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C₂²×C₁₉×C₅²⋊C₃ #19152891

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

Aliases

C₂²×C₁₉×C₅²⋊C₃

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂²×C₁₉⋊C₃×C₅²⋊C₃, A₄×C₁₉×C₅²⋊C₃, C₅²⋊C₃×C₂²⋊(C₁₉⋊C₃), …
maximal normal subgroup of	C₂²×C₁₉⋊C₃×C₅²⋊C₃, A₄×C₁₉×C₅²⋊C₃, C₅²⋊C₃×C₂²⋊(C₁₉⋊C₃), …
maximal quotient of	C₂²×C₁₉×C₅²⋊C₉, C₂×D₃×C₁₉×C₅²⋊C₃, C₂²×C₃×C₁₉×C₅²⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 148);