C₃×C₇×D₁₂ #92709

order	504
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂²×C₃×D₃×D₄ (order 576) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₇×D₁₂
unambiguous semidirect product	C₄⋊(C₃×D₃×C₇)

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 135);