C₅×#71252 #14291175

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#71252

Splittings

Hall	C₃×C₅ ⋊ #1663
Sylow	C₃ ⋊ C₅×#1663

Subgroups

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#491	C₂
socle, prime radical	C₂²×C₃×C₅	#120
hypercenter	C₅×#491	D₃
hypocenter	C₃	C₅×#1663
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#491

344 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 1920

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 16873);