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C₅×D₃×D₅×C₁₉ #19152868

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

Aliases

direct product	C₅×D₃×D₅×C₁₉
unambiguous semidirect product	(C₅×D₃)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	D₁₅⋊(C₂×C₅×C₁₉)

Splittings

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

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₅×D₉×C₁₉, C₅×D₃×D₅×C₁₉⋊C₃, D₃×C₁₉×#3874, …
maximal normal subgroup of	C₅×D₃×D₅×C₁₉⋊C₃, C₃×C₅×D₃×D₅×C₁₉
maximal quotient of	C₅×D₅×D₉×C₁₉, C₃×C₅×D₃×D₅×C₁₉, C₅×D₅×C₃⋊D₃×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 125);