Copied to
clipboard

G = C19order 19

Cyclic group

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

Aliases: C19, also denoted Z19, SmallGroup(19,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C19
C1 — C19
C1 — C19
C1 — C19
C1 — C19

Generators and relations for C19
 G = < a | a19=1 >


Character table of C19

 class 119A19B19C19D19E19F19G19H19I19J19K19L19M19N19O19P19Q19R
 size 1111111111111111111
ρ11111111111111111111    trivial
ρ21ζ1918ζ192ζ193ζ194ζ195ζ196ζ197ζ198ζ199ζ1910ζ1911ζ1912ζ1913ζ1914ζ1915ζ1916ζ1917ζ19    linear of order 19 faithful
ρ31ζ1917ζ194ζ196ζ198ζ1910ζ1912ζ1914ζ1916ζ1918ζ19ζ193ζ195ζ197ζ199ζ1911ζ1913ζ1915ζ192    linear of order 19 faithful
ρ41ζ1916ζ196ζ199ζ1912ζ1915ζ1918ζ192ζ195ζ198ζ1911ζ1914ζ1917ζ19ζ194ζ197ζ1910ζ1913ζ193    linear of order 19 faithful
ρ51ζ1915ζ198ζ1912ζ1916ζ19ζ195ζ199ζ1913ζ1917ζ192ζ196ζ1910ζ1914ζ1918ζ193ζ197ζ1911ζ194    linear of order 19 faithful
ρ61ζ1914ζ1910ζ1915ζ19ζ196ζ1911ζ1916ζ192ζ197ζ1912ζ1917ζ193ζ198ζ1913ζ1918ζ194ζ199ζ195    linear of order 19 faithful
ρ71ζ1913ζ1912ζ1918ζ195ζ1911ζ1917ζ194ζ1910ζ1916ζ193ζ199ζ1915ζ192ζ198ζ1914ζ19ζ197ζ196    linear of order 19 faithful
ρ81ζ1912ζ1914ζ192ζ199ζ1916ζ194ζ1911ζ1918ζ196ζ1913ζ19ζ198ζ1915ζ193ζ1910ζ1917ζ195ζ197    linear of order 19 faithful
ρ91ζ1911ζ1916ζ195ζ1913ζ192ζ1910ζ1918ζ197ζ1915ζ194ζ1912ζ19ζ199ζ1917ζ196ζ1914ζ193ζ198    linear of order 19 faithful
ρ101ζ1910ζ1918ζ198ζ1917ζ197ζ1916ζ196ζ1915ζ195ζ1914ζ194ζ1913ζ193ζ1912ζ192ζ1911ζ19ζ199    linear of order 19 faithful
ρ111ζ199ζ19ζ1911ζ192ζ1912ζ193ζ1913ζ194ζ1914ζ195ζ1915ζ196ζ1916ζ197ζ1917ζ198ζ1918ζ1910    linear of order 19 faithful
ρ121ζ198ζ193ζ1914ζ196ζ1917ζ199ζ19ζ1912ζ194ζ1915ζ197ζ1918ζ1910ζ192ζ1913ζ195ζ1916ζ1911    linear of order 19 faithful
ρ131ζ197ζ195ζ1917ζ1910ζ193ζ1915ζ198ζ19ζ1913ζ196ζ1918ζ1911ζ194ζ1916ζ199ζ192ζ1914ζ1912    linear of order 19 faithful
ρ141ζ196ζ197ζ19ζ1914ζ198ζ192ζ1915ζ199ζ193ζ1916ζ1910ζ194ζ1917ζ1911ζ195ζ1918ζ1912ζ1913    linear of order 19 faithful
ρ151ζ195ζ199ζ194ζ1918ζ1913ζ198ζ193ζ1917ζ1912ζ197ζ192ζ1916ζ1911ζ196ζ19ζ1915ζ1910ζ1914    linear of order 19 faithful
ρ161ζ194ζ1911ζ197ζ193ζ1918ζ1914ζ1910ζ196ζ192ζ1917ζ1913ζ199ζ195ζ19ζ1916ζ1912ζ198ζ1915    linear of order 19 faithful
ρ171ζ193ζ1913ζ1910ζ197ζ194ζ19ζ1917ζ1914ζ1911ζ198ζ195ζ192ζ1918ζ1915ζ1912ζ199ζ196ζ1916    linear of order 19 faithful
ρ181ζ192ζ1915ζ1913ζ1911ζ199ζ197ζ195ζ193ζ19ζ1918ζ1916ζ1914ζ1912ζ1910ζ198ζ196ζ194ζ1917    linear of order 19 faithful
ρ191ζ19ζ1917ζ1916ζ1915ζ1914ζ1913ζ1912ζ1911ζ1910ζ199ζ198ζ197ζ196ζ195ζ194ζ193ζ192ζ1918    linear of order 19 faithful

Permutation representations of C19
Regular action on 19 points - transitive group 19T1
Generators in S19
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19)

G:=sub<Sym(19)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)])

G:=TransitiveGroup(19,1);

Matrix representation of C19 in GL1(𝔽191) generated by

150
G:=sub<GL(1,GF(191))| [150] >;

C19 in GAP, Magma, Sage, TeX

C_{19}
% in TeX

G:=Group("C19");
// GroupNames label

G:=SmallGroup(19,1);
// by ID

G=gap.SmallGroup(19,1);
# by ID

G:=PCGroup([1,-19]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^19=1>;
// generators/relations

׿
×
𝔽