C₅×#71246 #14291139

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

Aliases

direct product

C₅×#71246

Splittings

Fitting	C₃×C₅×#489 ⋊ C₂
Hall	C₃×C₅ ⋊ #1662
Sylow	C₃ ⋊ C₅×#1662

Subgroups

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#489	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5684	C₂
hypercenter	C₅×#489	D₃
hypocenter	C₃	C₅×#1662
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#489

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

normal subgroups only

This group has 392 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) = 960

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

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

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, 16837);