C₉×D₇₃₇ #27210693

order	13266
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₇₃₇
unambiguous semidirect product	C₁₁⋊(C₉×D₆₇)

Splittings

Fitting, Hall	C₉×C₁₁×C₆₇ ⋊ C₂
derived, Hall	C₁₁×C₆₇ ⋊ C₂×C₉
Hall	C₉×C₆₇ ⋊ D₁₁
Hall	C₉×C₁₁ ⋊ D₆₇
Sylow	C₆₇ ⋊ C₉×D₁₁
Sylow	C₁₁ ⋊ C₉×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇₃₇
commutator, hypocenter	C₁₁×C₆₇	C₂×C₉
Frattini	C₃	C₃×D₇₃₇
Fitting	C₉×C₁₁×C₆₇	C₂
socle, cosocle	C₃×C₁₁×C₆₇	C₂×C₃
prime radical	C₃×D₇₃₇	C₃
LCS	G ▷ C₁₁×C₆₇
UCS	C₁ ◁ C₉

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:

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

Conjugacy classes & character table

3330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₁×D₆₇, D₉×D₇₃₇, D₉₉⋊D₆₇, …
maximal normal subgroup of	C₉×D₁₁×D₆₇, D₉×D₇₃₇, D₉₉⋊D₆₇, …
maximal quotient of	C₉×Dic₇₃₇, C₂×C₉×D₇₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 7);

C9×D737 #27210693