direct product, cyclic, abelian, monomial
Aliases: C104, also denoted Z104, SmallGroup(104,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C104 |
| C1 — C104 |
| C1 — C104 |
Generators and relations for C104
G = < a | a104=1 >
Smallest permutation representation of C104
►Regular action on 104 points
Generators in S104
(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)
G:=sub<Sym(104)| (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)>;
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) );
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)]])
C104 is a maximal subgroup of
C13⋊2C16 C8⋊D13 C104⋊C2 D104 Dic52
104 conjugacy classes
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 13A | ··· | 13L | 26A | ··· | 26L | 52A | ··· | 52X | 104A | ··· | 104AV |
| order | 1 | 2 | 4 | 4 | 8 | 8 | 8 | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 | 104 | ··· | 104 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||
| image | C1 | C2 | C4 | C8 | C13 | C26 | C52 | C104 |
| kernel | C104 | C52 | C26 | C13 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 12 | 12 | 24 | 48 |
Matrix representation of C104 ►in GL1(𝔽313) generated by
| 245 |
G:=sub<GL(1,GF(313))| [245] >;
C104 in GAP, Magma, Sage, TeX
C_{104} % in TeX
G:=Group("C104"); // GroupNames label
G:=SmallGroup(104,2);
// by ID
G=gap.SmallGroup(104,2);
# by ID
G:=PCGroup([4,-2,-13,-2,-2,104,34]);
// Polycyclic
G:=Group<a|a^104=1>;
// generators/relations
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