Dic₃⋊(C₃⋊Dic₃) #88805

order	432
isoclinism	isoclinic class of #6290
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃³ ⋊ C₄⋊C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×C₃⋊D₃
commutator	C₂×C₃³	C₂×C₄
Fitting, socle, prime radical, cosocle	C₂²×C₃³	C₂²
hypocenter	C₃³	C₄⋊C₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂²

220 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 452);