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C₃₁×C₁₉⋊AGL(1,𝔽₅) #26044528

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

Aliases

direct product	C₃₁×C₁₉⋊AGL(1,𝔽₅)
unambiguous semidirect product	C₁₉⋊(AGL(1,𝔽₅)×C₃₁)

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₃₁ ⋊ C₄
derived, Hall	C₅×C₁₉ ⋊ C₄×C₃₁
Hall	C₁₉×C₃₁ ⋊ AGL(1,𝔽₅)
Hall	C₅×C₃₁ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ AGL(1,𝔽₅)×C₃₁
Sylow	C₅ ⋊ C₃₁×Dic₁₉

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1271 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×(C₁₉⋊C₃)⋊AGL(1,𝔽₅), #47977643, #47977644, …
maximal normal subgroup of	C₃₁×(C₁₉⋊C₃)⋊AGL(1,𝔽₅), #47977643, #47977644, …
maximal quotient of	C₃×C₃₁×C₁₉⋊AGL(1,𝔽₅), C₃₁×C₃⋊(C₁₉⋊AGL(1,𝔽₅))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 22);