C₃×C₅×#396 #11751371

order	960
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

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

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 156 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) = 480

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5566);