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C₃×D₅²×C₁₉ #19152861

order	5700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₅²×C₁₉
unambiguous semidirect product	(C₅×D₅)⋊(C₂×C₃×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₅²
commutator, hypocenter	C₅²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

912 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅²×#4294, C₉×D₅²×C₁₉, C₃×D₅²×C₁₉⋊C₃, …
maximal normal subgroup of	D₅²×#4294, C₉×D₅²×C₁₉, C₃×D₅²×C₁₉⋊C₃, …
maximal quotient of	C₉×D₅²×C₁₉, C₃²×D₅²×C₁₉, C₃×D₅×C₁₉×D₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 118);