C₃×C₅×#2203 #14275237

order	1920
nilpotency class	4
isoclinism	isoclinic class of #2202
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃×C₅×#2203

Subgroups

	subgroup	G/H
center, socle	C₂×C₃×C₅	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂³×C₃×C₅
prime radical	C₃×C₅×#454	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×Q₈ ◁ G

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

normal subgroups only

This group has 432 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)(11,20)(12,24)(13,16)(14,19)(15,21)(17,27)(18,29)(22,37)(23,35)(25,33)(26,34)(28,38)(30,36)(31,39)(32,40);(9,11,14,23)(10,15,19,33)(12,25,27,21)(13,28,29,22)(16,31,18,32)(17,35,24,20)(26,39,30,40)(34,37,36,38);(10,16)(13,29)(15,31)(17,36)(18,19)(20,37)(22,28)(24,34)(26,30)(32,33)(35,38)(39,40)

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, 935);