D₅×Dic₃ #1198

order	120
isoclinism	isoclinic class of D₃×D₅
automorphism	Aut(G) = C₂²×D₃×AGL(1,𝔽₅) (order 480) · Inn(G) = D₃×D₅ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

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

32 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)(4,5,7,8,6)(9,10,11,12);(1,2,3)(5,6)(7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(120, 8);