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C₁₉×C₃⋊(C₃⋊(C₅⋊D₅)) #22555591

order	8550
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₅⋊D₅))
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))
unambiguous semidirect product	C₃⋊(C₁₉×C₃⋊(C₅⋊D₅))
unambiguous semidirect product	C₅⋊(C₁₉×C₃⋊D₁₅)

Splittings

Fitting, socle, Hall	C₃²×C₅²×C₁₉ ⋊ C₂
derived, Hall	C₃²×C₅² ⋊ C₂×C₁₉
Hall	C₅²×C₁₉ ⋊ C₃⋊D₃
Hall	C₃²×C₁₉ ⋊ C₅⋊D₅
Sylow	C₅² ⋊ C₃⋊D₃×C₁₉
Sylow	C₃² ⋊ C₁₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(C₃⋊(C₅⋊D₅))
commutator, hypocenter	C₃²×C₅²	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₁₉

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2166 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₉×C₃⋊(C₃⋊(C₅⋊D₅)), C₃⋊D₃×C₁₉×C₅⋊D₅, #30685912, …
maximal normal subgroup of	D₁₉×C₃⋊(C₃⋊(C₅⋊D₅)), C₃⋊D₃×C₁₉×C₅⋊D₅, #30685912, …
maximal quotient of	C₁₉×C₃⋊(C₃⋊#1039), C₂×C₁₉×C₃⋊(C₃⋊(C₅⋊D₅))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 129);