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C₃×D₇×C₁₉×ΓL(1,𝔽₈) #30660792

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃×D₇×C₁₉×ΓL(1,𝔽₈)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₇×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₇×C₁₉×AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)⋊D₁₉, C₃×D₇×ΓL(1,𝔽₈)×D₁₉, …
maximal normal subgroup of	C₃×D₇×C₁₉×AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)⋊D₁₉, C₃×D₇×ΓL(1,𝔽₈)×D₁₉, …
maximal quotient of	C₃×C₁₉×ΓL(1,𝔽₈)×Dic₇, C₂×C₃×D₇×C₁₉×ΓL(1,𝔽₈)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 319);