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D₅×C₁₉×D₁₅ #19152883

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

Aliases

direct product	D₅×C₁₉×D₁₅
unambiguous semidirect product	(C₃×D₅)⋊(D₅×C₁₉)
unambiguous semidirect product	(C₅×D₅)⋊(D₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₂²
derived, Hall	C₃×C₅² ⋊ C₂²×C₁₉
Hall	C₅²×C₁₉ ⋊ C₂×D₃
Hall	C₃×C₁₉ ⋊ D₅²
Sylow	C₅² ⋊ C₂×D₃×C₁₉
Sylow	C₃ ⋊ D₅²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₁₅
commutator, hypocenter	C₃×C₅²	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

684 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×C₁₉×D₄₅, D₅×D₁₅×C₁₉⋊C₃, C₁₉×#3874⋊D₃, …
maximal normal subgroup of	D₅×D₁₅×C₁₉⋊C₃, C₃×D₅×C₁₉×D₁₅
maximal quotient of	D₅×C₁₉×D₄₅, C₃×D₅×C₁₉×D₁₅, D₅×C₁₉×C₃⋊D₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 140);