direct product, cyclic, abelian, monomial
Aliases: C133, also denoted Z133, SmallGroup(133,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C133 |
| C1 — C133 |
| C1 — C133 |
Generators and relations for C133
G = < a | a133=1 >
Smallest permutation representation of C133
►Regular action on 133 points
Generators in S133
(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)
G:=sub<Sym(133)| (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)>;
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) );
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)]])
C133 is a maximal subgroup of
D133 C133⋊C3 C133⋊4C3
133 conjugacy classes
| class | 1 | 7A | ··· | 7F | 19A | ··· | 19R | 133A | ··· | 133DD |
| order | 1 | 7 | ··· | 7 | 19 | ··· | 19 | 133 | ··· | 133 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C7 | C19 | C133 |
| kernel | C133 | C19 | C7 | C1 |
| # reps | 1 | 6 | 18 | 108 |
Matrix representation of C133 ►in GL1(𝔽1597) generated by
| 957 |
G:=sub<GL(1,GF(1597))| [957] >;
C133 in GAP, Magma, Sage, TeX
C_{133} % in TeX
G:=Group("C133"); // GroupNames label
G:=SmallGroup(133,1);
// by ID
G=gap.SmallGroup(133,1);
# by ID
G:=PCGroup([2,-7,-19]);
// Polycyclic
G:=Group<a|a^133=1>;
// generators/relations
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