D₃×A₅ #67191

order	360
isoclinism	isoclinic class of D₃×A₅
automorphism	Aut(G) = D₃×S₅ (order 720) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×A₅
unambiguous semidirect product	C₃⋊(C₂×A₅)

Fitting	C₃ ⋊ C₂×A₅
socle, derived	C₃×A₅ ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₃×A₅	C₂
Fitting, cosocle	C₃	C₂×A₅
LCS	G ▷ C₃×A₅
UCS	C₁

47 conjugacy classes of subgroups.

minimal degree	μ(G) = 8
transitive degree	μ_t(G) = 15

A minimal faithful permutation representation — 2 generators on 8 points:

(2,3)(4,5,6);(1,2,3)(6,8,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 121);