C₃×C₅×#2011 #14275045

order	1920
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

1020 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 743);