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G = C127⋊C3order 381 = 3·127

The semidirect product of C127 and C3 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C127⋊C3, SmallGroup(381,1)

Series: Derived Chief Lower central Upper central

C1C127 — C127⋊C3
C1C127 — C127⋊C3
C127 — C127⋊C3
C1

Generators and relations for C127⋊C3
 G = < a,b | a127=b3=1, bab-1=a19 >

127C3

Smallest permutation representation of C127⋊C3
On 127 points: primitive
Generators in S127
(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)
(2 108 20)(3 88 39)(4 68 58)(5 48 77)(6 28 96)(7 8 115)(9 95 26)(10 75 45)(11 55 64)(12 35 83)(13 15 102)(14 122 121)(16 82 32)(17 62 51)(18 42 70)(19 22 89)(21 109 127)(23 69 38)(24 49 57)(25 29 76)(27 116 114)(30 56 44)(31 36 63)(33 123 101)(34 103 120)(37 43 50)(40 110 107)(41 90 126)(46 117 94)(47 97 113)(52 124 81)(53 104 100)(54 84 119)(59 111 87)(60 91 106)(61 71 125)(65 118 74)(66 98 93)(67 78 112)(72 105 80)(73 85 99)(79 92 86)

G:=sub<Sym(127)| (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), (2,108,20)(3,88,39)(4,68,58)(5,48,77)(6,28,96)(7,8,115)(9,95,26)(10,75,45)(11,55,64)(12,35,83)(13,15,102)(14,122,121)(16,82,32)(17,62,51)(18,42,70)(19,22,89)(21,109,127)(23,69,38)(24,49,57)(25,29,76)(27,116,114)(30,56,44)(31,36,63)(33,123,101)(34,103,120)(37,43,50)(40,110,107)(41,90,126)(46,117,94)(47,97,113)(52,124,81)(53,104,100)(54,84,119)(59,111,87)(60,91,106)(61,71,125)(65,118,74)(66,98,93)(67,78,112)(72,105,80)(73,85,99)(79,92,86)>;

G:=Group( (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), (2,108,20)(3,88,39)(4,68,58)(5,48,77)(6,28,96)(7,8,115)(9,95,26)(10,75,45)(11,55,64)(12,35,83)(13,15,102)(14,122,121)(16,82,32)(17,62,51)(18,42,70)(19,22,89)(21,109,127)(23,69,38)(24,49,57)(25,29,76)(27,116,114)(30,56,44)(31,36,63)(33,123,101)(34,103,120)(37,43,50)(40,110,107)(41,90,126)(46,117,94)(47,97,113)(52,124,81)(53,104,100)(54,84,119)(59,111,87)(60,91,106)(61,71,125)(65,118,74)(66,98,93)(67,78,112)(72,105,80)(73,85,99)(79,92,86) );

G=PermutationGroup([(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)], [(2,108,20),(3,88,39),(4,68,58),(5,48,77),(6,28,96),(7,8,115),(9,95,26),(10,75,45),(11,55,64),(12,35,83),(13,15,102),(14,122,121),(16,82,32),(17,62,51),(18,42,70),(19,22,89),(21,109,127),(23,69,38),(24,49,57),(25,29,76),(27,116,114),(30,56,44),(31,36,63),(33,123,101),(34,103,120),(37,43,50),(40,110,107),(41,90,126),(46,117,94),(47,97,113),(52,124,81),(53,104,100),(54,84,119),(59,111,87),(60,91,106),(61,71,125),(65,118,74),(66,98,93),(67,78,112),(72,105,80),(73,85,99),(79,92,86)])

45 conjugacy classes

class 1 3A3B127A···127AP
order133127···127
size11271273···3

45 irreducible representations

dim113
type+
imageC1C3C127⋊C3
kernelC127⋊C3C127C1
# reps1242

Matrix representation of C127⋊C3 in GL3(𝔽2287) generated by

116010
139601
100
,
11261822
03131664
017951973
G:=sub<GL(3,GF(2287))| [1160,1396,1,1,0,0,0,1,0],[1,0,0,126,313,1795,1822,1664,1973] >;

C127⋊C3 in GAP, Magma, Sage, TeX

C_{127}\rtimes C_3
% in TeX

G:=Group("C127:C3");
// GroupNames label

G:=SmallGroup(381,1);
// by ID

G=gap.SmallGroup(381,1);
# by ID

G:=PCGroup([2,-3,-127,1285]);
// Polycyclic

G:=Group<a,b|a^127=b^3=1,b*a*b^-1=a^19>;
// generators/relations

Export

Subgroup lattice of C127⋊C3 in TeX

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