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D₃×C₁₉×C₅⋊D₅ #19152879

order	5700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₃×C₁₉×C₅⋊D₅
unambiguous semidirect product	(C₅×D₃)⋊(D₅×C₁₉)

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₂²
derived, Hall	C₃×C₅² ⋊ C₂²×C₁₉
Hall	C₅²×C₁₉ ⋊ C₂×D₃
Hall	C₃×C₁₉ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ C₂×D₃×C₁₉
Sylow	C₃ ⋊ C₂×C₁₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₃×C₅⋊D₅
commutator, hypocenter	C₃×C₅²	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₁₉

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

798 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×C₁₉×C₅⋊D₅, D₃×C₅⋊D₅×C₁₉⋊C₃, D₃×C₁₉×(C₅⋊D₅)⋊C₃, …
maximal normal subgroup of	D₃×C₅⋊D₅×C₁₉⋊C₃, D₃×C₁₉×(C₅⋊D₅)⋊C₃, D₃×(C₅⋊D₅)⋊(C₁₉⋊C₃), …
maximal quotient of	D₉×C₁₉×C₅⋊D₅, C₃×D₃×C₁₉×C₅⋊D₅, C₃⋊D₃×C₁₉×C₅⋊D₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 136);