C₃×C₅×#1662 #14274696

order	1920
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃×C₅×#1662

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₃×C₅×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3)(4,5,6,7,8)(9,10,14,18)(11,19,21,24)(12,17,13,16)(15,22,23,20)(25,26,29,32)(27,33,35,40)(28,36,38,31)(30,37,39,34);(9,11)(10,15)(12,22)(13,20)(14,21)(16,24)(17,19)(18,23)(25,27,29,35)(26,30,32,39)(28,37,38,34)(31,40,36,33);(9,11)(10,15)(12,20)(13,22)(14,21)(16,19)(17,24)(18,23)(28,38)(31,36)(33,40)(34,37)

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 394);