Finite Group Databasebeta

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C₉×C₁₉×#595 #26042572

order	11628
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×#595

Splittings

Fitting, Hall	C₉×C₁₇×C₁₉ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₉×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₄×C₉
Hall	C₉×C₁₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	#595
commutator, hypocenter	C₁₇	C₄×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×#595
Fitting	C₉×C₁₇×C₁₉	C₄
socle	C₃×C₁₇×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×D₁₇	C₂×C₃
cosocle	C₃×D₁₇	C₂×C₃×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₉×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 20);