C₃×C₅×B(4,𝔽₂) #11751432

order	960
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂×C₃×C₅	#120
commutator, Frattini, cosocle	C₂³	C₂³×C₃×C₅
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂³×C₃×C₅ ◁ G

396 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

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

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5627);