C₃×#1131 #66590

order	336
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂⁴×AGL(1,𝔽₇) (order 672) · Inn(G) = C₂×D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

general semilinear	ΓL(1,𝔽₁₆₉)
direct product	C₃×#1131

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 168

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 59);