C₃²×C₅×#120 #13088229

order	1440
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃²×C₅ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₃²×C₅×#120

	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

780 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 360

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4546);