order	336
isoclinism	isoclinic class of D₃×AGL(1,𝔽₈)
automorphism	Aut(G) = D₃×AΓL(1,𝔽₈) (order 1008) · Inn(G) = G · Out(G) = C₃
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×AGL(1,𝔽₈)
unambiguous semidirect product	C₃⋊(C₂×AGL(1,𝔽₈))
unambiguous semidirect product	(C₂³×D₃)⋊C₇
unambiguous semidirect product	(C₃×AGL(1,𝔽₈))⋊C₂

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂³×C₃	C₂×C₇
LCS	G ▷ C₂³×C₃
UCS	C₁

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

(2,3,4,6,8,5,7)(10,11);(1,5)(2,3)(4,8)(6,7)(9,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 211);