C₃×C₅×#123 #91852

order	480
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

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

156 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 928);