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G = C₃²  order 9 = 3²

Elementary abelian group of type [3,3]

direct product, p-group, elementary abelian, monomial

Aliases: C₃², SmallGroup(9,2)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Generators and relations for C₃²
 G = < a,b | a³=b³=1, ab=ba >

Character table of C₃²

(1 2 3)(4 5 6)(7 8 9)

(1 9 5)(2 7 6)(3 8 4)

G:=sub<Sym(9)| (1,2,3)(4,5,6)(7,8,9), (1,9,5)(2,7,6)(3,8,4)>;

G:=Group( (1,2,3)(4,5,6)(7,8,9), (1,9,5)(2,7,6)(3,8,4) );

G=PermutationGroup([[(1,2,3),(4,5,6),(7,8,9)], [(1,9,5),(2,7,6),(3,8,4)]])

G:=TransitiveGroup(9,2);

C₃² is a maximal subgroup of   C₃⋊S₃  He₃  3_-¹⁺²
C₃² is a maximal quotient of   He₃  3_-¹⁺²

Matrix representation of C₃² ►in GL₂(𝔽₇) generated by

G:=sub<GL(2,GF(7))| [2,0,0,1],[1,0,0,4] >;

C₃² in GAP, Magma, Sage, TeX

C_3^2

% in TeX

G:=Group("C3^2");

// GroupNames label

G:=SmallGroup(9,2);

// by ID

G=gap.SmallGroup(9,2);

# by ID

G:=PCGroup([2,-3,3]:ExponentLimit:=1);

// Polycyclic

G:=Group<a,b|a^3=b^3=1,a*b=b*a>;

// generators/relations

Export

Subgroup lattice of C₃² in TeX
Character table of C₃² in TeX