Finite Group Databasebeta

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C₄×C₁₉×C₃₁⋊C₉ #35234305

order	21204
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₁₉×C₃₁⋊C₉
unambiguous semidirect product	(C₄×C₃₁)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₃₁ ⋊ C₄×C₉×C₁₉
Hall	C₄×C₁₉×C₃₁ ⋊ C₉
Hall	C₁₉×C₃₁ ⋊ C₄×C₉
Hall	C₄×C₃₁ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₉	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₂×C₁₉×C₃₁⋊C₃
Fitting	C₃×C₄×C₁₉×C₃₁	C₃
socle, prime radical	C₂×C₃×C₁₉×C₃₁	C₂×C₃
cosocle	C₂×C₃×C₃₁	C₂×C₃×C₁₉
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₄×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 21204

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21204, 2);