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C₁₉×C₂²⋊(C₅²⋊C₃) #19152895

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

Aliases

direct product	C₁₉×C₂²⋊(C₅²⋊C₃)
unambiguous semidirect product	C₂²⋊(C₁₉×C₅²⋊C₃)
unambiguous semidirect product	C₅²⋊(A₄×C₁₉)

Splittings

Fitting, socle, Hall	C₂²×C₅²×C₁₉ ⋊ C₃
derived, Hall	C₂²×C₅² ⋊ C₃×C₁₉
Hall	C₅²×C₁₉ ⋊ A₄
Hall	C₂²×C₁₉ ⋊ C₅²⋊C₃
Sylow	C₅² ⋊ A₄×C₁₉
Sylow	C₂² ⋊ C₁₉×C₅²⋊C₃

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

684 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 152);