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Dic₃×C₁₉×C₁₃₉ #44540071

order	31692
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉×C₁₃₉
unambiguous semidirect product	C₃⋊(C₄×C₁₉×C₁₃₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₉×C₁₃₉
Hall	C₃×C₁₉×C₁₃₉ ⋊ C₄
Hall	C₃×C₁₃₉ ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄×C₁₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₃₉	D₃
commutator, hypocenter	C₃	C₄×C₁₉×C₁₃₉
Frattini	C₂	D₃×C₁₉×C₁₃₉
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₁₃₉	C₂
cosocle	C₂×C₃	C₂×C₁₉×C₁₃₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₃₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 31692

Conjugacy classes & character table

15846 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31692, 9);