C₂×#986 #5922

order	192
automorphism	Aut(G) = S₄×B(4,𝔽₂) (order 1536) · Inn(G) = C₂×S₄ · Out(G) = #120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂×#41 ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂³

	subgroup	G/H
center, socle	C₂²	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂³
Frattini	C₂	C₂²×S₄
Fitting	C₂×#41	D₃
hypercenter	C₂×C₄	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

169 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1481);