Finite Group Databasebeta

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C₁₉×C₉⋊#595 #26042576

order	11628
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₉⋊#595
unambiguous semidirect product	C₉⋊(C₁₉×#595)

Splittings

Fitting, Hall	C₉×C₁₇×C₁₉ ⋊ C₄
derived, Hall	C₉×C₁₇ ⋊ C₄×C₁₉
Hall	C₁₇×C₁₉ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ #595
Sylow	C₁₇ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×#595

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#595
commutator, hypocenter	C₉×C₁₇	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#595
Fitting	C₉×C₁₇×C₁₉	C₄
socle	C₃×C₁₇×C₁₉	Dic₃
prime radical	C₃×C₁₉×D₁₇	D₃
cosocle	C₉×D₁₇	C₂×C₁₉
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

912 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 24);