Finite Group Databasebeta

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C₂×C₁₉×C₄₉⋊C₉ #30660488

order	16758
isoclinism	isoclinic class of C₄₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₄₉⋊C₃
commutator, hypocenter	C₄₉	C₂×C₉×C₁₉
Frattini	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)
Fitting	C₂×C₃×C₁₉×C₄₉	C₃
socle, prime radical	C₂×C₃×C₇×C₁₉	ΓL(1,𝔽₈)
cosocle	C₃×C₄₉	C₂×C₃×C₁₉
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₃×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16758

Conjugacy classes & character table

2166 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₉×C₄₉⋊C₉, C₁₉×Dic₄₉⋊C₉, (C₄₉⋊C₉)⋊Dic₁₉, …
maximal normal subgroup of	Dic₁₉×C₄₉⋊C₉, C₁₉×Dic₄₉⋊C₉, (C₄₉⋊C₉)⋊Dic₁₉, …
maximal quotient of	C₄×C₁₉×C₄₉⋊C₉, C₂²×C₁₉×C₄₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 15);