C₃⋊(#120⋊C₃) #63763

order	288
isoclinism	isoclinic class of C₃⋊(#120⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂²

Aliases

unambiguous semidirect product	C₃⋊(#120⋊C₃)
unambiguous semidirect product	#953⋊C₃

C₂⁴×C₃ ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂⁴×C₃	C₂×C₃
Frattini	C₂²	D₃×A₄
socle	C₂²×C₃	C₂×A₄
LCS	G ▷ C₂⁴×C₃
UCS	C₁

77 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

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

Polycyclic presentation:

2,3,2^4,3|c^a=cef,d^a=df,g^a=g^2,c^b=cd,d^b=c,e^b=f,f^b=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 411);