C₃×Dic₇⋊C₄ #66597

order	336
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂⁵×AGL(1,𝔽₇) (order 1344) · Inn(G) = C₂×D₇ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ C₄⋊C₄
Sylow	C₇ ⋊ C₃×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 336

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 66);