C₃×#986 #64256

order	288
automorphism	Aut(G) = C₂×D₄×S₄ (order 384) · Inn(G) = C₂×S₄ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₃×#41 ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂²×C₃

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

89 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 904);