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C₁₉×AGL(1,𝔽₅)×C₃₁ #26044526

order	11780
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×AGL(1,𝔽₅)×C₃₁

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₃₁ ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₁₉×C₃₁
Hall	C₅×C₃₁ ⋊ C₄×C₁₉
Hall	C₅×C₁₉ ⋊ C₄×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₃₁	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₁₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₃₁	C₄
prime radical	D₅×C₁₉×C₃₁	C₂
cosocle	D₅	C₂×C₁₉×C₃₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₉×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2945 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×AGL(1,𝔽₅)×C₃₁⋊C₃, AGL(1,𝔽₅)×C₃₁×C₁₉⋊C₃, AGL(1,𝔽₅)×#13183714, …
maximal normal subgroup of	C₁₉×AGL(1,𝔽₅)×C₃₁⋊C₃, AGL(1,𝔽₅)×C₃₁×C₁₉⋊C₃, AGL(1,𝔽₅)×#13183714, …
maximal quotient of	C₃×C₁₉×AGL(1,𝔽₅)×C₃₁, C₁₉×C₃₁×ΓL(1,𝔽₁₆)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 20);