Finite Group Databasebeta

← Prev (#30685583) Next (#30685585) →

C₉×(C₅⋊D₅)⋊D₁₉ #30685584

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×(C₅⋊D₅)⋊D₁₉

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₂²
derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×C₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ D₅²
Sylow	C₅² ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₉×D₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₉	(C₅⋊D₅)⋊D₁₉
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₃×(C₅⋊D₅)⋊D₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle, cosocle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×(C₅⋊D₅)⋊D₁₉	C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₉

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 221);