C₃×C₅×#2208 #14275242

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×D₈	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

332 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3)(4,5,6,7,8)(10,12)(13,14,17,21)(15,18,24,27)(16,25,23,20)(19,28,26,22);(9,10,11,12);(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 940);