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Dic₃×C₁₉×C₁₀₉ #38733135

order	24852
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₁₀₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉×C₁₀₉
unambiguous semidirect product	C₃⋊(C₄×C₁₉×C₁₀₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₉×C₁₀₉
Hall	C₃×C₁₉×C₁₀₉ ⋊ C₄
Hall	C₃×C₁₀₉ ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄×C₁₀₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₀₉	D₃
commutator, hypocenter	C₃	C₄×C₁₉×C₁₀₉
Frattini	C₂	D₃×C₁₉×C₁₀₉
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₁₀₉	C₂
cosocle	C₂×C₃	C₂×C₁₉×C₁₀₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₀₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24852

Conjugacy classes & character table

12426 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24852, 9);