Finite Group Databasebeta

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C₃×C₁₃×C₁₉×#261 #50310475

order	38532
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₁₃×C₁₉×#261

Splittings

Fitting, socle, Hall	C₃×C₁₃²×C₁₉ ⋊ C₄
derived	C₁₃ ⋊ C₃×C₄×C₁₃×C₁₉
Hall	C₁₃²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₁₃² ⋊ C₄×C₁₉
Sylow	C₁₃² ⋊ C₃×C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	#261
commutator, hypocenter	C₁₃	C₃×C₄×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₉	C₄
prime radical	C₃×C₁₃×C₁₉×D₁₃	C₂
cosocle	D₁₃	C₂×C₃×C₁₃×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2964

Conjugacy classes & character table

5187 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 357);