C₅×#72146 #14297270

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#72146

Splittings

Hall	C₃×C₅ ⋊ #1794
Sylow	C₃ ⋊ C₅×#1794

Subgroups

	subgroup	G/H
center	C₄×C₅	#953
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#585	C₂
socle	C₂×C₃×C₅	#379
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#585	D₃
hypocenter	C₃	C₅×#1794
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#585

1096 conjugacy classes of subgroups.

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22968);

C5×#72146 #14297270