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C₁₃×ΓL(1,𝔽₈)×D₂₁ #26039686

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×ΓL(1,𝔽₈)×D₂₁
unambiguous semidirect product	C₃⋊(C₁₃×D₇×ΓL(1,𝔽₈))

Splittings

Fitting, socle	C₃×C₇²×C₁₃ ⋊ C₂×C₃
derived	C₃×C₇² ⋊ C₂×C₃×C₁₃
Hall	C₃×C₇×C₁₃×ΓL(1,𝔽₈) ⋊ C₂
Hall	C₇²×C₁₃ ⋊ C₃×D₃
Hall	C₃×C₇×ΓL(1,𝔽₈) ⋊ C₂×C₁₃
Sylow	C₇² ⋊ C₃×D₃×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	ΓL(1,𝔽₈)×D₂₁
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₃

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₃×AGL(1,𝔽₇)×D₂₁, D₂₁×ΓL(1,𝔽₈)⋊D₁₃, C₁₃×(C₃⋊AGL(1,𝔽₇))⋊D₇, …
maximal normal subgroup of	C₁₃×AGL(1,𝔽₇)×D₂₁, D₂₁×ΓL(1,𝔽₈)⋊D₁₃, C₁₃×(C₃⋊AGL(1,𝔽₇))⋊D₇, …
maximal quotient of	C₁₃×ΓL(1,𝔽₈)×Dic₂₁, C₂×C₁₃×ΓL(1,𝔽₈)×D₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 329);