(C₂²⋊C₉)⋊C₉ #66355

order	324
isoclinism	isoclinic class of C₉⋊A₄
automorphism	Aut(G) = C₃²×C₃⋊(C₃⋊S₄) (order 1944) · Inn(G) = C₃×A₄ · Out(G) = C₃×C₃⋊D₃
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

(C₂²⋊C₉)⋊C₉

C₂² ⋊ C₉⋊C₉

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 2 generators on 22 points:

(1,4)(2,3)(5,6,8,7,9,11,10,12,13)(15,18,19)(17,21,22);(2,3,4)(14,15,17,16,19,21,20,18,22)

Polycyclic presentation:

3^4,2^2|a^3=d,b^3=c,b^a=bd,e^a=f,f^a=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 47);