C₂²×C₃⋊D₁₅ #67231

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

Aliases

C₂²×C₃⋊D₁₅

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 161);