direct product, metabelian, supersoluble, monomial
Aliases: C32×Q8⋊3S3, C12.7C62, D6.3C62, Dic3.5C62, (S3×C12)⋊7C6, (C3×D12)⋊9C6, D12⋊4(C3×C6), C12.63(S3×C6), C6.8(C2×C62), C2.9(S3×C62), (Q8×C33)⋊5C2, Q8⋊4(S3×C32), (C3×C12).190D6, C33⋊33(C4○D4), (Q8×C32)⋊19S3, (Q8×C32)⋊15C6, (C32×D12)⋊15C2, (C32×C6).82C23, (C32×C12).53C22, (C32×Dic3).35C22, C4.7(S3×C3×C6), C6.80(S3×C2×C6), (C4×S3)⋊3(C3×C6), (S3×C3×C12)⋊11C2, (C3×Q8)⋊5(C3×C6), (C3×Q8)⋊9(C3×S3), C3⋊3(C32×C4○D4), (S3×C6).18(C2×C6), (C3×C12).57(C2×C6), C32⋊15(C3×C4○D4), (S3×C3×C6).32C22, (C3×C6).56(C22×C6), (C3×C6).201(C22×S3), (C3×Dic3).23(C2×C6), SmallGroup(432,707)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C32×Q8⋊3S3
G = < a,b,c,d,e,f | a3=b3=c4=e3=f2=1, d2=c2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, dcd-1=fcf=c-1, ce=ec, de=ed, df=fd, fef=e-1 >
Subgroups: 576 in 288 conjugacy classes, 138 normal (16 characteristic)
C1, C2, C2, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C2×C4, D4, Q8, C32, C32, C32, Dic3, C12, C12, D6, C2×C6, C4○D4, C3×S3, C3×C6, C3×C6, C3×C6, C4×S3, D12, C2×C12, C3×D4, C3×Q8, C3×Q8, C3×Q8, C33, C3×Dic3, C3×C12, C3×C12, S3×C6, C62, Q8⋊3S3, C3×C4○D4, S3×C32, C32×C6, S3×C12, C3×D12, C6×C12, D4×C32, Q8×C32, Q8×C32, Q8×C32, C32×Dic3, C32×C12, S3×C3×C6, C3×Q8⋊3S3, C32×C4○D4, S3×C3×C12, C32×D12, Q8×C33, C32×Q8⋊3S3
Quotients: C1, C2, C3, C22, S3, C6, C23, C32, D6, C2×C6, C4○D4, C3×S3, C3×C6, C22×S3, C22×C6, S3×C6, C62, Q8⋊3S3, C3×C4○D4, S3×C32, S3×C2×C6, C2×C62, S3×C3×C6, C3×Q8⋊3S3, C32×C4○D4, S3×C62, C32×Q8⋊3S3
►On 144 points
Generators in S144
(1 59 7)(2 60 8)(3 57 5)(4 58 6)(9 30 27)(10 31 28)(11 32 25)(12 29 26)(13 39 34)(14 40 35)(15 37 36)(16 38 33)(17 144 126)(18 141 127)(19 142 128)(20 143 125)(21 118 113)(22 119 114)(23 120 115)(24 117 116)(41 46 95)(42 47 96)(43 48 93)(44 45 94)(49 75 70)(50 76 71)(51 73 72)(52 74 69)(53 66 62)(54 67 63)(55 68 64)(56 65 61)(77 82 131)(78 83 132)(79 84 129)(80 81 130)(85 111 106)(86 112 107)(87 109 108)(88 110 105)(89 102 98)(90 103 99)(91 104 100)(92 101 97)(121 139 135)(122 140 136)(123 137 133)(124 138 134)
(1 29 14)(2 30 15)(3 31 16)(4 32 13)(5 10 33)(6 11 34)(7 12 35)(8 9 36)(17 22 139)(18 23 140)(19 24 137)(20 21 138)(25 39 58)(26 40 59)(27 37 60)(28 38 57)(41 64 71)(42 61 72)(43 62 69)(44 63 70)(45 54 49)(46 55 50)(47 56 51)(48 53 52)(65 73 96)(66 74 93)(67 75 94)(68 76 95)(77 100 107)(78 97 108)(79 98 105)(80 99 106)(81 90 85)(82 91 86)(83 92 87)(84 89 88)(101 109 132)(102 110 129)(103 111 130)(104 112 131)(113 124 125)(114 121 126)(115 122 127)(116 123 128)(117 133 142)(118 134 143)(119 135 144)(120 136 141)
(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 46 3 48)(2 45 4 47)(5 43 7 41)(6 42 8 44)(9 63 11 61)(10 62 12 64)(13 51 15 49)(14 50 16 52)(17 109 19 111)(18 112 20 110)(21 129 23 131)(22 132 24 130)(25 65 27 67)(26 68 28 66)(29 55 31 53)(30 54 32 56)(33 69 35 71)(34 72 36 70)(37 75 39 73)(38 74 40 76)(57 93 59 95)(58 96 60 94)(77 118 79 120)(78 117 80 119)(81 114 83 116)(82 113 84 115)(85 126 87 128)(86 125 88 127)(89 122 91 124)(90 121 92 123)(97 133 99 135)(98 136 100 134)(101 137 103 139)(102 140 104 138)(105 141 107 143)(106 144 108 142)
(1 14 29)(2 15 30)(3 16 31)(4 13 32)(5 33 10)(6 34 11)(7 35 12)(8 36 9)(17 22 139)(18 23 140)(19 24 137)(20 21 138)(25 58 39)(26 59 40)(27 60 37)(28 57 38)(41 71 64)(42 72 61)(43 69 62)(44 70 63)(45 49 54)(46 50 55)(47 51 56)(48 52 53)(65 96 73)(66 93 74)(67 94 75)(68 95 76)(77 100 107)(78 97 108)(79 98 105)(80 99 106)(81 90 85)(82 91 86)(83 92 87)(84 89 88)(101 109 132)(102 110 129)(103 111 130)(104 112 131)(113 124 125)(114 121 126)(115 122 127)(116 123 128)(117 133 142)(118 134 143)(119 135 144)(120 136 141)
(1 84)(2 83)(3 82)(4 81)(5 77)(6 80)(7 79)(8 78)(9 97)(10 100)(11 99)(12 98)(13 85)(14 88)(15 87)(16 86)(17 73)(18 76)(19 75)(20 74)(21 93)(22 96)(23 95)(24 94)(25 103)(26 102)(27 101)(28 104)(29 89)(30 92)(31 91)(32 90)(33 107)(34 106)(35 105)(36 108)(37 109)(38 112)(39 111)(40 110)(41 120)(42 119)(43 118)(44 117)(45 116)(46 115)(47 114)(48 113)(49 128)(50 127)(51 126)(52 125)(53 124)(54 123)(55 122)(56 121)(57 131)(58 130)(59 129)(60 132)(61 135)(62 134)(63 133)(64 136)(65 139)(66 138)(67 137)(68 140)(69 143)(70 142)(71 141)(72 144)
G:=sub<Sym(144)| (1,59,7)(2,60,8)(3,57,5)(4,58,6)(9,30,27)(10,31,28)(11,32,25)(12,29,26)(13,39,34)(14,40,35)(15,37,36)(16,38,33)(17,144,126)(18,141,127)(19,142,128)(20,143,125)(21,118,113)(22,119,114)(23,120,115)(24,117,116)(41,46,95)(42,47,96)(43,48,93)(44,45,94)(49,75,70)(50,76,71)(51,73,72)(52,74,69)(53,66,62)(54,67,63)(55,68,64)(56,65,61)(77,82,131)(78,83,132)(79,84,129)(80,81,130)(85,111,106)(86,112,107)(87,109,108)(88,110,105)(89,102,98)(90,103,99)(91,104,100)(92,101,97)(121,139,135)(122,140,136)(123,137,133)(124,138,134), (1,29,14)(2,30,15)(3,31,16)(4,32,13)(5,10,33)(6,11,34)(7,12,35)(8,9,36)(17,22,139)(18,23,140)(19,24,137)(20,21,138)(25,39,58)(26,40,59)(27,37,60)(28,38,57)(41,64,71)(42,61,72)(43,62,69)(44,63,70)(45,54,49)(46,55,50)(47,56,51)(48,53,52)(65,73,96)(66,74,93)(67,75,94)(68,76,95)(77,100,107)(78,97,108)(79,98,105)(80,99,106)(81,90,85)(82,91,86)(83,92,87)(84,89,88)(101,109,132)(102,110,129)(103,111,130)(104,112,131)(113,124,125)(114,121,126)(115,122,127)(116,123,128)(117,133,142)(118,134,143)(119,135,144)(120,136,141), (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), (1,46,3,48)(2,45,4,47)(5,43,7,41)(6,42,8,44)(9,63,11,61)(10,62,12,64)(13,51,15,49)(14,50,16,52)(17,109,19,111)(18,112,20,110)(21,129,23,131)(22,132,24,130)(25,65,27,67)(26,68,28,66)(29,55,31,53)(30,54,32,56)(33,69,35,71)(34,72,36,70)(37,75,39,73)(38,74,40,76)(57,93,59,95)(58,96,60,94)(77,118,79,120)(78,117,80,119)(81,114,83,116)(82,113,84,115)(85,126,87,128)(86,125,88,127)(89,122,91,124)(90,121,92,123)(97,133,99,135)(98,136,100,134)(101,137,103,139)(102,140,104,138)(105,141,107,143)(106,144,108,142), (1,14,29)(2,15,30)(3,16,31)(4,13,32)(5,33,10)(6,34,11)(7,35,12)(8,36,9)(17,22,139)(18,23,140)(19,24,137)(20,21,138)(25,58,39)(26,59,40)(27,60,37)(28,57,38)(41,71,64)(42,72,61)(43,69,62)(44,70,63)(45,49,54)(46,50,55)(47,51,56)(48,52,53)(65,96,73)(66,93,74)(67,94,75)(68,95,76)(77,100,107)(78,97,108)(79,98,105)(80,99,106)(81,90,85)(82,91,86)(83,92,87)(84,89,88)(101,109,132)(102,110,129)(103,111,130)(104,112,131)(113,124,125)(114,121,126)(115,122,127)(116,123,128)(117,133,142)(118,134,143)(119,135,144)(120,136,141), (1,84)(2,83)(3,82)(4,81)(5,77)(6,80)(7,79)(8,78)(9,97)(10,100)(11,99)(12,98)(13,85)(14,88)(15,87)(16,86)(17,73)(18,76)(19,75)(20,74)(21,93)(22,96)(23,95)(24,94)(25,103)(26,102)(27,101)(28,104)(29,89)(30,92)(31,91)(32,90)(33,107)(34,106)(35,105)(36,108)(37,109)(38,112)(39,111)(40,110)(41,120)(42,119)(43,118)(44,117)(45,116)(46,115)(47,114)(48,113)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,131)(58,130)(59,129)(60,132)(61,135)(62,134)(63,133)(64,136)(65,139)(66,138)(67,137)(68,140)(69,143)(70,142)(71,141)(72,144)>;
G:=Group( (1,59,7)(2,60,8)(3,57,5)(4,58,6)(9,30,27)(10,31,28)(11,32,25)(12,29,26)(13,39,34)(14,40,35)(15,37,36)(16,38,33)(17,144,126)(18,141,127)(19,142,128)(20,143,125)(21,118,113)(22,119,114)(23,120,115)(24,117,116)(41,46,95)(42,47,96)(43,48,93)(44,45,94)(49,75,70)(50,76,71)(51,73,72)(52,74,69)(53,66,62)(54,67,63)(55,68,64)(56,65,61)(77,82,131)(78,83,132)(79,84,129)(80,81,130)(85,111,106)(86,112,107)(87,109,108)(88,110,105)(89,102,98)(90,103,99)(91,104,100)(92,101,97)(121,139,135)(122,140,136)(123,137,133)(124,138,134), (1,29,14)(2,30,15)(3,31,16)(4,32,13)(5,10,33)(6,11,34)(7,12,35)(8,9,36)(17,22,139)(18,23,140)(19,24,137)(20,21,138)(25,39,58)(26,40,59)(27,37,60)(28,38,57)(41,64,71)(42,61,72)(43,62,69)(44,63,70)(45,54,49)(46,55,50)(47,56,51)(48,53,52)(65,73,96)(66,74,93)(67,75,94)(68,76,95)(77,100,107)(78,97,108)(79,98,105)(80,99,106)(81,90,85)(82,91,86)(83,92,87)(84,89,88)(101,109,132)(102,110,129)(103,111,130)(104,112,131)(113,124,125)(114,121,126)(115,122,127)(116,123,128)(117,133,142)(118,134,143)(119,135,144)(120,136,141), (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), (1,46,3,48)(2,45,4,47)(5,43,7,41)(6,42,8,44)(9,63,11,61)(10,62,12,64)(13,51,15,49)(14,50,16,52)(17,109,19,111)(18,112,20,110)(21,129,23,131)(22,132,24,130)(25,65,27,67)(26,68,28,66)(29,55,31,53)(30,54,32,56)(33,69,35,71)(34,72,36,70)(37,75,39,73)(38,74,40,76)(57,93,59,95)(58,96,60,94)(77,118,79,120)(78,117,80,119)(81,114,83,116)(82,113,84,115)(85,126,87,128)(86,125,88,127)(89,122,91,124)(90,121,92,123)(97,133,99,135)(98,136,100,134)(101,137,103,139)(102,140,104,138)(105,141,107,143)(106,144,108,142), (1,14,29)(2,15,30)(3,16,31)(4,13,32)(5,33,10)(6,34,11)(7,35,12)(8,36,9)(17,22,139)(18,23,140)(19,24,137)(20,21,138)(25,58,39)(26,59,40)(27,60,37)(28,57,38)(41,71,64)(42,72,61)(43,69,62)(44,70,63)(45,49,54)(46,50,55)(47,51,56)(48,52,53)(65,96,73)(66,93,74)(67,94,75)(68,95,76)(77,100,107)(78,97,108)(79,98,105)(80,99,106)(81,90,85)(82,91,86)(83,92,87)(84,89,88)(101,109,132)(102,110,129)(103,111,130)(104,112,131)(113,124,125)(114,121,126)(115,122,127)(116,123,128)(117,133,142)(118,134,143)(119,135,144)(120,136,141), (1,84)(2,83)(3,82)(4,81)(5,77)(6,80)(7,79)(8,78)(9,97)(10,100)(11,99)(12,98)(13,85)(14,88)(15,87)(16,86)(17,73)(18,76)(19,75)(20,74)(21,93)(22,96)(23,95)(24,94)(25,103)(26,102)(27,101)(28,104)(29,89)(30,92)(31,91)(32,90)(33,107)(34,106)(35,105)(36,108)(37,109)(38,112)(39,111)(40,110)(41,120)(42,119)(43,118)(44,117)(45,116)(46,115)(47,114)(48,113)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,131)(58,130)(59,129)(60,132)(61,135)(62,134)(63,133)(64,136)(65,139)(66,138)(67,137)(68,140)(69,143)(70,142)(71,141)(72,144) );
G=PermutationGroup([[(1,59,7),(2,60,8),(3,57,5),(4,58,6),(9,30,27),(10,31,28),(11,32,25),(12,29,26),(13,39,34),(14,40,35),(15,37,36),(16,38,33),(17,144,126),(18,141,127),(19,142,128),(20,143,125),(21,118,113),(22,119,114),(23,120,115),(24,117,116),(41,46,95),(42,47,96),(43,48,93),(44,45,94),(49,75,70),(50,76,71),(51,73,72),(52,74,69),(53,66,62),(54,67,63),(55,68,64),(56,65,61),(77,82,131),(78,83,132),(79,84,129),(80,81,130),(85,111,106),(86,112,107),(87,109,108),(88,110,105),(89,102,98),(90,103,99),(91,104,100),(92,101,97),(121,139,135),(122,140,136),(123,137,133),(124,138,134)], [(1,29,14),(2,30,15),(3,31,16),(4,32,13),(5,10,33),(6,11,34),(7,12,35),(8,9,36),(17,22,139),(18,23,140),(19,24,137),(20,21,138),(25,39,58),(26,40,59),(27,37,60),(28,38,57),(41,64,71),(42,61,72),(43,62,69),(44,63,70),(45,54,49),(46,55,50),(47,56,51),(48,53,52),(65,73,96),(66,74,93),(67,75,94),(68,76,95),(77,100,107),(78,97,108),(79,98,105),(80,99,106),(81,90,85),(82,91,86),(83,92,87),(84,89,88),(101,109,132),(102,110,129),(103,111,130),(104,112,131),(113,124,125),(114,121,126),(115,122,127),(116,123,128),(117,133,142),(118,134,143),(119,135,144),(120,136,141)], [(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)], [(1,46,3,48),(2,45,4,47),(5,43,7,41),(6,42,8,44),(9,63,11,61),(10,62,12,64),(13,51,15,49),(14,50,16,52),(17,109,19,111),(18,112,20,110),(21,129,23,131),(22,132,24,130),(25,65,27,67),(26,68,28,66),(29,55,31,53),(30,54,32,56),(33,69,35,71),(34,72,36,70),(37,75,39,73),(38,74,40,76),(57,93,59,95),(58,96,60,94),(77,118,79,120),(78,117,80,119),(81,114,83,116),(82,113,84,115),(85,126,87,128),(86,125,88,127),(89,122,91,124),(90,121,92,123),(97,133,99,135),(98,136,100,134),(101,137,103,139),(102,140,104,138),(105,141,107,143),(106,144,108,142)], [(1,14,29),(2,15,30),(3,16,31),(4,13,32),(5,33,10),(6,34,11),(7,35,12),(8,36,9),(17,22,139),(18,23,140),(19,24,137),(20,21,138),(25,58,39),(26,59,40),(27,60,37),(28,57,38),(41,71,64),(42,72,61),(43,69,62),(44,70,63),(45,49,54),(46,50,55),(47,51,56),(48,52,53),(65,96,73),(66,93,74),(67,94,75),(68,95,76),(77,100,107),(78,97,108),(79,98,105),(80,99,106),(81,90,85),(82,91,86),(83,92,87),(84,89,88),(101,109,132),(102,110,129),(103,111,130),(104,112,131),(113,124,125),(114,121,126),(115,122,127),(116,123,128),(117,133,142),(118,134,143),(119,135,144),(120,136,141)], [(1,84),(2,83),(3,82),(4,81),(5,77),(6,80),(7,79),(8,78),(9,97),(10,100),(11,99),(12,98),(13,85),(14,88),(15,87),(16,86),(17,73),(18,76),(19,75),(20,74),(21,93),(22,96),(23,95),(24,94),(25,103),(26,102),(27,101),(28,104),(29,89),(30,92),(31,91),(32,90),(33,107),(34,106),(35,105),(36,108),(37,109),(38,112),(39,111),(40,110),(41,120),(42,119),(43,118),(44,117),(45,116),(46,115),(47,114),(48,113),(49,128),(50,127),(51,126),(52,125),(53,124),(54,123),(55,122),(56,121),(57,131),(58,130),(59,129),(60,132),(61,135),(62,134),(63,133),(64,136),(65,139),(66,138),(67,137),(68,140),(69,143),(70,142),(71,141),(72,144)]])
135 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | ··· | 3H | 3I | ··· | 3Q | 4A | 4B | 4C | 4D | 4E | 6A | ··· | 6H | 6I | ··· | 6Q | 6R | ··· | 6AO | 12A | ··· | 12X | 12Y | ··· | 12AN | 12AO | ··· | 12BO |
| order | 1 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 3 | ··· | 3 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | ··· | 6 | 6 | ··· | 6 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 6 | 6 | 6 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 3 | 3 | 1 | ··· | 1 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 3 | ··· | 3 | 4 | ··· | 4 |
135 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | S3 | D6 | C4○D4 | C3×S3 | S3×C6 | C3×C4○D4 | Q8⋊3S3 | C3×Q8⋊3S3 |
| kernel | C32×Q8⋊3S3 | S3×C3×C12 | C32×D12 | Q8×C33 | C3×Q8⋊3S3 | S3×C12 | C3×D12 | Q8×C32 | Q8×C32 | C3×C12 | C33 | C3×Q8 | C12 | C32 | C32 | C3 |
| # reps | 1 | 3 | 3 | 1 | 8 | 24 | 24 | 8 | 1 | 3 | 2 | 8 | 24 | 16 | 1 | 8 |
Matrix representation of C32×Q8⋊3S3 ►in GL4(𝔽13) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 9 |
| 3 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 5 |
| 0 | 0 | 10 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 6 |
| 0 | 0 | 4 | 12 |
| 9 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 5 | 4 |
| 0 | 0 | 7 | 8 |
G:=sub<GL(4,GF(13))| [1,0,0,0,0,1,0,0,0,0,9,0,0,0,0,9],[3,0,0,0,0,3,0,0,0,0,1,0,0,0,0,1],[12,0,0,0,0,12,0,0,0,0,12,10,0,0,5,1],[1,0,0,0,0,1,0,0,0,0,1,4,0,0,6,12],[9,0,0,0,0,3,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,0,5,7,0,0,4,8] >;
C32×Q8⋊3S3 in GAP, Magma, Sage, TeX
C_3^2\times Q_8\rtimes_3S_3
% in TeX
G:=Group("C3^2xQ8:3S3"); // GroupNames label
G:=SmallGroup(432,707);
// by ID
G=gap.SmallGroup(432,707);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-3,-2,-3,512,1598,807,394,14118]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^3=b^3=c^4=e^3=f^2=1,d^2=c^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,b*e=e*b,b*f=f*b,d*c*d^-1=f*c*f=c^-1,c*e=e*c,d*e=e*d,d*f=f*d,f*e*f=e^-1>;
// generators/relations