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G = C49order 49 = 72

Cyclic group

p-group, cyclic, abelian, monomial

Aliases: C49, also denoted Z49, SmallGroup(49,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C49
C1C7 — C49
C1 — C49
C1 — C49
C1C7C7C7C7C7C7 — C49

Generators and relations for C49
 G = < a | a49=1 >


Smallest permutation representation of C49
Regular action on 49 points
Generators in S49
(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)

G:=sub<Sym(49)| (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)>;

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) );

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)])

49 conjugacy classes

class 1 7A···7F49A···49AP
order17···749···49
size11···11···1

49 irreducible representations

dim111
type+
imageC1C7C49
kernelC49C7C1
# reps1642

Matrix representation of C49 in GL1(𝔽197) generated by

193
G:=sub<GL(1,GF(197))| [193] >;

C49 in GAP, Magma, Sage, TeX

C_{49}
% in TeX

G:=Group("C49");
// GroupNames label

G:=SmallGroup(49,1);
// by ID

G=gap.SmallGroup(49,1);
# by ID

G:=PCGroup([2,-7,-7,14]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^49=1>;
// generators/relations

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