Finite Group Databasebeta

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C₄×C₁₉×C₁₃₉⋊C₃ #44540064

order	31692
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10564

Conjugacy classes & character table

3724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31692, 2);