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C₄₉×C₁₃⋊C₉ #19153184

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

Aliases

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

Splittings

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

Subgroups

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

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5733, 3);