Finite Group Databasebeta

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C₉×C₁₃×C₅⋊D₅ #19154337

order	5850
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₉×C₁₃×C₅⋊D₅
unambiguous semidirect product	C₅⋊(C₉×D₅×C₁₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×C₅⋊D₅
Fitting	C₅²×C₉×C₁₃	C₂
socle	C₃×C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₉×C₁₃

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₃×#1043, C₉×#13049929, C₉×C₁₃×#1044, …
maximal normal subgroup of	C₉×C₁₃×#1043, C₉×#13049929, C₉×C₁₃×#1044, …
maximal quotient of	C₉×C₁₃×#1039, C₂×C₉×C₁₃×C₅⋊D₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 53);