C₃×#1142 #66601

order	336
isoclinism	isoclinic class of #1141
automorphism	Aut(G) = C₂²×D₄×AGL(1,𝔽₇) (order 1344) · Inn(G) = C₂²⋊D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ SD₁₆
Sylow	C₇ ⋊ C₃×SD₁₆

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 70);