order	168
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₇) (order 672) · Inn(G) = C₂×D₇ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₄

Splittings

Hall	C₃×C₇ ⋊ Q₈
Sylow	C₇ ⋊ C₃×Q₈

24 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(168, 24);