Finite Group Databasebeta

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C₄×C₅×C₁₉×C₁₉⋊C₃ #36343147

order	21660
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₅×C₁₉×C₁₉⋊C₃
unambiguous semidirect product	(C₄×C₁₉)⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₄×C₅×C₁₉)⋊(C₃×C₁₉)

Splittings

Fitting, Hall	C₄×C₅×C₁₉² ⋊ C₃
derived	C₁₉ ⋊ C₃×C₄×C₅×C₁₉
Hall	C₅×C₁₉² ⋊ C₃×C₄
Hall	C₄×C₁₉² ⋊ C₃×C₅
Sylow	C₁₉² ⋊ C₃×C₄×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅×C₁₉	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃×C₄×C₅×C₁₉
Frattini	C₂	C₂×C₅×C₁₉×C₁₉⋊C₃
Fitting	C₄×C₅×C₁₉²	C₃
socle	C₂×C₅×C₁₉²	C₂×C₃
prime radical	C₂×C₅×C₁₉×C₁₉⋊C₃	C₂
cosocle	C₂×C₁₉	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₅×C₁₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1140

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 71);