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D₃×ΓL(1,𝔽₈)×C₄₃ #19129387

order	5418
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×ΓL(1,𝔽₈)×C₄₃
unambiguous semidirect product	C₃⋊(C₂×ΓL(1,𝔽₈)×C₄₃)
unambiguous semidirect product	(D₃×C₇)⋊(C₃×C₄₃)

Splittings

Fitting, socle	C₃×C₇×C₄₃ ⋊ C₂×C₃
derived	C₃×C₇ ⋊ C₂×C₃×C₄₃
Hall	C₃×ΓL(1,𝔽₈)×C₄₃ ⋊ C₂
Hall	C₇×C₄₃ ⋊ C₃×D₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂×C₄₃
Sylow	C₇ ⋊ C₃×D₃×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	D₃×ΓL(1,𝔽₈)
commutator, hypocenter	C₃×C₇	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₄₃	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

645 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₇)×C₄₃, D₃×ΓL(1,𝔽₈)⋊D₄₃, D₃×ΓL(1,𝔽₈)×D₄₃, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₄₃, D₃×ΓL(1,𝔽₈)⋊D₄₃, D₃×ΓL(1,𝔽₈)×D₄₃, …
maximal quotient of	Dic₃×ΓL(1,𝔽₈)×C₄₃, C₂×D₃×ΓL(1,𝔽₈)×C₄₃, C₅×D₃×ΓL(1,𝔽₈)×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5418, 66);