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C₁₉⋊C₃×C₃⋊(C₅⋊D₅) #22555562

order	8550
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₅

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

351 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₉⋊C₃×C₃⋊(C₅⋊D₅), (C₃⋊(D₁₉⋊C₃))⋊(C₅⋊D₅), D₃×C₅⋊D₅×C₁₉⋊C₃, …
maximal normal subgroup of	D₁₉⋊C₃×C₃⋊(C₅⋊D₅), (C₃⋊(D₁₉⋊C₃))⋊(C₅⋊D₅), D₃×C₅⋊D₅×C₁₉⋊C₃, …
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, 100);