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G = C105order 105 = 3·5·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C105, also denoted Z105, SmallGroup(105,2)

Series: Derived Chief Lower central Upper central

C1 — C105
C1C7C35 — C105
C1 — C105
C1 — C105

Generators and relations for C105
 G = < a | a105=1 >


Smallest permutation representation of C105
Regular action on 105 points
Generators in S105
(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)

G:=sub<Sym(105)| (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)>;

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) );

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)])

C105 is a maximal subgroup of   D105

105 conjugacy classes

class 1 3A3B5A5B5C5D7A···7F15A···15H21A···21L35A···35X105A···105AV
order13355557···715···1521···2135···35105···105
size11111111···11···11···11···11···1

105 irreducible representations

dim11111111
type+
imageC1C3C5C7C15C21C35C105
kernelC105C35C21C15C7C5C3C1
# reps12468122448

Matrix representation of C105 in GL1(𝔽211) generated by

136
G:=sub<GL(1,GF(211))| [136] >;

C105 in GAP, Magma, Sage, TeX

C_{105}
% in TeX

G:=Group("C105");
// GroupNames label

G:=SmallGroup(105,2);
// by ID

G=gap.SmallGroup(105,2);
# by ID

G:=PCGroup([3,-3,-5,-7]);
// Polycyclic

G:=Group<a|a^105=1>;
// generators/relations

Export

Subgroup lattice of C105 in TeX

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