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C₃×ΓL(1,𝔽₈)×D₉₁ #26039627

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

C₃×ΓL(1,𝔽₈)×D₉₁

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃	ΓL(1,𝔽₈)×D₉₁
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×AGL(1,𝔽₇)×D₉₁, C₃×(ΓL(1,𝔽₈)⋊D₇)⋊D₁₃, C₃×D₇×ΓL(1,𝔽₈)×D₁₃, …
maximal normal subgroup of	C₃×AGL(1,𝔽₇)×D₉₁, C₃×(ΓL(1,𝔽₈)⋊D₇)⋊D₁₃, C₃×D₇×ΓL(1,𝔽₈)×D₁₃, …
maximal quotient of	C₃×ΓL(1,𝔽₈)×Dic₉₁, C₂×C₃×ΓL(1,𝔽₈)×D₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 270);