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C₁₉×C₃₁⋊AGL(1,𝔽₅) #26044527

order	11780
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₃₁ ⋊ C₄
derived, Hall	C₅×C₃₁ ⋊ C₄×C₁₉
Hall	C₁₉×C₃₁ ⋊ AGL(1,𝔽₅)
Hall	C₅×C₁₉ ⋊ Dic₃₁
Sylow	C₃₁ ⋊ C₁₉×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₁₉×Dic₃₁

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1235 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×(C₃₁⋊C₃)⋊AGL(1,𝔽₅), #47977647, #47977648, …
maximal normal subgroup of	C₁₉×(C₃₁⋊C₃)⋊AGL(1,𝔽₅), #47977647, #47977648, …
maximal quotient of	C₃×C₁₉×C₃₁⋊AGL(1,𝔽₅), C₁₉×C₃⋊(C₃₁⋊AGL(1,𝔽₅))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 21);