direct product, metabelian, supersoluble, monomial
Aliases: C32×Q8⋊2S3, C12.3C62, C33⋊25SD16, C12.59(S3×C6), D12.2(C3×C6), (C3×D12).7C6, (Q8×C33)⋊1C2, Q8⋊3(S3×C32), C6.9(D4×C32), (C3×C12).186D6, (Q8×C32)⋊18S3, (Q8×C32)⋊12C6, C3⋊3(C32×SD16), (C32×C6).68D4, (C32×D12).5C2, C32⋊14(C3×SD16), (C32×C12).25C22, C3⋊C8⋊3(C3×C6), C4.3(S3×C3×C6), (C3×C3⋊C8)⋊10C6, (C3×Q8)⋊8(C3×S3), (C3×Q8)⋊3(C3×C6), (C32×C3⋊C8)⋊17C2, (C3×C6).64(C3×D4), C6.55(C3×C3⋊D4), (C3×C12).44(C2×C6), C2.6(C32×C3⋊D4), (C3×C6).124(C3⋊D4), SmallGroup(432,477)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C32×Q8⋊2S3
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, fdf=c-1d, fef=e-1 >
Subgroups: 384 in 168 conjugacy classes, 66 normal (22 characteristic)
C1, C2, C2, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C8, D4, Q8, C32, C32, C32, C12, C12, C12, D6, C2×C6, SD16, C3×S3, C3×C6, C3×C6, C3×C6, C3⋊C8, C24, D12, C3×D4, C3×Q8, C3×Q8, C3×Q8, C33, C3×C12, C3×C12, C3×C12, S3×C6, C62, Q8⋊2S3, C3×SD16, S3×C32, C32×C6, C3×C3⋊C8, C3×C24, C3×D12, D4×C32, Q8×C32, Q8×C32, Q8×C32, C32×C12, C32×C12, S3×C3×C6, C3×Q8⋊2S3, C32×SD16, C32×C3⋊C8, C32×D12, Q8×C33, C32×Q8⋊2S3
Quotients: C1, C2, C3, C22, S3, C6, D4, C32, D6, C2×C6, SD16, C3×S3, C3×C6, C3⋊D4, C3×D4, S3×C6, C62, Q8⋊2S3, C3×SD16, S3×C32, C3×C3⋊D4, D4×C32, S3×C3×C6, C3×Q8⋊2S3, C32×SD16, C32×C3⋊D4, C32×Q8⋊2S3
►On 144 points
Generators in S144
(1 38 28)(2 39 25)(3 40 26)(4 37 27)(5 131 126)(6 132 127)(7 129 128)(8 130 125)(9 136 118)(10 133 119)(11 134 120)(12 135 117)(13 35 30)(14 36 31)(15 33 32)(16 34 29)(17 43 22)(18 44 23)(19 41 24)(20 42 21)(45 75 68)(46 76 65)(47 73 66)(48 74 67)(49 78 59)(50 79 60)(51 80 57)(52 77 58)(53 70 64)(54 71 61)(55 72 62)(56 69 63)(81 114 104)(82 115 101)(83 116 102)(84 113 103)(85 111 95)(86 112 96)(87 109 93)(88 110 94)(89 106 100)(90 107 97)(91 108 98)(92 105 99)(121 143 138)(122 144 139)(123 141 140)(124 142 137)
(1 16 17)(2 13 18)(3 14 19)(4 15 20)(5 10 143)(6 11 144)(7 12 141)(8 9 142)(21 27 32)(22 28 29)(23 25 30)(24 26 31)(33 42 37)(34 43 38)(35 44 39)(36 41 40)(45 56 51)(46 53 52)(47 54 49)(48 55 50)(57 68 63)(58 65 64)(59 66 61)(60 67 62)(69 80 75)(70 77 76)(71 78 73)(72 79 74)(81 92 87)(82 89 88)(83 90 85)(84 91 86)(93 104 99)(94 101 100)(95 102 97)(96 103 98)(105 109 114)(106 110 115)(107 111 116)(108 112 113)(117 123 128)(118 124 125)(119 121 126)(120 122 127)(129 135 140)(130 136 137)(131 133 138)(132 134 139)
(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 48 3 46)(2 47 4 45)(5 112 7 110)(6 111 8 109)(9 114 11 116)(10 113 12 115)(13 54 15 56)(14 53 16 55)(17 50 19 52)(18 49 20 51)(21 57 23 59)(22 60 24 58)(25 66 27 68)(26 65 28 67)(29 62 31 64)(30 61 32 63)(33 69 35 71)(34 72 36 70)(37 75 39 73)(38 74 40 76)(41 77 43 79)(42 80 44 78)(81 120 83 118)(82 119 84 117)(85 125 87 127)(86 128 88 126)(89 121 91 123)(90 124 92 122)(93 132 95 130)(94 131 96 129)(97 137 99 139)(98 140 100 138)(101 133 103 135)(102 136 104 134)(105 144 107 142)(106 143 108 141)
(1 17 16)(2 18 13)(3 19 14)(4 20 15)(5 10 143)(6 11 144)(7 12 141)(8 9 142)(21 32 27)(22 29 28)(23 30 25)(24 31 26)(33 37 42)(34 38 43)(35 39 44)(36 40 41)(45 51 56)(46 52 53)(47 49 54)(48 50 55)(57 63 68)(58 64 65)(59 61 66)(60 62 67)(69 75 80)(70 76 77)(71 73 78)(72 74 79)(81 92 87)(82 89 88)(83 90 85)(84 91 86)(93 104 99)(94 101 100)(95 102 97)(96 103 98)(105 109 114)(106 110 115)(107 111 116)(108 112 113)(117 123 128)(118 124 125)(119 121 126)(120 122 127)(129 135 140)(130 136 137)(131 133 138)(132 134 139)
(1 82)(2 81)(3 84)(4 83)(5 80)(6 79)(7 78)(8 77)(9 76)(10 75)(11 74)(12 73)(13 92)(14 91)(15 90)(16 89)(17 88)(18 87)(19 86)(20 85)(21 95)(22 94)(23 93)(24 96)(25 104)(26 103)(27 102)(28 101)(29 100)(30 99)(31 98)(32 97)(33 107)(34 106)(35 105)(36 108)(37 116)(38 115)(39 114)(40 113)(41 112)(42 111)(43 110)(44 109)(45 119)(46 118)(47 117)(48 120)(49 128)(50 127)(51 126)(52 125)(53 124)(54 123)(55 122)(56 121)(57 131)(58 130)(59 129)(60 132)(61 140)(62 139)(63 138)(64 137)(65 136)(66 135)(67 134)(68 133)(69 143)(70 142)(71 141)(72 144)
G:=sub<Sym(144)| (1,38,28)(2,39,25)(3,40,26)(4,37,27)(5,131,126)(6,132,127)(7,129,128)(8,130,125)(9,136,118)(10,133,119)(11,134,120)(12,135,117)(13,35,30)(14,36,31)(15,33,32)(16,34,29)(17,43,22)(18,44,23)(19,41,24)(20,42,21)(45,75,68)(46,76,65)(47,73,66)(48,74,67)(49,78,59)(50,79,60)(51,80,57)(52,77,58)(53,70,64)(54,71,61)(55,72,62)(56,69,63)(81,114,104)(82,115,101)(83,116,102)(84,113,103)(85,111,95)(86,112,96)(87,109,93)(88,110,94)(89,106,100)(90,107,97)(91,108,98)(92,105,99)(121,143,138)(122,144,139)(123,141,140)(124,142,137), (1,16,17)(2,13,18)(3,14,19)(4,15,20)(5,10,143)(6,11,144)(7,12,141)(8,9,142)(21,27,32)(22,28,29)(23,25,30)(24,26,31)(33,42,37)(34,43,38)(35,44,39)(36,41,40)(45,56,51)(46,53,52)(47,54,49)(48,55,50)(57,68,63)(58,65,64)(59,66,61)(60,67,62)(69,80,75)(70,77,76)(71,78,73)(72,79,74)(81,92,87)(82,89,88)(83,90,85)(84,91,86)(93,104,99)(94,101,100)(95,102,97)(96,103,98)(105,109,114)(106,110,115)(107,111,116)(108,112,113)(117,123,128)(118,124,125)(119,121,126)(120,122,127)(129,135,140)(130,136,137)(131,133,138)(132,134,139), (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), (1,48,3,46)(2,47,4,45)(5,112,7,110)(6,111,8,109)(9,114,11,116)(10,113,12,115)(13,54,15,56)(14,53,16,55)(17,50,19,52)(18,49,20,51)(21,57,23,59)(22,60,24,58)(25,66,27,68)(26,65,28,67)(29,62,31,64)(30,61,32,63)(33,69,35,71)(34,72,36,70)(37,75,39,73)(38,74,40,76)(41,77,43,79)(42,80,44,78)(81,120,83,118)(82,119,84,117)(85,125,87,127)(86,128,88,126)(89,121,91,123)(90,124,92,122)(93,132,95,130)(94,131,96,129)(97,137,99,139)(98,140,100,138)(101,133,103,135)(102,136,104,134)(105,144,107,142)(106,143,108,141), (1,17,16)(2,18,13)(3,19,14)(4,20,15)(5,10,143)(6,11,144)(7,12,141)(8,9,142)(21,32,27)(22,29,28)(23,30,25)(24,31,26)(33,37,42)(34,38,43)(35,39,44)(36,40,41)(45,51,56)(46,52,53)(47,49,54)(48,50,55)(57,63,68)(58,64,65)(59,61,66)(60,62,67)(69,75,80)(70,76,77)(71,73,78)(72,74,79)(81,92,87)(82,89,88)(83,90,85)(84,91,86)(93,104,99)(94,101,100)(95,102,97)(96,103,98)(105,109,114)(106,110,115)(107,111,116)(108,112,113)(117,123,128)(118,124,125)(119,121,126)(120,122,127)(129,135,140)(130,136,137)(131,133,138)(132,134,139), (1,82)(2,81)(3,84)(4,83)(5,80)(6,79)(7,78)(8,77)(9,76)(10,75)(11,74)(12,73)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,95)(22,94)(23,93)(24,96)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,107)(34,106)(35,105)(36,108)(37,116)(38,115)(39,114)(40,113)(41,112)(42,111)(43,110)(44,109)(45,119)(46,118)(47,117)(48,120)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,131)(58,130)(59,129)(60,132)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,143)(70,142)(71,141)(72,144)>;
G:=Group( (1,38,28)(2,39,25)(3,40,26)(4,37,27)(5,131,126)(6,132,127)(7,129,128)(8,130,125)(9,136,118)(10,133,119)(11,134,120)(12,135,117)(13,35,30)(14,36,31)(15,33,32)(16,34,29)(17,43,22)(18,44,23)(19,41,24)(20,42,21)(45,75,68)(46,76,65)(47,73,66)(48,74,67)(49,78,59)(50,79,60)(51,80,57)(52,77,58)(53,70,64)(54,71,61)(55,72,62)(56,69,63)(81,114,104)(82,115,101)(83,116,102)(84,113,103)(85,111,95)(86,112,96)(87,109,93)(88,110,94)(89,106,100)(90,107,97)(91,108,98)(92,105,99)(121,143,138)(122,144,139)(123,141,140)(124,142,137), (1,16,17)(2,13,18)(3,14,19)(4,15,20)(5,10,143)(6,11,144)(7,12,141)(8,9,142)(21,27,32)(22,28,29)(23,25,30)(24,26,31)(33,42,37)(34,43,38)(35,44,39)(36,41,40)(45,56,51)(46,53,52)(47,54,49)(48,55,50)(57,68,63)(58,65,64)(59,66,61)(60,67,62)(69,80,75)(70,77,76)(71,78,73)(72,79,74)(81,92,87)(82,89,88)(83,90,85)(84,91,86)(93,104,99)(94,101,100)(95,102,97)(96,103,98)(105,109,114)(106,110,115)(107,111,116)(108,112,113)(117,123,128)(118,124,125)(119,121,126)(120,122,127)(129,135,140)(130,136,137)(131,133,138)(132,134,139), (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), (1,48,3,46)(2,47,4,45)(5,112,7,110)(6,111,8,109)(9,114,11,116)(10,113,12,115)(13,54,15,56)(14,53,16,55)(17,50,19,52)(18,49,20,51)(21,57,23,59)(22,60,24,58)(25,66,27,68)(26,65,28,67)(29,62,31,64)(30,61,32,63)(33,69,35,71)(34,72,36,70)(37,75,39,73)(38,74,40,76)(41,77,43,79)(42,80,44,78)(81,120,83,118)(82,119,84,117)(85,125,87,127)(86,128,88,126)(89,121,91,123)(90,124,92,122)(93,132,95,130)(94,131,96,129)(97,137,99,139)(98,140,100,138)(101,133,103,135)(102,136,104,134)(105,144,107,142)(106,143,108,141), (1,17,16)(2,18,13)(3,19,14)(4,20,15)(5,10,143)(6,11,144)(7,12,141)(8,9,142)(21,32,27)(22,29,28)(23,30,25)(24,31,26)(33,37,42)(34,38,43)(35,39,44)(36,40,41)(45,51,56)(46,52,53)(47,49,54)(48,50,55)(57,63,68)(58,64,65)(59,61,66)(60,62,67)(69,75,80)(70,76,77)(71,73,78)(72,74,79)(81,92,87)(82,89,88)(83,90,85)(84,91,86)(93,104,99)(94,101,100)(95,102,97)(96,103,98)(105,109,114)(106,110,115)(107,111,116)(108,112,113)(117,123,128)(118,124,125)(119,121,126)(120,122,127)(129,135,140)(130,136,137)(131,133,138)(132,134,139), (1,82)(2,81)(3,84)(4,83)(5,80)(6,79)(7,78)(8,77)(9,76)(10,75)(11,74)(12,73)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,95)(22,94)(23,93)(24,96)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,107)(34,106)(35,105)(36,108)(37,116)(38,115)(39,114)(40,113)(41,112)(42,111)(43,110)(44,109)(45,119)(46,118)(47,117)(48,120)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,131)(58,130)(59,129)(60,132)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,143)(70,142)(71,141)(72,144) );
G=PermutationGroup([[(1,38,28),(2,39,25),(3,40,26),(4,37,27),(5,131,126),(6,132,127),(7,129,128),(8,130,125),(9,136,118),(10,133,119),(11,134,120),(12,135,117),(13,35,30),(14,36,31),(15,33,32),(16,34,29),(17,43,22),(18,44,23),(19,41,24),(20,42,21),(45,75,68),(46,76,65),(47,73,66),(48,74,67),(49,78,59),(50,79,60),(51,80,57),(52,77,58),(53,70,64),(54,71,61),(55,72,62),(56,69,63),(81,114,104),(82,115,101),(83,116,102),(84,113,103),(85,111,95),(86,112,96),(87,109,93),(88,110,94),(89,106,100),(90,107,97),(91,108,98),(92,105,99),(121,143,138),(122,144,139),(123,141,140),(124,142,137)], [(1,16,17),(2,13,18),(3,14,19),(4,15,20),(5,10,143),(6,11,144),(7,12,141),(8,9,142),(21,27,32),(22,28,29),(23,25,30),(24,26,31),(33,42,37),(34,43,38),(35,44,39),(36,41,40),(45,56,51),(46,53,52),(47,54,49),(48,55,50),(57,68,63),(58,65,64),(59,66,61),(60,67,62),(69,80,75),(70,77,76),(71,78,73),(72,79,74),(81,92,87),(82,89,88),(83,90,85),(84,91,86),(93,104,99),(94,101,100),(95,102,97),(96,103,98),(105,109,114),(106,110,115),(107,111,116),(108,112,113),(117,123,128),(118,124,125),(119,121,126),(120,122,127),(129,135,140),(130,136,137),(131,133,138),(132,134,139)], [(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)], [(1,48,3,46),(2,47,4,45),(5,112,7,110),(6,111,8,109),(9,114,11,116),(10,113,12,115),(13,54,15,56),(14,53,16,55),(17,50,19,52),(18,49,20,51),(21,57,23,59),(22,60,24,58),(25,66,27,68),(26,65,28,67),(29,62,31,64),(30,61,32,63),(33,69,35,71),(34,72,36,70),(37,75,39,73),(38,74,40,76),(41,77,43,79),(42,80,44,78),(81,120,83,118),(82,119,84,117),(85,125,87,127),(86,128,88,126),(89,121,91,123),(90,124,92,122),(93,132,95,130),(94,131,96,129),(97,137,99,139),(98,140,100,138),(101,133,103,135),(102,136,104,134),(105,144,107,142),(106,143,108,141)], [(1,17,16),(2,18,13),(3,19,14),(4,20,15),(5,10,143),(6,11,144),(7,12,141),(8,9,142),(21,32,27),(22,29,28),(23,30,25),(24,31,26),(33,37,42),(34,38,43),(35,39,44),(36,40,41),(45,51,56),(46,52,53),(47,49,54),(48,50,55),(57,63,68),(58,64,65),(59,61,66),(60,62,67),(69,75,80),(70,76,77),(71,73,78),(72,74,79),(81,92,87),(82,89,88),(83,90,85),(84,91,86),(93,104,99),(94,101,100),(95,102,97),(96,103,98),(105,109,114),(106,110,115),(107,111,116),(108,112,113),(117,123,128),(118,124,125),(119,121,126),(120,122,127),(129,135,140),(130,136,137),(131,133,138),(132,134,139)], [(1,82),(2,81),(3,84),(4,83),(5,80),(6,79),(7,78),(8,77),(9,76),(10,75),(11,74),(12,73),(13,92),(14,91),(15,90),(16,89),(17,88),(18,87),(19,86),(20,85),(21,95),(22,94),(23,93),(24,96),(25,104),(26,103),(27,102),(28,101),(29,100),(30,99),(31,98),(32,97),(33,107),(34,106),(35,105),(36,108),(37,116),(38,115),(39,114),(40,113),(41,112),(42,111),(43,110),(44,109),(45,119),(46,118),(47,117),(48,120),(49,128),(50,127),(51,126),(52,125),(53,124),(54,123),(55,122),(56,121),(57,131),(58,130),(59,129),(60,132),(61,140),(62,139),(63,138),(64,137),(65,136),(66,135),(67,134),(68,133),(69,143),(70,142),(71,141),(72,144)]])
108 conjugacy classes
| class | 1 | 2A | 2B | 3A | ··· | 3H | 3I | ··· | 3Q | 4A | 4B | 6A | ··· | 6H | 6I | ··· | 6Q | 6R | ··· | 6Y | 8A | 8B | 12A | ··· | 12H | 12I | ··· | 12AQ | 24A | ··· | 24P |
| order | 1 | 2 | 2 | 3 | ··· | 3 | 3 | ··· | 3 | 4 | 4 | 6 | ··· | 6 | 6 | ··· | 6 | 6 | ··· | 6 | 8 | 8 | 12 | ··· | 12 | 12 | ··· | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 12 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 12 | ··· | 12 | 6 | 6 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 |
108 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | ||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | S3 | D4 | D6 | SD16 | C3×S3 | C3⋊D4 | C3×D4 | S3×C6 | C3×SD16 | C3×C3⋊D4 | Q8⋊2S3 | C3×Q8⋊2S3 |
| kernel | C32×Q8⋊2S3 | C32×C3⋊C8 | C32×D12 | Q8×C33 | C3×Q8⋊2S3 | C3×C3⋊C8 | C3×D12 | Q8×C32 | Q8×C32 | C32×C6 | C3×C12 | C33 | C3×Q8 | C3×C6 | C3×C6 | C12 | C32 | C6 | C32 | C3 |
| # reps | 1 | 1 | 1 | 1 | 8 | 8 | 8 | 8 | 1 | 1 | 1 | 2 | 8 | 2 | 8 | 8 | 16 | 16 | 1 | 8 |
Matrix representation of C32×Q8⋊2S3 ►in GL6(𝔽73)
| 64 | 0 | 0 | 0 | 0 | 0 |
| 0 | 64 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 |
| 0 | 0 | 0 | 64 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 0 | 1 |
| 0 | 0 | 0 | 0 | 72 | 0 |
| 0 | 37 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 6 |
| 0 | 0 | 0 | 0 | 6 | 67 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 64 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 32 | 37 | 0 | 0 | 0 | 0 |
| 71 | 41 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
G:=sub<GL(6,GF(73))| [64,0,0,0,0,0,0,64,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,64,0,0,0,0,0,0,64,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,1,0],[0,2,0,0,0,0,37,0,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,6,6,0,0,0,0,6,67],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,0,0,0,0,0,0,64,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[32,71,0,0,0,0,37,41,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72] >;
C32×Q8⋊2S3 in GAP, Magma, Sage, TeX
C_3^2\times Q_8\rtimes_2S_3
% in TeX
G:=Group("C3^2xQ8:2S3"); // GroupNames label
G:=SmallGroup(432,477);
// by ID
G=gap.SmallGroup(432,477);
# by ID
G:=PCGroup([7,-2,-2,-3,-3,-2,-2,-3,533,512,3784,1901,102,14118]);
// 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,f*d*f=c^-1*d,f*e*f=e^-1>;
// generators/relations