Finite Group Databasebeta

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C₁₃×C₁₉×#3866 #49143166

order	36556
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×C₁₉×#3866

Splittings

Fitting, socle, Hall	C₁₃×C₁₉×C₃₇ ⋊ C₄
derived, Sylow	C₃₇ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₉×C₃₇ ⋊ C₄×C₁₃
Hall	C₁₃×C₃₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	#3866
commutator, hypocenter	C₃₇	C₄×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉×C₃₇	C₄
prime radical	C₁₃×C₁₉×D₃₇	C₂
cosocle	D₃₇	C₂×C₁₃×C₁₉
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₁₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9139

Conjugacy classes & character table

3211 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36556, 10);