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C₃×C₁₉×C₁₁⋊Dic₁₁ #42119967

order	27588
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₃×C₁₉×C₁₁⋊Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₃×C₁₉×Dic₁₁)

Splittings

derived, Sylow	C₁₁² ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₁²×C₁₉ ⋊ C₄
Hall	C₁₁²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₁₁² ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₁₁⋊D₁₁
commutator, hypocenter	C₁₁²	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×C₁₁⋊D₁₁
Fitting, socle, prime radical	C₂×C₃×C₁₁²×C₁₉	C₂
cosocle	C₂×C₁₁²	C₂×C₃×C₁₉
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃×C₁₉

168 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, 59);