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C₂×C₃×C₁₉×C₅⋊D₅ #19152900

order	5700
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅⋊D₅×#4294, C₂×C₁₉×(C₅⋊D₅)⋊C₉, C₂×(C₅⋊D₅)⋊#4294, …
maximal normal subgroup of	C₂×C₅⋊D₅×#4294, C₂×C₁₉×(C₅⋊D₅)⋊C₉, C₂×(C₅⋊D₅)⋊#4294, …
maximal quotient of	C₂×C₉×C₁₉×C₅⋊D₅, C₃×D₃×C₁₉×C₅⋊D₅, C₂×C₃×C₁₉×C₃⋊(C₅⋊D₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 157);