C₃⋊(A₅⋊C₄) #10623944

order	720
isoclinism	isoclinic class of ΓL(2,𝔽₄)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₃⋊(A₅⋊C₄)
unambiguous semidirect product	A₅⋊Dic₃

C₃×A₅ ⋊ C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	ΓL(2,𝔽₄)
commutator, hypocenter	C₃×A₅	C₄
Fitting	C₂×C₃	S₅
socle, prime radical, cosocle	C₂×C₃×A₅	C₂
LCS	G ▷ C₃×A₅
UCS	C₁ ◁ C₂

79 conjugacy classes of subgroups.

μ_t(G) = 36

Permutation generators:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 413);