D₃×C₇×Q₈ #66721

order	336
automorphism	Aut(G) = C₂²×C₃×D₃×S₄ (order 1728) · Inn(G) = C₂²×D₃ · Out(G) = C₂²×C₃×D₃
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

D₃×C₇×Q₈

76 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 190);