C₃×C₅×#2201 #14275235

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2199
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃×C₅×#2201

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₅	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂³×C₃×C₅
prime radical	C₃×C₅×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×D₄ ◁ G

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

normal subgroups only

This group has 452 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)(11,19)(12,16)(13,17)(14,18)(15,21)(20,36)(22,35)(23,34)(24,30)(25,31)(26,33)(27,37)(28,38)(29,39)(32,40);(9,11,14,22)(10,15,18,28)(12,23,25,20)(13,21,26,38)(16,29,31,27)(17,19,33,35)(24,39,40,37)(30,34,32,36);(9,12,14,25)(10,16,18,31)(11,20,22,23)(13,24,26,40)(15,27,28,29)(17,32,33,30)(19,34,35,36)(21,37,38,39)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 933);