Finite Group Databasebeta

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C₉×C₁₉×#6157 #49136221

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×#6157

Splittings

Fitting, Hall	C₉×C₁₉×C₅₃ ⋊ C₄
derived, Sylow	C₅₃ ⋊ C₄×C₉×C₁₉
Hall	C₁₉×C₅₃ ⋊ C₄×C₉
Hall	C₉×C₅₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	#6157
commutator, hypocenter	C₅₃	C₄×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×#6157
Fitting	C₉×C₁₉×C₅₃	C₄
socle	C₃×C₁₉×C₅₃	C₃×C₄
prime radical	C₃×C₁₉×D₅₃	C₂×C₃
cosocle	C₃×D₅₃	C₂×C₃×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₉×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9063

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 20);