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C₂²×C₅²×C₁₉⋊C₃ #19152890

order	5700
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅²×C₁₉⋊C₃

Splittings

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

Subgroups

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

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂²×C₅²×#4296, C₂²×C₅²⋊#4296, C₂²×C₁₉⋊C₃×C₅²⋊C₃, …
maximal normal subgroup of	C₂²×C₅²×#4296, C₂²×C₅²⋊#4296, C₂²×C₁₉⋊C₃×C₅²⋊C₃, …
maximal quotient of	C₂²×C₅²×#4294, C₂×C₅²×D₃×C₁₉⋊C₃, C₂²×C₃×C₅²×C₁₉⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 147);