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C₂×C₁₉×(C₅⋊D₅)⋊C₃ #19152845

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

Aliases

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

Splittings

Fitting, socle	C₂×C₅²×C₁₉ ⋊ C₂×C₃
derived, Sylow	C₅² ⋊ C₂²×C₃×C₁₉
Hall	C₂×C₁₉×C₅⋊D₅ ⋊ C₃
Hall	C₁₉×C₅²⋊C₃ ⋊ C₂²
Hall	C₅²×C₁₉ ⋊ C₂²×C₃
Hall	C₂×C₅⋊D₅ ⋊ C₃×C₁₉
Hall	C₅²⋊C₃ ⋊ C₂²×C₁₉

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 102);