D₁₁×C₅₉ #13049893

order	1298
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₁×C₅₉
unambiguous semidirect product	C₁₁⋊(C₂×C₅₉)

Splittings

Fitting, socle, Hall	C₁₁×C₅₉ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₅₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 649

A minimal faithful permutation representation — 2 generators on 70 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(2,11)(3,10)(4,9)(5,8)(6,7)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₁×D₅₉, C₂×D₁₁×C₅₉, C₃×D₁₁×C₅₉, …
maximal normal subgroup of	D₁₁×D₅₉, C₂×D₁₁×C₅₉, C₃×D₁₁×C₅₉, …
maximal quotient of	Dic₁₁×C₅₉, C₂×D₁₁×C₅₉, C₃×D₁₁×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1298, 1);

D11×C59 #13049893