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C₅×C₁₉×ΓL(1,𝔽₁₆) #19152865

order	5700
isoclinism	isoclinic class of ΓL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×ΓL(1,𝔽₁₆)
unambiguous semidirect product	C₃⋊(C₅×C₁₉×AGL(1,𝔽₅))

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₄
derived	C₃×C₅ ⋊ C₄×C₅×C₁₉
Hall	C₅²×C₁₉ ⋊ Dic₃
Hall	C₃×C₅² ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₅×AGL(1,𝔽₅)
Sylow	C₅² ⋊ Dic₃×C₁₉
Sylow	C₃ ⋊ C₅×C₁₉×AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₉	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₄×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₅×C₁₉

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 122);