C₅×C₁₉×D₁₁ #14523452

order	2090
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₁₉×D₁₁

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₁₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1045

A minimal faithful permutation representation — 2 generators on 35 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)(25,26,27,28,29,30,31,32,33,34,35);(26,35)(27,34)(28,33)(29,32)(30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 4);