C₃⋊D₃×Dic₅ #67136

order	360
isoclinism	isoclinic class of D₅×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₃⋊D₃
commutator, hypocenter	C₃²×C₅	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₅	C₂²
prime radical	C₂×C₅×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 66);