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G = C16order 16 = 24

Cyclic group

p-group, cyclic, abelian, monomial

Aliases: C16, also denoted Z16, SmallGroup(16,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C16
C1C2C4C8 — C16
C1 — C16
C1 — C16
C1C2C2C2C2C4C4C8 — C16

Generators and relations for C16
 G = < a | a16=1 >


Character table of C16

 class 124A4B8A8B8C8D16A16B16C16D16E16F16G16H
 size 1111111111111111
ρ11111111111111111    trivial
ρ211111111-1-1-1-1-1-1-1-1    linear of order 2
ρ31-1-iiζ162ζ1610ζ166ζ1614ζ1615ζ169ζ165ζ1611ζ163ζ1613ζ167ζ16    linear of order 16 faithful
ρ411-1-1ii-i-iζ87ζ8ζ85ζ83ζ83ζ85ζ87ζ8    linear of order 8
ρ51-1i-iζ166ζ1614ζ162ζ1610ζ1613ζ1611ζ1615ζ16ζ169ζ167ζ165ζ163    linear of order 16 faithful
ρ61-1-iiζ1610ζ162ζ1614ζ166ζ1611ζ1613ζ169ζ167ζ1615ζ16ζ163ζ165    linear of order 16 faithful
ρ711-1-1-i-iiiζ85ζ83ζ87ζ8ζ8ζ87ζ85ζ83    linear of order 8
ρ81-1i-iζ1614ζ166ζ1610ζ162ζ169ζ1615ζ163ζ1613ζ165ζ1611ζ16ζ167    linear of order 16 faithful
ρ91111-1-1-1-1-iii-i-ii-ii    linear of order 4
ρ101-1-iiζ162ζ1610ζ166ζ1614ζ167ζ16ζ1613ζ163ζ1611ζ165ζ1615ζ169    linear of order 16 faithful
ρ1111-1-1ii-i-iζ83ζ85ζ8ζ87ζ87ζ8ζ83ζ85    linear of order 8
ρ121-1i-iζ166ζ1614ζ162ζ1610ζ165ζ163ζ167ζ169ζ16ζ1615ζ1613ζ1611    linear of order 16 faithful
ρ131111-1-1-1-1i-i-iii-ii-i    linear of order 4
ρ141-1-iiζ1610ζ162ζ1614ζ166ζ163ζ165ζ16ζ1615ζ167ζ169ζ1611ζ1613    linear of order 16 faithful
ρ1511-1-1-i-iiiζ8ζ87ζ83ζ85ζ85ζ83ζ8ζ87    linear of order 8
ρ161-1i-iζ1614ζ166ζ1610ζ162ζ16ζ167ζ1611ζ165ζ1613ζ163ζ169ζ1615    linear of order 16 faithful

Permutation representations of C16
Regular action on 16 points - transitive group 16T1
Generators in S16
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16)

G:=sub<Sym(16)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)])

G:=TransitiveGroup(16,1);

Polynomial with Galois group C16 over ℚ
actionf(x)Disc(f)
16T1x16+x15+x14+x13+x12+x11+x10+x9+x8+x7+x6+x5+x4+x3+x2+x+11715

Matrix representation of C16 in GL1(𝔽17) generated by

7
G:=sub<GL(1,GF(17))| [7] >;

C16 in GAP, Magma, Sage, TeX

C_{16}
% in TeX

G:=Group("C16");
// GroupNames label

G:=SmallGroup(16,1);
// by ID

G=gap.SmallGroup(16,1);
# by ID

G:=PCGroup([4,-2,-2,-2,-2,8,21,34]);
// Polycyclic

G:=Group<a|a^16=1>;
// generators/relations

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