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C₉×C₅⋊D₆₅ #19154338

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

Aliases

direct product	C₉×C₅⋊D₆₅
unambiguous semidirect product	C₅⋊(C₉×D₆₅)

Splittings

Fitting, Hall	C₅²×C₉×C₁₃ ⋊ C₂
derived, Hall	C₅²×C₁₃ ⋊ C₂×C₉
Hall	C₅²×C₉ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ C₅⋊D₅
Sylow	C₅² ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₅⋊D₆₅
commutator, hypocenter	C₅²×C₁₃	C₂×C₉
Frattini	C₃	C₃×C₅⋊D₆₅
Fitting	C₅²×C₉×C₁₃	C₂
socle	C₃×C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₉

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1476 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#13049928, C₉×#13049927, C₉×#13049931, …
maximal normal subgroup of	C₉×#13049928, C₉×#13049927, C₉×#13049931, …
maximal quotient of	C₉×#13049918, C₂×C₉×C₅⋊D₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 54);