D₃×#672 #90932

order	480
isoclinism	isoclinic class of D₃×D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₁₆
Fitting, cosocle	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×C₅×D₃	C₈
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₈

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

(2,3)(4,5)(6,7,8)(9,10,11,14,12,15,17,20,13,16,18,21,19,22,23,24);(1,2,4,5,3)(7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 8);