D₃×Dic₁₅ #67148

order	360
isoclinism	isoclinic class of D₃×D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×Dic₁₅
unambiguous semidirect product	(C₃×D₃)⋊Dic₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₅
commutator, hypocenter	C₃²×C₅	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₅	C₂²
prime radical	C₂×C₃×C₅×D₃	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 78);