C₃×C₅×D₁₂ #67167

order	360
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₄×D₃×D₄ (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₅×D₁₂
unambiguous semidirect product	C₄⋊(C₃×C₅×D₃)

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 97);