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G = C4×D29order 232 = 23·29

Direct product of C4 and D29

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

Aliases: C4×D29, C1162C2, C2.1D58, D58.2C2, Dic292C2, C58.2C22, C292(C2×C4), SmallGroup(232,5)

Series: Derived Chief Lower central Upper central

C1C29 — C4×D29
C1C29C58D58 — C4×D29
C29 — C4×D29
C1C4

Generators and relations for C4×D29
 G = < a,b,c | a4=b29=c2=1, ab=ba, ac=ca, cbc=b-1 >

29C2
29C2
29C22
29C4
29C2×C4

Smallest permutation representation of C4×D29
On 116 points
Generators in S116
(1 103 39 65)(2 104 40 66)(3 105 41 67)(4 106 42 68)(5 107 43 69)(6 108 44 70)(7 109 45 71)(8 110 46 72)(9 111 47 73)(10 112 48 74)(11 113 49 75)(12 114 50 76)(13 115 51 77)(14 116 52 78)(15 88 53 79)(16 89 54 80)(17 90 55 81)(18 91 56 82)(19 92 57 83)(20 93 58 84)(21 94 30 85)(22 95 31 86)(23 96 32 87)(24 97 33 59)(25 98 34 60)(26 99 35 61)(27 100 36 62)(28 101 37 63)(29 102 38 64)
(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)
(1 29)(2 28)(3 27)(4 26)(5 25)(6 24)(7 23)(8 22)(9 21)(10 20)(11 19)(12 18)(13 17)(14 16)(30 47)(31 46)(32 45)(33 44)(34 43)(35 42)(36 41)(37 40)(38 39)(48 58)(49 57)(50 56)(51 55)(52 54)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 87)(72 86)(73 85)(74 84)(75 83)(76 82)(77 81)(78 80)(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(116)| (1,103,39,65)(2,104,40,66)(3,105,41,67)(4,106,42,68)(5,107,43,69)(6,108,44,70)(7,109,45,71)(8,110,46,72)(9,111,47,73)(10,112,48,74)(11,113,49,75)(12,114,50,76)(13,115,51,77)(14,116,52,78)(15,88,53,79)(16,89,54,80)(17,90,55,81)(18,91,56,82)(19,92,57,83)(20,93,58,84)(21,94,30,85)(22,95,31,86)(23,96,32,87)(24,97,33,59)(25,98,34,60)(26,99,35,61)(27,100,36,62)(28,101,37,63)(29,102,38,64), (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), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)(48,58)(49,57)(50,56)(51,55)(52,54)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,87)(72,86)(73,85)(74,84)(75,83)(76,82)(77,81)(78,80)(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( (1,103,39,65)(2,104,40,66)(3,105,41,67)(4,106,42,68)(5,107,43,69)(6,108,44,70)(7,109,45,71)(8,110,46,72)(9,111,47,73)(10,112,48,74)(11,113,49,75)(12,114,50,76)(13,115,51,77)(14,116,52,78)(15,88,53,79)(16,89,54,80)(17,90,55,81)(18,91,56,82)(19,92,57,83)(20,93,58,84)(21,94,30,85)(22,95,31,86)(23,96,32,87)(24,97,33,59)(25,98,34,60)(26,99,35,61)(27,100,36,62)(28,101,37,63)(29,102,38,64), (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), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)(48,58)(49,57)(50,56)(51,55)(52,54)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,87)(72,86)(73,85)(74,84)(75,83)(76,82)(77,81)(78,80)(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([(1,103,39,65),(2,104,40,66),(3,105,41,67),(4,106,42,68),(5,107,43,69),(6,108,44,70),(7,109,45,71),(8,110,46,72),(9,111,47,73),(10,112,48,74),(11,113,49,75),(12,114,50,76),(13,115,51,77),(14,116,52,78),(15,88,53,79),(16,89,54,80),(17,90,55,81),(18,91,56,82),(19,92,57,83),(20,93,58,84),(21,94,30,85),(22,95,31,86),(23,96,32,87),(24,97,33,59),(25,98,34,60),(26,99,35,61),(27,100,36,62),(28,101,37,63),(29,102,38,64)], [(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)], [(1,29),(2,28),(3,27),(4,26),(5,25),(6,24),(7,23),(8,22),(9,21),(10,20),(11,19),(12,18),(13,17),(14,16),(30,47),(31,46),(32,45),(33,44),(34,43),(35,42),(36,41),(37,40),(38,39),(48,58),(49,57),(50,56),(51,55),(52,54),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,87),(72,86),(73,85),(74,84),(75,83),(76,82),(77,81),(78,80),(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)])

C4×D29 is a maximal subgroup of   C8⋊D29  D29⋊C8  C116.C4  C116⋊C4  D1165C2  D42D29  Q82D29
C4×D29 is a maximal quotient of   C8⋊D29  C58.D4  D58⋊C4

64 conjugacy classes

class 1 2A2B2C4A4B4C4D29A···29N58A···58N116A···116AB
order1222444429···2958···58116···116
size1129291129292···22···22···2

64 irreducible representations

dim11111222
type++++++
imageC1C2C2C2C4D29D58C4×D29
kernelC4×D29Dic29C116D58D29C4C2C1
# reps11114141428

Matrix representation of C4×D29 in GL2(𝔽233) generated by

1440
0144
,
01
232179
,
01
10
G:=sub<GL(2,GF(233))| [144,0,0,144],[0,232,1,179],[0,1,1,0] >;

C4×D29 in GAP, Magma, Sage, TeX

C_4\times D_{29}
% in TeX

G:=Group("C4xD29");
// GroupNames label

G:=SmallGroup(232,5);
// by ID

G=gap.SmallGroup(232,5);
# by ID

G:=PCGroup([4,-2,-2,-2,-29,21,3587]);
// Polycyclic

G:=Group<a,b,c|a^4=b^29=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C4×D29 in TeX

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