metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: Dic29, C29⋊2C4, C58.C2, C2.D29, SmallGroup(116,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — Dic29 |
Generators and relations for Dic29
G = < a,b | a58=1, b2=a29, bab-1=a-1 >
Smallest permutation representation of Dic29
►Regular action on 116 points
Generators in S116
(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)
(1 109 30 80)(2 108 31 79)(3 107 32 78)(4 106 33 77)(5 105 34 76)(6 104 35 75)(7 103 36 74)(8 102 37 73)(9 101 38 72)(10 100 39 71)(11 99 40 70)(12 98 41 69)(13 97 42 68)(14 96 43 67)(15 95 44 66)(16 94 45 65)(17 93 46 64)(18 92 47 63)(19 91 48 62)(20 90 49 61)(21 89 50 60)(22 88 51 59)(23 87 52 116)(24 86 53 115)(25 85 54 114)(26 84 55 113)(27 83 56 112)(28 82 57 111)(29 81 58 110)
G:=sub<Sym(116)| (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), (1,109,30,80)(2,108,31,79)(3,107,32,78)(4,106,33,77)(5,105,34,76)(6,104,35,75)(7,103,36,74)(8,102,37,73)(9,101,38,72)(10,100,39,71)(11,99,40,70)(12,98,41,69)(13,97,42,68)(14,96,43,67)(15,95,44,66)(16,94,45,65)(17,93,46,64)(18,92,47,63)(19,91,48,62)(20,90,49,61)(21,89,50,60)(22,88,51,59)(23,87,52,116)(24,86,53,115)(25,85,54,114)(26,84,55,113)(27,83,56,112)(28,82,57,111)(29,81,58,110)>;
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), (1,109,30,80)(2,108,31,79)(3,107,32,78)(4,106,33,77)(5,105,34,76)(6,104,35,75)(7,103,36,74)(8,102,37,73)(9,101,38,72)(10,100,39,71)(11,99,40,70)(12,98,41,69)(13,97,42,68)(14,96,43,67)(15,95,44,66)(16,94,45,65)(17,93,46,64)(18,92,47,63)(19,91,48,62)(20,90,49,61)(21,89,50,60)(22,88,51,59)(23,87,52,116)(24,86,53,115)(25,85,54,114)(26,84,55,113)(27,83,56,112)(28,82,57,111)(29,81,58,110) );
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)], [(1,109,30,80),(2,108,31,79),(3,107,32,78),(4,106,33,77),(5,105,34,76),(6,104,35,75),(7,103,36,74),(8,102,37,73),(9,101,38,72),(10,100,39,71),(11,99,40,70),(12,98,41,69),(13,97,42,68),(14,96,43,67),(15,95,44,66),(16,94,45,65),(17,93,46,64),(18,92,47,63),(19,91,48,62),(20,90,49,61),(21,89,50,60),(22,88,51,59),(23,87,52,116),(24,86,53,115),(25,85,54,114),(26,84,55,113),(27,83,56,112),(28,82,57,111),(29,81,58,110)]])
Dic29 is a maximal subgroup of
C29⋊C8 Dic58 C4×D29 C29⋊D4 Dic87
Dic29 is a maximal quotient of C29⋊2C8 Dic87
32 conjugacy classes
| class | 1 | 2 | 4A | 4B | 29A | ··· | 29N | 58A | ··· | 58N |
| order | 1 | 2 | 4 | 4 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | 29 | 29 | 2 | ··· | 2 | 2 | ··· | 2 |
32 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | - | |
| image | C1 | C2 | C4 | D29 | Dic29 |
| kernel | Dic29 | C58 | C29 | C2 | C1 |
| # reps | 1 | 1 | 2 | 14 | 14 |
Matrix representation of Dic29 ►in GL3(𝔽233) generated by
| 232 | 0 | 0 |
| 0 | 28 | 232 |
| 0 | 1 | 0 |
| 89 | 0 | 0 |
| 0 | 225 | 29 |
| 0 | 38 | 8 |
G:=sub<GL(3,GF(233))| [232,0,0,0,28,1,0,232,0],[89,0,0,0,225,38,0,29,8] >;
Dic29 in GAP, Magma, Sage, TeX
{\rm Dic}_{29} % in TeX
G:=Group("Dic29"); // GroupNames label
G:=SmallGroup(116,1);
// by ID
G=gap.SmallGroup(116,1);
# by ID
G:=PCGroup([3,-2,-2,-29,6,1010]);
// Polycyclic
G:=Group<a,b|a^58=1,b^2=a^29,b*a*b^-1=a^-1>;
// generators/relations
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