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C₂×C₁₃⋊(C₅²⋊C₉) #19154333

order	5850
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₁₃⋊(C₅²⋊C₉)
unambiguous semidirect product	(C₂×C₁₃)⋊(C₅²⋊C₉)
unambiguous semidirect product	(C₂×C₅²)⋊(C₁₃⋊C₉)

Splittings

derived, Hall	C₅²×C₁₃ ⋊ C₂×C₉
Hall	C₂×C₅²×C₁₃ ⋊ C₉
Hall	C₂×C₅² ⋊ C₁₃⋊C₉
Hall	C₂×C₁₃ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₂×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₅²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₁₃	C₂×C₉
Frattini	C₃	C₂×C₁₃⋊(C₅²⋊C₃)
Fitting, socle	C₂×C₃×C₅²×C₁₃	C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₂×C₃

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

666 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₁₃⋊(C₅²⋊C₉), #1039⋊(C₁₃⋊C₉), #26043239, …
maximal normal subgroup of	Dic₁₃⋊(C₅²⋊C₉), #1039⋊(C₁₃⋊C₉), #26043239, …
maximal quotient of	C₄×C₁₃⋊(C₅²⋊C₉), C₂²×C₁₃⋊(C₅²⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 49);