C₃×#985 #64255

order	288
isoclinism	isoclinic class of #226
automorphism	Aut(G) = C₂³×S₄ (order 192) · Inn(G) = S₄ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₃×C₄	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₃
Frattini	C₂	C₂×C₃×S₄
Fitting	C₃×#41	D₃
socle	C₂×C₃	C₂×S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₃×C₄

83 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 903);