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G = C104order 104 = 23·13

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C104, also denoted Z104, SmallGroup(104,2)

Series: Derived Chief Lower central Upper central

C1 — C104
C1C2C4C52 — 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   C132C16  C8⋊D13  C104⋊C2  D104  Dic52

104 conjugacy classes

class 1  2 4A4B8A8B8C8D13A···13L26A···26L52A···52X104A···104AV
order1244888813···1326···2652···52104···104
size111111111···11···11···11···1

104 irreducible representations

dim11111111
type++
imageC1C2C4C8C13C26C52C104
kernelC104C52C26C13C8C4C2C1
# reps112412122448

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

Export

Subgroup lattice of C104 in TeX

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