C₁₁×D₉×C₆₇ #27210694

order	13266
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉×C₆₇
unambiguous semidirect product	C₉⋊(C₂×C₁₁×C₆₇)

Splittings

Fitting, Hall	C₉×C₁₁×C₆₇ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₁×C₆₇
Hall	C₉×C₆₇ ⋊ C₂×C₁₁
Hall	C₉×C₁₁ ⋊ C₂×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁×C₆₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₁×C₆₇
Frattini	C₃	D₃×C₁₁×C₆₇
Fitting	C₉×C₁₁×C₆₇	C₂
socle	C₃×C₁₁×C₆₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₁×C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 6633

A minimal faithful permutation representation — 2 generators on 87 points:

(2,4)(3,7)(5,8)(6,9)(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);(1,6,4,3,8,5,7,2,9)

Conjugacy classes & character table

4422 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁×D₉×D₆₇, D₉×D₁₁×C₆₇, D₉×D₇₃₇, …
maximal normal subgroup of	C₁₁×D₉×D₆₇, D₉×D₁₁×C₆₇, D₉×D₇₃₇, …
maximal quotient of	C₁₁×Dic₉×C₆₇, C₂×C₁₁×D₉×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 8);

C11×D9×C67 #27210694