C₅×C₁₁×D₁₉ #14523451

order	2090
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₁×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₅×C₁₁)

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₅×C₁₁
Hall	C₁₁×C₁₉ ⋊ C₂×C₅
Hall	C₅×C₁₉ ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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);(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×D₁₁×D₁₉, D₅×C₁₁×D₁₉, D₁₉×D₅₅, …
maximal normal subgroup of	C₅×D₁₁×D₁₉, D₅×C₁₁×D₁₉, D₁₉×D₅₅, …
maximal quotient of	C₅×C₁₁×Dic₁₉, C₂×C₅×C₁₁×D₁₉, C₅×C₇×C₁₁×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 3);

C5×C11×D19 #14523451