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C₂×C₉×C₅⋊D₉₅ #30685622

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

Aliases

direct product	C₂×C₉×C₅⋊D₉₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₉₅)

Splittings

Fitting	C₂×C₅²×C₉×C₁₉ ⋊ C₂
derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×C₉×C₁₉ ⋊ C₂²
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	C₂×C₉	C₅⋊D₉₅
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₃×C₅⋊D₉₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅⋊D₉₅	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₉

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

Conjugacy classes & character table

4302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 259);