Dic₃×#170 #91168

order	480
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₄×C₈
Fitting, socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×Dic₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 244);