C₅×#71361 #14293579

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅×#71361

Splittings

Hall	C₃×C₅ ⋊ #1710
Sylow	C₃ ⋊ C₅×#1710

Subgroups

	subgroup	G/H
center	C₂²×C₅	#940
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#500	C₂
socle, prime radical	C₂²×C₃×C₅	#127
hypercenter	C₅×#500	D₃
hypocenter	C₃	C₅×#1710
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#500

336 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 130 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)(6,7)(10,15)(14,23)(16,20)(17,24)(25,27,29,35,28,34,36,40)(26,31,32,33,30,38,37,39);(7,8)(9,11,12,18,13,19,21,22)(10,14,16,17,15,23,20,24)(26,30)(31,38)(32,37)(33,39);(9,10,13,15)(11,17,19,24)(12,20,21,16)(14,22,23,18)(25,26)(27,33)(28,30)(29,37)(31,35)(32,36)(34,39)(38,40)

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19277);