C₄⋊(C₃⋊Dic₃) #3751

order	144
isoclinism	isoclinic class of #634
automorphism	Aut(G) = #120×AGL(2,𝔽₃) (order 13824) · Inn(G) = C₂×C₃⋊D₃ · Out(G) = D₄×GL(2,𝔽₃)
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃² ⋊ C₄⋊C₄

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 14 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 94);