C₃×C₅×#2239 #14275273

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×C₅×#2239

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₅	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₅×M₁₆ ◁ G

248 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 480

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

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

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, 971);