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C₅×C₁₉×C₉⋊AGL(1,𝔽₅) #30685586

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

Aliases

direct product	C₅×C₁₉×C₉⋊AGL(1,𝔽₅)
unambiguous semidirect product	C₉⋊(C₅×C₁₉×AGL(1,𝔽₅))

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₄
derived	C₅×C₉ ⋊ C₄×C₅×C₁₉
Hall	C₅²×C₁₉ ⋊ Dic₉
Hall	C₅²×C₉ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₅×AGL(1,𝔽₅)
Sylow	C₅² ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₅×C₁₉×AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₄×C₅×C₁₉
Frattini	C₃	C₅×C₁₉×ΓL(1,𝔽₁₆)
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₅×D₅×C₁₉	D₃
cosocle	C₉×D₅	C₂×C₅×C₁₉
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅×C₁₉

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 223);