C₁₉×D₅₅ #14523456

order	2090
isoclinism	isoclinic class of D₅₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₅₅
unambiguous semidirect product	C₅⋊(C₁₉×D₁₁)
unambiguous semidirect product	C₁₁⋊(D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₉	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ 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);(21,24)(22,23)(26,35)(27,34)(28,33)(29,32)(30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 8);