Finite Group Databasebeta

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C₃×C₁₉×Dic₁₂₁ #42119915

order	27588
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₁₂₁
unambiguous semidirect product	C₁₂₁⋊(C₃×C₄×C₁₉)

Splittings

derived, Sylow	C₁₂₁ ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₉×C₁₂₁ ⋊ C₄
Hall	C₁₉×C₁₂₁ ⋊ C₃×C₄
Hall	C₃×C₁₂₁ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₂₁
commutator, hypocenter	C₁₂₁	C₃×C₄×C₁₉
Frattini	C₂×C₁₁	C₃×C₁₉×D₁₁
Fitting	C₂×C₃×C₁₉×C₁₂₁	C₂
socle, prime radical	C₂×C₃×C₁₁×C₁₉	D₁₁
cosocle	C₂×C₁₂₁	C₂×C₃×C₁₉
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₃×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 27588

Conjugacy classes & character table

7068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 7);