C₂×#226 #981

order	96
isoclinism	isoclinic class of #226
automorphism	Aut(G) = D₄×S₄ (order 192) · Inn(G) = S₄ · Out(G) = D₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle, hypercenter	C₂²	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²
Frattini	C₂	C₂×S₄
Fitting	C₂×Q₈	D₃
prime radical	C₂×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

39 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 188);