metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C151⋊C3, SmallGroup(453,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C151 — C151⋊C3 |
Generators and relations for C151⋊C3
G = < a,b | a151=b3=1, bab-1=a118 >
Smallest permutation representation of C151⋊C3
►On 151 points: primitive
Generators in S151
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151)
(2 33 119)(3 65 86)(4 97 53)(5 129 20)(6 10 138)(7 42 105)(8 74 72)(9 106 39)(11 19 124)(12 51 91)(13 83 58)(14 115 25)(15 147 143)(16 28 110)(17 60 77)(18 92 44)(21 37 96)(22 69 63)(23 101 30)(24 133 148)(26 46 82)(27 78 49)(29 142 134)(31 55 68)(32 87 35)(34 151 120)(36 64 54)(38 128 139)(40 41 73)(43 137 125)(45 50 59)(47 114 144)(48 146 111)(52 123 130)(56 100 149)(57 132 116)(61 109 135)(62 141 102)(66 118 121)(67 150 88)(70 95 140)(71 127 107)(75 104 126)(76 136 93)(79 81 145)(80 113 112)(84 90 131)(85 122 98)(89 99 117)(94 108 103)
G:=sub<Sym(151)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151), (2,33,119)(3,65,86)(4,97,53)(5,129,20)(6,10,138)(7,42,105)(8,74,72)(9,106,39)(11,19,124)(12,51,91)(13,83,58)(14,115,25)(15,147,143)(16,28,110)(17,60,77)(18,92,44)(21,37,96)(22,69,63)(23,101,30)(24,133,148)(26,46,82)(27,78,49)(29,142,134)(31,55,68)(32,87,35)(34,151,120)(36,64,54)(38,128,139)(40,41,73)(43,137,125)(45,50,59)(47,114,144)(48,146,111)(52,123,130)(56,100,149)(57,132,116)(61,109,135)(62,141,102)(66,118,121)(67,150,88)(70,95,140)(71,127,107)(75,104,126)(76,136,93)(79,81,145)(80,113,112)(84,90,131)(85,122,98)(89,99,117)(94,108,103)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151), (2,33,119)(3,65,86)(4,97,53)(5,129,20)(6,10,138)(7,42,105)(8,74,72)(9,106,39)(11,19,124)(12,51,91)(13,83,58)(14,115,25)(15,147,143)(16,28,110)(17,60,77)(18,92,44)(21,37,96)(22,69,63)(23,101,30)(24,133,148)(26,46,82)(27,78,49)(29,142,134)(31,55,68)(32,87,35)(34,151,120)(36,64,54)(38,128,139)(40,41,73)(43,137,125)(45,50,59)(47,114,144)(48,146,111)(52,123,130)(56,100,149)(57,132,116)(61,109,135)(62,141,102)(66,118,121)(67,150,88)(70,95,140)(71,127,107)(75,104,126)(76,136,93)(79,81,145)(80,113,112)(84,90,131)(85,122,98)(89,99,117)(94,108,103) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151)], [(2,33,119),(3,65,86),(4,97,53),(5,129,20),(6,10,138),(7,42,105),(8,74,72),(9,106,39),(11,19,124),(12,51,91),(13,83,58),(14,115,25),(15,147,143),(16,28,110),(17,60,77),(18,92,44),(21,37,96),(22,69,63),(23,101,30),(24,133,148),(26,46,82),(27,78,49),(29,142,134),(31,55,68),(32,87,35),(34,151,120),(36,64,54),(38,128,139),(40,41,73),(43,137,125),(45,50,59),(47,114,144),(48,146,111),(52,123,130),(56,100,149),(57,132,116),(61,109,135),(62,141,102),(66,118,121),(67,150,88),(70,95,140),(71,127,107),(75,104,126),(76,136,93),(79,81,145),(80,113,112),(84,90,131),(85,122,98),(89,99,117),(94,108,103)]])
53 conjugacy classes
| class | 1 | 3A | 3B | 151A | ··· | 151AX |
| order | 1 | 3 | 3 | 151 | ··· | 151 |
| size | 1 | 151 | 151 | 3 | ··· | 3 |
53 irreducible representations
| dim | 1 | 1 | 3 |
| type | + | ||
| image | C1 | C3 | C151⋊C3 |
| kernel | C151⋊C3 | C151 | C1 |
| # reps | 1 | 2 | 50 |
Matrix representation of C151⋊C3 ►in GL3(𝔽907) generated by
| 350 | 1 | 0 |
| 236 | 0 | 1 |
| 1 | 0 | 0 |
| 1 | 622 | 770 |
| 0 | 243 | 388 |
| 0 | 836 | 663 |
G:=sub<GL(3,GF(907))| [350,236,1,1,0,0,0,1,0],[1,0,0,622,243,836,770,388,663] >;
C151⋊C3 in GAP, Magma, Sage, TeX
C_{151}\rtimes C_3 % in TeX
G:=Group("C151:C3"); // GroupNames label
G:=SmallGroup(453,1);
// by ID
G=gap.SmallGroup(453,1);
# by ID
G:=PCGroup([2,-3,-151,385]);
// Polycyclic
G:=Group<a,b|a^151=b^3=1,b*a*b^-1=a^118>;
// generators/relations
Export