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G = C63order 63 = 32·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C63, also denoted Z63, SmallGroup(63,2)

Series: Derived Chief Lower central Upper central

C1 — C63
C1C3C21 — C63
C1 — C63
C1 — C63

Generators and relations for C63
 G = < a | a63=1 >


Smallest permutation representation of C63
Regular action on 63 points
Generators in S63
(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)

G:=sub<Sym(63)| (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)>;

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) );

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)])

C63 is a maximal subgroup of   D63  C7⋊C27  C63⋊C3  C633C3

63 conjugacy classes

class 1 3A3B7A···7F9A···9F21A···21L63A···63AJ
order1337···79···921···2163···63
size1111···11···11···11···1

63 irreducible representations

dim111111
type+
imageC1C3C7C9C21C63
kernelC63C21C9C7C3C1
# reps12661236

Matrix representation of C63 in GL1(𝔽127) generated by

115
G:=sub<GL(1,GF(127))| [115] >;

C63 in GAP, Magma, Sage, TeX

C_{63}
% in TeX

G:=Group("C63");
// GroupNames label

G:=SmallGroup(63,2);
// by ID

G=gap.SmallGroup(63,2);
# by ID

G:=PCGroup([3,-3,-7,-3,63]);
// Polycyclic

G:=Group<a|a^63=1>;
// generators/relations

Export

Subgroup lattice of C63 in TeX

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