Finite Group Databasebeta

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D₃×C₁₉×C₅²⋊C₃ #22555569

order	8550
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	D₃×C₁₉×C₅²⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₅²⋊C₃)
unambiguous semidirect product	(C₅²×D₃)⋊(C₃×C₁₉)

Splittings

Fitting, socle	C₃×C₅²×C₁₉ ⋊ C₂×C₃
derived	C₃×C₅² ⋊ C₂×C₃×C₁₉
Hall	C₃×C₁₉×C₅²⋊C₃ ⋊ C₂
Hall	C₅²×C₁₉ ⋊ C₃×D₃
Hall	C₃×C₅²⋊C₃ ⋊ C₂×C₁₉
Sylow	C₅² ⋊ C₃×D₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₃×C₅²⋊C₃
commutator, hypocenter	C₃×C₅²	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₁₉

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

627 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₁₉×#3874, D₃×C₁₉⋊#3874, D₃×C₁₉×(C₅⋊D₅)⋊C₃, …
maximal normal subgroup of	D₃×C₁₉×#3874, D₃×C₁₉⋊#3874, D₃×C₁₉×(C₅⋊D₅)⋊C₃, …
maximal quotient of	Dic₃×C₁₉×C₅²⋊C₃, C₂×D₃×C₁₉×C₅²⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 107);