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C₁₃×C₄₉⋊C₉ #19153183

order	5733
isoclinism	isoclinic class of C₄₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₄₉⋊C₉
unambiguous semidirect product	C₄₉⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₄₉ ⋊ C₉×C₁₃
Hall	C₁₃×C₄₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₄₉⋊C₃
commutator, hypocenter	C₄₉	C₉×C₁₃
Frattini	C₃×C₇	C₁₃×ΓL(1,𝔽₈)
Fitting	C₃×C₁₃×C₄₉	C₃
socle	C₃×C₇×C₁₃	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₁₃

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

741 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₃×C₄₉⋊C₉, C₁₃×D₄₉⋊C₉, (C₄₉⋊C₉)⋊D₁₃, …
maximal normal subgroup of	D₁₃×C₄₉⋊C₉, C₁₃×D₄₉⋊C₉, (C₄₉⋊C₉)⋊D₁₃, …
maximal quotient of	C₂×C₁₃×C₄₉⋊C₉, C₁₃×C₂²⋊(C₄₉⋊C₉), C₅×C₁₃×C₄₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5733, 2);