Finite Group Databasebeta

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C₁₉×C₃₁×C₂²⋊C₉ #35234356

order	21204
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×C₃₁×C₂²⋊C₉
unambiguous semidirect product	C₂²⋊(C₉×C₁₉×C₃₁)

Splittings

derived, Sylow	C₂² ⋊ C₉×C₁₉×C₃₁
Hall	C₂²×C₁₉×C₃₁ ⋊ C₉
Hall	C₂²×C₃₁ ⋊ C₉×C₁₉
Hall	C₂²×C₁₉ ⋊ C₉×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉×C₃₁	A₄
commutator, hypocenter	C₂²	C₉×C₁₉×C₃₁
Frattini	C₃	A₄×C₁₉×C₃₁
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₃₁	C₃
cosocle	C₂²×C₃	C₃×C₁₉×C₃₁
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₉×C₃₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10602

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(21204, 53);