C₁₉×Dic₂₀ #13095068

order	1520
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×Dic₂₀

Splittings

Hall	C₅×C₁₉ ⋊ Q₁₆
Sylow	C₅ ⋊ Q₁₆×C₁₉

Subgroups

	subgroup	G/H
center	C₂×C₁₉	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₁₉
Frattini	C₄	C₂×D₅×C₁₉
Fitting	C₅×C₈×C₁₉	C₂
socle, prime radical	C₂×C₅×C₁₉	D₄
hypercenter	C₈×C₁₉	D₅
hypocenter	C₅	Q₁₆×C₁₉
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ C₈×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)(20,21,22,23,24,25,26,27)(28,35,34,33,32,31,30,29)(36,37,38,39,40);(20,28,24,32)(21,29,25,33)(22,30,26,34)(23,31,27,35)(37,40)(38,39)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 52);

C19×Dic20 #13095068