metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: D145, C5⋊D29, C29⋊D5, C145⋊1C2, sometimes denoted D290 or Dih145 or Dih290, SmallGroup(290,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C145 — D145 |
Generators and relations for D145
G = < a,b | a145=b2=1, bab=a-1 >
Smallest permutation representation of D145
►On 145 points
Generators in S145
(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)
(1 145)(2 144)(3 143)(4 142)(5 141)(6 140)(7 139)(8 138)(9 137)(10 136)(11 135)(12 134)(13 133)(14 132)(15 131)(16 130)(17 129)(18 128)(19 127)(20 126)(21 125)(22 124)(23 123)(24 122)(25 121)(26 120)(27 119)(28 118)(29 117)(30 116)(31 115)(32 114)(33 113)(34 112)(35 111)(36 110)(37 109)(38 108)(39 107)(40 106)(41 105)(42 104)(43 103)(44 102)(45 101)(46 100)(47 99)(48 98)(49 97)(50 96)(51 95)(52 94)(53 93)(54 92)(55 91)(56 90)(57 89)(58 88)(59 87)(60 86)(61 85)(62 84)(63 83)(64 82)(65 81)(66 80)(67 79)(68 78)(69 77)(70 76)(71 75)(72 74)
G:=sub<Sym(145)| (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), (1,145)(2,144)(3,143)(4,142)(5,141)(6,140)(7,139)(8,138)(9,137)(10,136)(11,135)(12,134)(13,133)(14,132)(15,131)(16,130)(17,129)(18,128)(19,127)(20,126)(21,125)(22,124)(23,123)(24,122)(25,121)(26,120)(27,119)(28,118)(29,117)(30,116)(31,115)(32,114)(33,113)(34,112)(35,111)(36,110)(37,109)(38,108)(39,107)(40,106)(41,105)(42,104)(43,103)(44,102)(45,101)(46,100)(47,99)(48,98)(49,97)(50,96)(51,95)(52,94)(53,93)(54,92)(55,91)(56,90)(57,89)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)(66,80)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)>;
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), (1,145)(2,144)(3,143)(4,142)(5,141)(6,140)(7,139)(8,138)(9,137)(10,136)(11,135)(12,134)(13,133)(14,132)(15,131)(16,130)(17,129)(18,128)(19,127)(20,126)(21,125)(22,124)(23,123)(24,122)(25,121)(26,120)(27,119)(28,118)(29,117)(30,116)(31,115)(32,114)(33,113)(34,112)(35,111)(36,110)(37,109)(38,108)(39,107)(40,106)(41,105)(42,104)(43,103)(44,102)(45,101)(46,100)(47,99)(48,98)(49,97)(50,96)(51,95)(52,94)(53,93)(54,92)(55,91)(56,90)(57,89)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)(66,80)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74) );
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)], [(1,145),(2,144),(3,143),(4,142),(5,141),(6,140),(7,139),(8,138),(9,137),(10,136),(11,135),(12,134),(13,133),(14,132),(15,131),(16,130),(17,129),(18,128),(19,127),(20,126),(21,125),(22,124),(23,123),(24,122),(25,121),(26,120),(27,119),(28,118),(29,117),(30,116),(31,115),(32,114),(33,113),(34,112),(35,111),(36,110),(37,109),(38,108),(39,107),(40,106),(41,105),(42,104),(43,103),(44,102),(45,101),(46,100),(47,99),(48,98),(49,97),(50,96),(51,95),(52,94),(53,93),(54,92),(55,91),(56,90),(57,89),(58,88),(59,87),(60,86),(61,85),(62,84),(63,83),(64,82),(65,81),(66,80),(67,79),(68,78),(69,77),(70,76),(71,75),(72,74)]])
74 conjugacy classes
| class | 1 | 2 | 5A | 5B | 29A | ··· | 29N | 145A | ··· | 145BD |
| order | 1 | 2 | 5 | 5 | 29 | ··· | 29 | 145 | ··· | 145 |
| size | 1 | 145 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
74 irreducible representations
| dim | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | D5 | D29 | D145 |
| kernel | D145 | C145 | C29 | C5 | C1 |
| # reps | 1 | 1 | 2 | 14 | 56 |
Matrix representation of D145 ►in GL2(𝔽1451) generated by
| 22 | 903 |
| 548 | 662 |
| 22 | 903 |
| 1248 | 1429 |
G:=sub<GL(2,GF(1451))| [22,548,903,662],[22,1248,903,1429] >;
D145 in GAP, Magma, Sage, TeX
D_{145} % in TeX
G:=Group("D145"); // GroupNames label
G:=SmallGroup(290,3);
// by ID
G=gap.SmallGroup(290,3);
# by ID
G:=PCGroup([3,-2,-5,-29,49,2522]);
// Polycyclic
G:=Group<a,b|a^145=b^2=1,b*a*b=a^-1>;
// generators/relations
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