Finite Group Databasebeta

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C₂×C₁₉×(C₅⋊D₅)⋊C₉ #30685566

order	17100
isoclinism	isoclinic class of (C₅⋊D₅)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₁₉×(C₅⋊D₅)⋊C₉
unambiguous semidirect product	(C₂×C₅⋊D₅)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₅² ⋊ C₂²×C₉×C₁₉
Hall	C₁₉×C₅²⋊C₉ ⋊ C₂²
Hall	C₂×C₁₉×C₅⋊D₅ ⋊ C₉
Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²⋊C₉ ⋊ C₂²×C₁₉
Hall	C₂×C₅⋊D₅ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×(C₅⋊D₅)⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₅⋊D₅	C₃
cosocle	C₃×C₅²	C₂²×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 203);