C₁₁×D₉₅ #14523455

order	2090
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉₅
unambiguous semidirect product	C₅⋊(C₁₁×D₁₉)
unambiguous semidirect product	C₁₉⋊(D₅×C₁₁)

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₁₉ ⋊ C₂
derived, Hall	C₅×C₁₉ ⋊ C₂×C₁₁
Hall	C₁₁×C₁₉ ⋊ D₅
Hall	C₅×C₁₁ ⋊ D₁₉
Sylow	C₁₉ ⋊ D₅×C₁₁
Sylow	C₅ ⋊ C₁₁×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ 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);(13,16)(14,15)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₅×C₁₁×D₁₉, D₁₁×D₉₅, D₅₅⋊D₁₉, …
maximal normal subgroup of	D₅×C₁₁×D₁₉, D₁₁×D₉₅, D₅₅⋊D₁₉, …
maximal quotient of	C₁₁×Dic₉₅, C₂×C₁₁×D₉₅, C₇×C₁₁×D₉₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 7);

C11×D95 #14523455