C₃×C₅×#67 #67169

order	360
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂³×C₄×D₃ (order 192) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₃×C₅×#67

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 60

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 99);