Finite Group Databasebeta

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C₂×D₃×C₁₉×C₁₂₁ #42119939

order	27588
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉×C₁₂₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₁₉×C₁₂₁
unambiguous semidirect product	C₃⋊(C₂²×C₁₉×C₁₂₁)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₁₉×C₁₂₁)

Splittings

Fitting	C₂×C₃×C₁₉×C₁₂₁ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂²×C₁₉×C₁₂₁
Hall	C₃×C₁₉×C₁₂₁ ⋊ C₂²
Hall	C₃×C₁₂₁ ⋊ C₂²×C₁₉
Hall	C₃×C₁₉ ⋊ C₂²×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₂₁	D₃
commutator, hypocenter	C₃	C₂²×C₁₉×C₁₂₁
Frattini	C₁₁	C₂×D₃×C₁₁×C₁₉
Fitting	C₂×C₃×C₁₉×C₁₂₁	C₂
socle	C₂×C₃×C₁₁×C₁₉	C₂×C₁₁
prime radical	C₂×D₃×C₁₁×C₁₉	C₁₁
cosocle	C₃×C₁₁	C₂²×C₁₁×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₂₁

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13794

Conjugacy classes & character table

13794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 31);