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C₃×D₉×ΓL(1,𝔽₈) #11765718

order	1134
isoclinism	isoclinic class of D₉×ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

C₃×D₉×ΓL(1,𝔽₈)

Splittings

Fitting	C₃×C₇×C₉ ⋊ C₂×C₃
derived	C₇×C₉ ⋊ C₂×C₃²
Hall	C₃×C₉×ΓL(1,𝔽₈) ⋊ C₂
Sylow	C₇ ⋊ C₃²×D₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₉×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₃²
Frattini	C₃	C₃×D₃×ΓL(1,𝔽₈)
Fitting	C₃×C₇×C₉	C₂×C₃
socle	C₃²×C₇	C₃×D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₃

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 126

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×D₉×ΓL(1,𝔽₈), C₃×ΓL(1,𝔽₈)×AGL(1,ℤ/9), ΓL(1,𝔽₈)×D₉⋊C₉, …
maximal normal subgroup of	C₉×D₉×ΓL(1,𝔽₈), C₃×ΓL(1,𝔽₈)×AGL(1,ℤ/9), ΓL(1,𝔽₈)×D₉⋊C₉, …
maximal quotient of	C₉×D₉×ΓL(1,𝔽₈), ΓL(1,𝔽₈)×D₂₇⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 148);