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C₅×C₉×C₁₉⋊AGL(1,𝔽₅) #30685573

order	17100
isoclinism	isoclinic class of C₁₉⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×C₁₉⋊AGL(1,𝔽₅)

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₄
derived	C₅×C₁₉ ⋊ C₄×C₅×C₉
Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₅²×C₉ ⋊ Dic₁₉
Hall	C₉×C₁₉ ⋊ C₅×AGL(1,𝔽₅)
Sylow	C₅² ⋊ C₉×Dic₁₉
Sylow	C₁₉ ⋊ C₅×C₉×AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	C₁₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₉	C₄×C₅×C₉
Frattini	C₃	C₃×C₅×C₁₉⋊AGL(1,𝔽₅)
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical	C₃×C₅×D₅×C₁₉	C₂×C₃
cosocle	C₃×D₅×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅×C₉

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 210);