C₃×C₅×#537 #11756626

order	960
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

588 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10821);