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C₃×C₅×C₁₉×AGL(1,𝔽₅) #19152851

order	5700
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₅×C₁₉×AGL(1,𝔽₅)

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₄
derived	C₅ ⋊ C₃×C₄×C₅×C₁₉
Hall	C₅²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₅² ⋊ C₄×C₁₉
Sylow	C₅² ⋊ C₃×C₄×C₁₉

Subgroups

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

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×AGL(1,𝔽₅)×#4294, C₅×C₉×C₁₉×AGL(1,𝔽₅), C₃×C₅×AGL(1,𝔽₅)×C₁₉⋊C₃, …
maximal normal subgroup of	C₅×AGL(1,𝔽₅)×#4294, C₅×C₉×C₁₉×AGL(1,𝔽₅), C₃×C₅×AGL(1,𝔽₅)×C₁₉⋊C₃, …
maximal quotient of	C₅×C₉×C₁₉×AGL(1,𝔽₅), C₃²×C₅×C₁₉×AGL(1,𝔽₅), C₃×C₅×C₁₉×ΓL(1,𝔽₁₆)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 108);