Copied to
clipboard

G = C12.57S32  order 432 = 24·33

14th non-split extension by C12 of S32 acting via S32/C3×S3=C2

metabelian, supersoluble, monomial

Aliases: C12.57S32, (S3×C12)⋊5S3, (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

Derived series
C1 — C32×C6 — C12.57S32
Chief series
C1 — C3 — C32 — C33 — C32×C6 — S3×C3×C6 — C33⋊6D4 — C12.57S32
Lower central
C33 — C32×C6 — C12.57S32
Upper central
C1 — C2 — C4

Generators and relations for C12.57S32
 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, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C2×C4, D4, Q8, C32, C32, C32, Dic3, Dic3, C12, C12, C12, D6, D6, C2×C6, C4○D4, C3×S3, C3⋊S3, C3×C6, C3×C6, C3×C6, Dic6, C4×S3, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C3×D4, C33, C3×Dic3, C3⋊Dic3, C3×C12, C3×C12, C3×C12, S3×C6, S3×C6, C2×C3⋊S3, C62, C4○D12, D4⋊2S3, S3×C32, C3×C3⋊S3, C32×C6, S3×Dic3, D6⋊S3, S3×C12, C3×D12, C32⋊4Q8, C4×C3⋊S3, C12⋊S3, C32⋊7D4, C6×C12, C32×Dic3, C33⋊5C4, C32×C12, S3×C3×C6, C6×C3⋊S3, D12⋊5S3, C12.59D6, Dic3×C3⋊S3, C33⋊6D4, S3×C3×C12, C3×C12⋊S3, C33⋊8Q8, C12.57S32
Quotients: C1, C2, C22, S3, C23, D6, C4○D4, C3⋊S3, C22×S3, S32, C2×C3⋊S3, C4○D12, D4⋊2S3, C2×S32, C22×C3⋊S3, S3×C3⋊S3, D12⋊5S3, C12.59D6, C2×S3×C3⋊S3, C12.57S32

Smallest permutation representation of C12.57S32
►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 2A2B2C2D3A···3E3F3G3H3I4A4B4C4D4E6A···6E6F6G6H6I6J···6Q6R6S12A···12H12I···12Q12R···12Y
order122223···33333444446···666666···66612···1212···1212···12
size11618182···2444423354542···244446···636362···24···46···6

63 irreducible representations

dim111111222222224444
type+++++++++++++-+-
imageC1C2C2C2C2C2S3S3D6D6D6D6C4○D4C4○D12S32D4⋊2S3C2×S32D12⋊5S3
kernelC12.57S32Dic3×C3⋊S3C33⋊6D4S3×C3×C12C3×C12⋊S3C33⋊8Q8S3×C12C12⋊S3C3×Dic3C3×C12S3×C6C2×C3⋊S3C33C32C12C32C6C3
# reps1221114145422164148

Matrix representation of C12.57S32 ►in GL8(𝔽13)

10000000
01000000
000120000
001120000
00001000
00000100
00000010
00000001
,
10000000
01000000
00100000
00010000
000001200
000011200
00000010
00000001
,
10000000
01000000
00100000
00010000
00001000
00000100
000000012
000000112
,
34000000
410000000
001200000
001210000
00000100
00001000
00000001
00000010
,
05000000
80000000
001200000
000120000
000012000
000001200
00000001
00000010
,
27000000
711000000
00100000
001120000
000001200
000012000
00000010
00000001

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] >;
 

C12.57S32 in GAP, Magma, Sage, TeX 

C_{12}._{57}S_3^2
 
% in TeX
 
G:=Group("C12.57S3^2");
 
// 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
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁