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G = C17order 17

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial

Aliases: C17, also denoted Z17, SmallGroup(17,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C17
C1 — C17
C1 — C17
C1 — C17
C1 — C17

Generators and relations for C17
 G = < a | a17=1 >


Character table of C17

 class 117A17B17C17D17E17F17G17H17I17J17K17L17M17N17O17P
 size 11111111111111111
ρ111111111111111111    trivial
ρ21ζ1716ζ172ζ173ζ174ζ175ζ176ζ177ζ178ζ179ζ1710ζ1711ζ1712ζ1713ζ1714ζ1715ζ17    linear of order 17 faithful
ρ31ζ1715ζ174ζ176ζ178ζ1710ζ1712ζ1714ζ1716ζ17ζ173ζ175ζ177ζ179ζ1711ζ1713ζ172    linear of order 17 faithful
ρ41ζ1714ζ176ζ179ζ1712ζ1715ζ17ζ174ζ177ζ1710ζ1713ζ1716ζ172ζ175ζ178ζ1711ζ173    linear of order 17 faithful
ρ51ζ1713ζ178ζ1712ζ1716ζ173ζ177ζ1711ζ1715ζ172ζ176ζ1710ζ1714ζ17ζ175ζ179ζ174    linear of order 17 faithful
ρ61ζ1712ζ1710ζ1715ζ173ζ178ζ1713ζ17ζ176ζ1711ζ1716ζ174ζ179ζ1714ζ172ζ177ζ175    linear of order 17 faithful
ρ71ζ1711ζ1712ζ17ζ177ζ1713ζ172ζ178ζ1714ζ173ζ179ζ1715ζ174ζ1710ζ1716ζ175ζ176    linear of order 17 faithful
ρ81ζ1710ζ1714ζ174ζ1711ζ17ζ178ζ1715ζ175ζ1712ζ172ζ179ζ1716ζ176ζ1713ζ173ζ177    linear of order 17 faithful
ρ91ζ179ζ1716ζ177ζ1715ζ176ζ1714ζ175ζ1713ζ174ζ1712ζ173ζ1711ζ172ζ1710ζ17ζ178    linear of order 17 faithful
ρ101ζ178ζ17ζ1710ζ172ζ1711ζ173ζ1712ζ174ζ1713ζ175ζ1714ζ176ζ1715ζ177ζ1716ζ179    linear of order 17 faithful
ρ111ζ177ζ173ζ1713ζ176ζ1716ζ179ζ172ζ1712ζ175ζ1715ζ178ζ17ζ1711ζ174ζ1714ζ1710    linear of order 17 faithful
ρ121ζ176ζ175ζ1716ζ1710ζ174ζ1715ζ179ζ173ζ1714ζ178ζ172ζ1713ζ177ζ17ζ1712ζ1711    linear of order 17 faithful
ρ131ζ175ζ177ζ172ζ1714ζ179ζ174ζ1716ζ1711ζ176ζ17ζ1713ζ178ζ173ζ1715ζ1710ζ1712    linear of order 17 faithful
ρ141ζ174ζ179ζ175ζ17ζ1714ζ1710ζ176ζ172ζ1715ζ1711ζ177ζ173ζ1716ζ1712ζ178ζ1713    linear of order 17 faithful
ρ151ζ173ζ1711ζ178ζ175ζ172ζ1716ζ1713ζ1710ζ177ζ174ζ17ζ1715ζ1712ζ179ζ176ζ1714    linear of order 17 faithful
ρ161ζ172ζ1713ζ1711ζ179ζ177ζ175ζ173ζ17ζ1716ζ1714ζ1712ζ1710ζ178ζ176ζ174ζ1715    linear of order 17 faithful
ρ171ζ17ζ1715ζ1714ζ1713ζ1712ζ1711ζ1710ζ179ζ178ζ177ζ176ζ175ζ174ζ173ζ172ζ1716    linear of order 17 faithful

Permutation representations of C17
Regular action on 17 points - transitive group 17T1
Generators in S17
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)

G:=sub<Sym(17)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)])

G:=TransitiveGroup(17,1);

Matrix representation of C17 in GL1(𝔽103) generated by

100
G:=sub<GL(1,GF(103))| [100] >;

C17 in GAP, Magma, Sage, TeX

C_{17}
% in TeX

G:=Group("C17");
// GroupNames label

G:=SmallGroup(17,1);
// by ID

G=gap.SmallGroup(17,1);
# by ID

G:=PCGroup([1,-17]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^17=1>;
// generators/relations

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