34,111,53)(35,54,112)(36,109,55)(37,124,102)(38,103,121)(39,122,104)(40,101,123)(41,82,57)(42,58,83)(43,84,59)(44,60,81)(45,141,92)(46,89,142)(47,143,90)(48,91,144)(77,108,116)(78,113,105)(79,106,114)(80,115,107)(85,134,96)(86,93,135)(87,136,94)(88,95,133)(125,131,138)(126,139,132)(127,129,140)(128,137,130), (1,26,15)(2,27,16)(3,28,13)(4,25,14)(5,68,61)(6,65,62)(7,66,63)(8,67,64)(9,141,123)(10,142,124)(11,143,121)(12,144,122)(17,32,50)(18,29,51)(19,30,52)(20,31,49)(21,36,82)(22,33,83)(23,34,84)(24,35,81)(37,97,89)(38,98,90)(39,99,91)(40,100,92)(41,73,55)(42,74,56)(43,75,53)(44,76,54)(45,101,117)(46,102,118)(47,103,119)(48,104,120)(57,72,109)(58,69,110)(59,70,111)(60,71,112)(77,135,138)(78,136,139)(79,133,140)(80,134,137)(85,128,107)(86,125,108)(87,126,105)(88,127,106)(93,131,116)(94,132,113)(95,129,114)(96,130,115), (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), (1,85,3,87)(2,88,4,86)(5,77,7,79)(6,80,8,78)(9,112,11,110)(10,111,12,109)(13,126,15,128)(14,125,16,127)(17,131,19,129)(18,130,20,132)(21,89,23,91)(22,92,24,90)(25,108,27,106)(26,107,28,105)(29,96,31,94)(30,95,32,93)(33,100,35,98)(34,99,36,97)(37,84,39,82)(38,83,40,81)(41,102,43,104)(42,101,44,103)(45,76,47,74)(46,75,48,73)(49,113,51,115)(50,116,52,114)(53,120,55,118)(54,119,56,117)(57,124,59,122)(58,123,60,121)(61,135,63,133)(62,134,64,136)(65,137,67,139)(66,140,68,138)(69,141,71,143)(70,144,72,142) );
G=PermutationGroup([[(1,83),(2,84),(3,81),(4,82),(5,73),(6,74),(7,75),(8,76),(9,130),(10,131),(11,132),(12,129),(13,35),(14,36),(15,33),(16,34),(17,109),(18,110),(19,111),(20,112),(21,25),(22,26),(23,27),(24,28),(29,58),(30,59),(31,60),(32,57),(37,86),(38,87),(39,88),(40,85),(41,61),(42,62),(43,63),(44,64),(45,80),(46,77),(47,78),(48,79),(49,71),(50,72),(51,69),(52,70),(53,66),(54,67),(55,68),(56,65),(89,108),(90,105),(91,106),(92,107),(93,124),(94,121),(95,122),(96,123),(97,125),(98,126),(99,127),(100,128),(101,134),(102,135),(103,136),(104,133),(113,143),(114,144),(115,141),(116,142),(117,137),(118,138),(119,139),(120,140)], [(1,65,51),(2,52,66),(3,67,49),(4,50,68),(5,14,32),(6,29,15),(7,16,30),(8,31,13),(9,92,101),(10,102,89),(11,90,103),(12,104,91),(17,61,25),(18,26,62),(19,63,27),(20,28,64),(21,109,41),(22,42,110),(23,111,43),(24,44,112),(33,74,58),(34,59,75),(35,76,60),(36,57,73),(37,142,118),(38,119,143),(39,144,120),(40,117,141),(45,123,100),(46,97,124),(47,121,98),(48,99,122),(53,84,70),(54,71,81),(55,82,72),(56,69,83),(77,125,93),(78,94,126),(79,127,95),(80,96,128),(85,137,115),(86,116,138),(87,139,113),(88,114,140),(105,136,132),(106,129,133),(107,134,130),(108,131,135)], [(1,62,29),(2,30,63),(3,64,31),(4,32,61),(5,25,50),(6,51,26),(7,27,52),(8,49,28),(9,100,117),(10,118,97),(11,98,119),(12,120,99),(13,67,20),(14,17,68),(15,65,18),(16,19,66),(21,72,73),(22,74,69),(23,70,75),(24,76,71),(33,56,110),(34,111,53),(35,54,112),(36,109,55),(37,124,102),(38,103,121),(39,122,104),(40,101,123),(41,82,57),(42,58,83),(43,84,59),(44,60,81),(45,141,92),(46,89,142),(47,143,90),(48,91,144),(77,108,116),(78,113,105),(79,106,114),(80,115,107),(85,134,96),(86,93,135),(87,136,94),(88,95,133),(125,131,138),(126,139,132),(127,129,140),(128,137,130)], [(1,26,15),(2,27,16),(3,28,13),(4,25,14),(5,68,61),(6,65,62),(7,66,63),(8,67,64),(9,141,123),(10,142,124),(11,143,121),(12,144,122),(17,32,50),(18,29,51),(19,30,52),(20,31,49),(21,36,82),(22,33,83),(23,34,84),(24,35,81),(37,97,89),(38,98,90),(39,99,91),(40,100,92),(41,73,55),(42,74,56),(43,75,53),(44,76,54),(45,101,117),(46,102,118),(47,103,119),(48,104,120),(57,72,109),(58,69,110),(59,70,111),(60,71,112),(77,135,138),(78,136,139),(79,133,140),(80,134,137),(85,128,107),(86,125,108),(87,126,105),(88,127,106),(93,131,116),(94,132,113),(95,129,114),(96,130,115)], [(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)], [(1,85,3,87),(2,88,4,86),(5,77,7,79),(6,80,8,78),(9,112,11,110),(10,111,12,109),(13,126,15,128),(14,125,16,127),(17,131,19,129),(18,130,20,132),(21,89,23,91),(22,92,24,90),(25,108,27,106),(26,107,28,105),(29,96,31,94),(30,95,32,93),(33,100,35,98),(34,99,36,97),(37,84,39,82),(38,83,40,81),(41,102,43,104),(42,101,44,103),(45,76,47,74),(46,75,48,73),(49,113,51,115),(50,116,52,114),(53,120,55,118),(54,119,56,117),(57,124,59,122),(58,123,60,121),(61,135,63,133),(62,134,64,136),(65,137,67,139),(66,140,68,138),(69,141,71,143),(70,144,72,142)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 4D | 4E | 4F | 6A | ··· | 6O | 6P | ··· | 6AA | 12A | ··· | 12P | 12Q | 12R | 12S | 12T |
| order | 1 | 2 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | ··· | 6 | 12 | ··· | 12 | 12 | 12 | 12 | 12 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | 6 | 18 | 18 | 54 | 54 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 | 18 | 18 | 18 | 18 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | + | - | + |
| image | C1 | C2 | C2 | C2 | C2 | S3 | S3 | Q8 | D6 | D6 | D6 | Dic6 | S32 | C32⋊2Q8 | C2×S32 |
| kernel | C2×C33⋊4Q8 | C33⋊4Q8 | Dic3×C3×C6 | C6×C3⋊Dic3 | C2×C33⋊5C4 | C6×Dic3 | C2×C3⋊Dic3 | C32×C6 | C3×Dic3 | C3⋊Dic3 | C62 | C3×C6 | C2×C6 | C6 | C6 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 1 | 2 | 8 | 2 | 5 | 20 | 4 | 8 | 4 |
Matrix representation of C2×C33⋊4Q8 ►in GL8(𝔽13)
| 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 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 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 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 12 | 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 | 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 | 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 |
| 4 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 10 | 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 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 8 | 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 |
G:=sub<GL(8,GF(13))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[4,2,0,0,0,0,0,0,11,9,0,0,0,0,0,0,0,0,3,7,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[5,7,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
C2×C33⋊4Q8 in GAP, Magma, Sage, TeX
C_2\times C_3^3\rtimes_4Q_8
% in TeX
G:=Group("C2xC3^3:4Q8"); // GroupNames label
G:=SmallGroup(432,683);
// by ID
G=gap.SmallGroup(432,683);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,141,64,571,2028,14118]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=d^3=e^4=1,f^2=e^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,b*f=f*b,c*d=d*c,e*c*e^-1=c^-1,c*f=f*c,d*e=e*d,f*d*f^-1=d^-1,f*e*f^-1=e^-1>;
// generators/relations