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D₃×ΓL(1,𝔽₈)×C₇₃ #22604137

order	9198
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×ΓL(1,𝔽₈)×C₇₃
unambiguous semidirect product	C₃⋊(C₂×ΓL(1,𝔽₈)×C₇₃)
unambiguous semidirect product	(D₃×C₇)⋊(C₃×C₇₃)

Splittings

Fitting, socle	C₃×C₇×C₇₃ ⋊ C₂×C₃
derived	C₃×C₇ ⋊ C₂×C₃×C₇₃
Hall	C₃×ΓL(1,𝔽₈)×C₇₃ ⋊ C₂
Hall	C₇×C₇₃ ⋊ C₃×D₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂×C₇₃
Sylow	C₇ ⋊ C₃×D₃×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇₃	D₃×ΓL(1,𝔽₈)
commutator, hypocenter	C₃×C₇	C₂×C₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₇)×C₇₃, D₃×ΓL(1,𝔽₈)⋊D₇₃, D₃×ΓL(1,𝔽₈)×D₇₃, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₇₃, D₃×ΓL(1,𝔽₈)⋊D₇₃, D₃×ΓL(1,𝔽₈)×D₇₃, …
maximal quotient of	Dic₃×ΓL(1,𝔽₈)×C₇₃, C₂×D₃×ΓL(1,𝔽₈)×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 62);