C₁₉×#689 #13095078

order	1520
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#689

Splittings

Hall	C₅×C₁₉ ⋊ Q₁₆
Sylow	C₅ ⋊ Q₁₆×C₁₉

Subgroups

	subgroup	G/H
center	C₂×C₁₉	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₁₉
Frattini	C₄	C₂×D₅×C₁₉
Fitting	C₅×Q₈×C₁₉	C₂
socle, prime radical	C₂×C₅×C₁₉	D₄
hypercenter	Q₈×C₁₉	D₅
hypocenter	C₅	Q₁₆×C₁₉
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ Q₈×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1520

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 62);

C19×#689 #13095078