Finite Group Databasebeta

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C₉×C₁₉×#1039 #30685448

order	17100
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₉×C₁₉×#1039

Splittings

derived, Sylow	C₅² ⋊ C₄×C₉×C₁₉
Hall	C₅²×C₉×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₅²×C₉ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×C₅⋊D₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₅²	C₂×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₉×C₁₉

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

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, 85);