C₅×#69303 #14314427

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#69303

Splittings

Fitting	C₃×C₅×#364 ⋊ C₂
Hall	C₃×C₅ ⋊ #2153
Sylow	C₃ ⋊ C₅×#2153

Subgroups

	subgroup	G/H
center	C₅×C₈	D₃×D₄
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×#364	C₂
socle	C₂×C₃×C₅	C₂×C₄⋊C₈
prime radical	C₂²×C₅×D₃	M₁₆
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₅×#364	D₃
hypocenter	C₃	C₅×#2153
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₈ ◁ C₅×#364

304 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)(7,8)(11,21)(16,30)(20,34)(22,24)(23,36)(29,37)(31,39)(35,40);(6,7,8)(9,11,12,22,15,21,14,24)(10,16,17,20,19,30,25,34)(13,23,26,29,28,36,27,37)(18,31,32,35,33,39,38,40);(9,10,13,18,14,17,27,32,15,19,28,33,12,25,26,38)(11,20,23,35,24,30,37,39,21,34,36,40,22,16,29,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40125);

C5×#69303 #14314427