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C₂×C₅²×D₃×C₁₉ #19152902

order	5700
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅²×D₃×C₁₉
unambiguous semidirect product	C₃⋊(C₂²×C₅²×C₁₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅²×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₉	D₃
commutator, hypocenter	C₃	C₂²×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅²×C₁₉

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅²×D₉×C₁₉, C₂×C₅²×D₃×C₁₉⋊C₃, C₂×D₃×C₁₉×C₅²⋊C₃, …
maximal normal subgroup of	C₂×C₅²×D₃×C₁₉⋊C₃, C₂×D₃×C₁₉×C₅²⋊C₃, C₂×D₃×C₁₉⋊(C₅²⋊C₃), …
maximal quotient of	C₂×C₅²×D₉×C₁₉, C₅²×D₃²×C₁₉, C₂×C₅²×C₃⋊D₃×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 159);