C₂²×C₅×C₃⋊D₃ #67230

order	360
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₅×C₃⋊D₃

	subgroup	G/H
center, hypercenter	C₂²×C₅	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂³×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₅

192 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 160);