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C₃×C₁₃×D₇×ΓL(1,𝔽₈) #26039622

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₁₃×D₇×ΓL(1,𝔽₈)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₇×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₁₃×D₇×AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)⋊D₁₃, C₃×D₇×ΓL(1,𝔽₈)×D₁₃, …
maximal normal subgroup of	C₃×C₁₃×D₇×AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)⋊D₁₃, C₃×D₇×ΓL(1,𝔽₈)×D₁₃, …
maximal quotient of	C₃×C₁₃×ΓL(1,𝔽₈)×Dic₇, C₂×C₃×C₁₃×D₇×ΓL(1,𝔽₈)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 265);