(C₃⋊D₉)⋊C₄ #6191

order	216
isoclinism	isoclinic class of D₃×D₉
automorphism	Aut(G) = C₂²×D₃×AGL(1,ℤ/9) (order 1296) · Inn(G) = D₃×D₉ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

(C₃⋊D₉)⋊C₄

C₃×C₉ ⋊ C₂×C₄

58 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 16 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 28);