C₁₁×Dic₈₉ #16840950

order	3916
isoclinism	isoclinic class of D₈₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×Dic₈₉

Splittings

derived, Sylow	C₈₉ ⋊ C₄×C₁₁
Hall	C₁₁×C₈₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₈₉
commutator, hypocenter	C₈₉	C₄×C₁₁
Frattini	C₂	C₁₁×D₈₉
Fitting, socle, prime radical	C₂×C₁₁×C₈₉	C₂
cosocle	C₂×C₈₉	C₂×C₁₁
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₁₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 104
transitive degree	μ_t(G) = 3916

A minimal faithful permutation representation — 2 generators on 104 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(12,14,13,15)(17,104)(18,103)(19,102)(20,101)(21,100)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×Dic₈₉, C₁₁×Dic₂₆₇, C₅×C₁₁×Dic₈₉, …
maximal normal subgroup of	C₃×C₁₁×Dic₈₉, C₅×C₁₁×Dic₈₉, C₁₁⋊C₅×Dic₈₉, …
maximal quotient of	C₃×C₁₁×Dic₈₉, C₁₁×Dic₂₆₇, C₅×C₁₁×Dic₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3916, 5);

C11×Dic89 #16840950