order	240
isoclinism	isoclinic class of D₃×D₅
automorphism	Aut(G) = C₂⁴×D₃×AGL(1,𝔽₅) (order 1920) · Inn(G) = D₃×D₅ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×D₅
commutator, hypocenter	C₃×C₅	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 25);