order	240
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	Aut(G) = C₂²×D₃×AGL(1,𝔽₅) (order 480) · Inn(G) = D₃×AGL(1,𝔽₅) · Out(G) = C₂²
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	Dic₃×AGL(1,𝔽₅)
unambiguous semidirect product	(C₃×AGL(1,𝔽₅))⋊C₄
unambiguous semidirect product	ΓL(1,𝔽₁₆)⋊C₄

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₄²
Fitting, socle	C₂×C₃×C₅	C₂×C₄
prime radical, cosocle	C₂×C₃×D₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 95);