C₅×#69123 #14315239

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

Aliases

direct product

C₅×#69123

Splittings

Fitting	C₃×C₅×#350 ⋊ C₂
Hall	C₃×C₅ ⋊ #2171
Sylow	C₃ ⋊ C₅×#2171

Subgroups

	subgroup	G/H
center	C₅×C₈	D₃×D₄
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×#350	C₂
socle	C₂×C₃×C₅	C₈×D₄
prime radical	C₅×#950	C₄
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₅×#350	D₃
hypocenter	C₃	C₅×#2171
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₈ ◁ C₅×#350

288 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)(9,12,14,22,15,27,32,17,16,28,33,35,13,26,31,36)(10,18,20,37,19,30,38,40,21,11,23,25,29,24,39,34);(6,7,8)(9,11)(10,17)(12,23)(13,30)(14,25)(15,24)(16,18)(19,35)(20,28)(21,36)(22,29)(26,38)(27,39)(31,40)(32,34)(33,37);(9,10,14,20,15,19,32,38,16,21,33,23,13,29,31,39)(11,22,25,27,24,17,34,28,18,35,37,26,30,36,40,12)

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, 40937);

C5×#69123 #14315239