C₃⋊(C₃⋊SL(2,ℤ/4)) #88974

order	432
isoclinism	isoclinic class of C₃⋊(C₃⋊S₄)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂×C₃³

Aliases

unambiguous semidirect product	C₃⋊(C₃⋊SL(2,ℤ/4))
unambiguous semidirect product	A₄⋊(C₃⋊Dic₃)

C₃²×A₄ ⋊ C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊S₄)
commutator, hypocenter	C₃²×A₄	C₄
Fitting, socle	C₂³×C₃²	D₃
prime radical, cosocle	C₂×C₃²×A₄	C₂
LCS	G ▷ C₃²×A₄
UCS	C₁ ◁ C₂

210 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 4 generators on 14 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 621);