C₃×#1220 #67174

order	360
isoclinism	isoclinic class of Dic₃₀
automorphism	Aut(G) = C₂³×D₃×AGL(1,𝔽₅) (order 960) · Inn(G) = C₂×D₁₅ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 104);