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C₉×D₁₉×C₅⋊D₅ #30685581

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₉×D₁₉×C₅⋊D₅

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₂²
derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×C₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×C₅⋊D₅

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4275

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 218);