C₂²×C₃×D₁₅ #67229

order	360
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃×D₁₅

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₃

138 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 159);