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C₁₉×D₄₉⋊C₉ #30660481

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₄₉⋊C₉
unambiguous semidirect product	D₄₉⋊(C₉×C₁₉)
unambiguous semidirect product	(C₄₉⋊C₉)⋊(C₂×C₁₉)

Splittings

derived, Sylow	C₄₉ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₄₉⋊C₉ ⋊ C₂
Hall	C₁₉×D₄₉ ⋊ C₉
Hall	C₁₉×C₄₉ ⋊ C₂×C₉
Hall	C₄₉⋊C₉ ⋊ C₂×C₁₉
Hall	D₄₉ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₄₉⋊C₃
commutator, hypocenter	C₄₉	C₂×C₉×C₁₉
Frattini	C₃×C₇	C₁₉×AGL(1,𝔽₇)
Fitting	C₃×C₁₉×C₄₉	C₂×C₃
socle	C₃×C₇×C₁₉	AGL(1,𝔽₇)
prime radical	C₃×C₁₉×D₄₉	C₃
cosocle	C₃×C₄₉	C₂×C₃×C₁₉
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8379

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₉×D₄₉⋊C₉, C₂×C₁₉×D₄₉⋊C₉
maximal normal subgroup of	D₁₉×D₄₉⋊C₉, C₂×C₁₉×D₄₉⋊C₉
maximal quotient of	C₁₉×Dic₄₉⋊C₉, C₂×C₁₉×D₄₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 8);