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C₁₉×C₃⋊#5997 #26014027

order	11172
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₉×C₃⋊#5997
unambiguous semidirect product	C₃⋊(C₁₉×#5997)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₉ ⋊ C₄
derived, Hall	C₃×C₇² ⋊ C₄×C₁₉
Hall	C₇²×C₁₉ ⋊ Dic₃
Hall	C₃×C₁₉ ⋊ #5997
Sylow	C₇² ⋊ Dic₃×C₁₉
Sylow	C₃ ⋊ C₁₉×#5997

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#5997
commutator, hypocenter	C₃×C₇²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₄
prime radical	C₃×C₁₉×C₇⋊D₇	C₂
cosocle	C₃×C₇⋊D₇	C₂×C₁₉
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

798 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13183544, C₁₉×C₉⋊#5997, C₁₉⋊C₃×C₃⋊#5997, …
maximal normal subgroup of	C₁₉⋊C₃×C₃⋊#5997, C₁₉×C₃⋊(#5997⋊C₃), C₃⋊#26013942, …
maximal quotient of	C₁₉×C₉⋊#5997, C₃×C₁₉×C₃⋊#5997, C₁₉×C₃⋊(C₃⋊#5997)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 289);