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G = C3×D41order 246 = 2·3·41

Direct product of C3 and D41

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C3×D41, C41⋊C6, C1232C2, SmallGroup(246,2)

Series: Derived Chief Lower central Upper central

C1C41 — C3×D41
C1C41C123 — C3×D41
C41 — C3×D41
C1C3

Generators and relations for C3×D41
 G = < a,b,c | a3=b41=c2=1, ab=ba, ac=ca, cbc=b-1 >

41C2
41C6

Smallest permutation representation of C3×D41
On 123 points
Generators in S123
(1 103 55)(2 104 56)(3 105 57)(4 106 58)(5 107 59)(6 108 60)(7 109 61)(8 110 62)(9 111 63)(10 112 64)(11 113 65)(12 114 66)(13 115 67)(14 116 68)(15 117 69)(16 118 70)(17 119 71)(18 120 72)(19 121 73)(20 122 74)(21 123 75)(22 83 76)(23 84 77)(24 85 78)(25 86 79)(26 87 80)(27 88 81)(28 89 82)(29 90 42)(30 91 43)(31 92 44)(32 93 45)(33 94 46)(34 95 47)(35 96 48)(36 97 49)(37 98 50)(38 99 51)(39 100 52)(40 101 53)(41 102 54)
(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)
(1 41)(2 40)(3 39)(4 38)(5 37)(6 36)(7 35)(8 34)(9 33)(10 32)(11 31)(12 30)(13 29)(14 28)(15 27)(16 26)(17 25)(18 24)(19 23)(20 22)(42 67)(43 66)(44 65)(45 64)(46 63)(47 62)(48 61)(49 60)(50 59)(51 58)(52 57)(53 56)(54 55)(68 82)(69 81)(70 80)(71 79)(72 78)(73 77)(74 76)(83 122)(84 121)(85 120)(86 119)(87 118)(88 117)(89 116)(90 115)(91 114)(92 113)(93 112)(94 111)(95 110)(96 109)(97 108)(98 107)(99 106)(100 105)(101 104)(102 103)

G:=sub<Sym(123)| (1,103,55)(2,104,56)(3,105,57)(4,106,58)(5,107,59)(6,108,60)(7,109,61)(8,110,62)(9,111,63)(10,112,64)(11,113,65)(12,114,66)(13,115,67)(14,116,68)(15,117,69)(16,118,70)(17,119,71)(18,120,72)(19,121,73)(20,122,74)(21,123,75)(22,83,76)(23,84,77)(24,85,78)(25,86,79)(26,87,80)(27,88,81)(28,89,82)(29,90,42)(30,91,43)(31,92,44)(32,93,45)(33,94,46)(34,95,47)(35,96,48)(36,97,49)(37,98,50)(38,99,51)(39,100,52)(40,101,53)(41,102,54), (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), (1,41)(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(83,122)(84,121)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103)>;

G:=Group( (1,103,55)(2,104,56)(3,105,57)(4,106,58)(5,107,59)(6,108,60)(7,109,61)(8,110,62)(9,111,63)(10,112,64)(11,113,65)(12,114,66)(13,115,67)(14,116,68)(15,117,69)(16,118,70)(17,119,71)(18,120,72)(19,121,73)(20,122,74)(21,123,75)(22,83,76)(23,84,77)(24,85,78)(25,86,79)(26,87,80)(27,88,81)(28,89,82)(29,90,42)(30,91,43)(31,92,44)(32,93,45)(33,94,46)(34,95,47)(35,96,48)(36,97,49)(37,98,50)(38,99,51)(39,100,52)(40,101,53)(41,102,54), (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), (1,41)(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(83,122)(84,121)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103) );

G=PermutationGroup([(1,103,55),(2,104,56),(3,105,57),(4,106,58),(5,107,59),(6,108,60),(7,109,61),(8,110,62),(9,111,63),(10,112,64),(11,113,65),(12,114,66),(13,115,67),(14,116,68),(15,117,69),(16,118,70),(17,119,71),(18,120,72),(19,121,73),(20,122,74),(21,123,75),(22,83,76),(23,84,77),(24,85,78),(25,86,79),(26,87,80),(27,88,81),(28,89,82),(29,90,42),(30,91,43),(31,92,44),(32,93,45),(33,94,46),(34,95,47),(35,96,48),(36,97,49),(37,98,50),(38,99,51),(39,100,52),(40,101,53),(41,102,54)], [(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)], [(1,41),(2,40),(3,39),(4,38),(5,37),(6,36),(7,35),(8,34),(9,33),(10,32),(11,31),(12,30),(13,29),(14,28),(15,27),(16,26),(17,25),(18,24),(19,23),(20,22),(42,67),(43,66),(44,65),(45,64),(46,63),(47,62),(48,61),(49,60),(50,59),(51,58),(52,57),(53,56),(54,55),(68,82),(69,81),(70,80),(71,79),(72,78),(73,77),(74,76),(83,122),(84,121),(85,120),(86,119),(87,118),(88,117),(89,116),(90,115),(91,114),(92,113),(93,112),(94,111),(95,110),(96,109),(97,108),(98,107),(99,106),(100,105),(101,104),(102,103)])

C3×D41 is a maximal subgroup of   C41⋊Dic3

66 conjugacy classes

class 1  2 3A3B6A6B41A···41T123A···123AN
order12336641···41123···123
size1411141412···22···2

66 irreducible representations

dim111122
type+++
imageC1C2C3C6D41C3×D41
kernelC3×D41C123D41C41C3C1
# reps11222040

Matrix representation of C3×D41 in GL3(𝔽739) generated by

32000
010
001
,
100
07161
05494
,
73800
071771
024322
G:=sub<GL(3,GF(739))| [320,0,0,0,1,0,0,0,1],[1,0,0,0,716,54,0,1,94],[738,0,0,0,717,243,0,71,22] >;

C3×D41 in GAP, Magma, Sage, TeX

C_3\times D_{41}
% in TeX

G:=Group("C3xD41");
// GroupNames label

G:=SmallGroup(246,2);
// by ID

G=gap.SmallGroup(246,2);
# by ID

G:=PCGroup([3,-2,-3,-41,2162]);
// Polycyclic

G:=Group<a,b,c|a^3=b^41=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C3×D41 in TeX

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