C₃×#226 #3778

order	144
isoclinism	isoclinic class of #226
automorphism	Aut(G) = C₂²×S₄ (order 96) · Inn(G) = S₄ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, socle, hypercenter	C₂×C₃	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂×C₃
Frattini	C₂	C₃×S₄
Fitting	C₃×Q₈	D₃
prime radical	C₃×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

29 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

(1,15,10,7,5,6,12,13)(2,3,14,9,8,11,16,4)(17,18,19);(3,9,12)(4,10,11)(6,13,16)(7,14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 121);