Finite Group Databasebeta

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C₂×C₉×C₁₉×C₅⋊D₅ #30685621

order	17100
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₉×C₁₉×C₅⋊D₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₅×C₁₉)

Splittings

Fitting	C₂×C₅²×C₉×C₁₉ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂²×C₉×C₁₉
Hall	C₅²×C₉×C₁₉ ⋊ C₂²
Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×C₉ ⋊ C₂²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×C₅⋊D₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₅⋊D₅	C₃
cosocle	C₃×C₅²	C₂²×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₉×C₁₉

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 258);