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G = D₁₇  order 34 = 2·17

Dihedral group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: D₁₇, C₁₇⋊C₂, sometimes denoted D₃₄ or Dih₁₇ or Dih₃₄, SmallGroup(34,1)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for D₁₇
 G = < a,b | a¹⁷=b²=1, bab=a^-1 >

Character table of D₁₇

(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)

(1 17)(2 16)(3 15)(4 14)(5 13)(6 12)(7 11)(8 10)

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

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

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

G:=TransitiveGroup(17,2);

D₁₇ is a maximal subgroup of
 C₁₇⋊C₄
 D_17p: D₅₁  D₈₅  D₁₁₉  D₁₈₇  D₂₂₁ ...
D₁₇ is a maximal quotient of
 Dic₁₇
 D_17p: D₅₁  D₈₅  D₁₁₉  D₁₈₇  D₂₂₁ ...

Matrix representation of D₁₇ ►in GL₂(𝔽₁₀₃) generated by

G:=sub<GL(2,GF(103))| [27,1,102,0],[27,7,102,76] >;

D₁₇ in GAP, Magma, Sage, TeX

D_{17}

% in TeX

G:=Group("D17");

// GroupNames label

G:=SmallGroup(34,1);

// by ID

G=gap.SmallGroup(34,1);

# by ID

G:=PCGroup([2,-2,-17,129]);

// Polycyclic

G:=Group<a,b|a^17=b^2=1,b*a*b=a^-1>;

// generators/relations

Export

Subgroup lattice of D₁₇ in TeX
Character table of D₁₇ in TeX