C₃²×C₅×#127 #13088236

order	1440
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃²×C₅ · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₃²×C₅×#127

	subgroup	G/H
center, socle	C₂²×C₃²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃²×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₅ ◁ G

648 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4553);