Finite Group Databasebeta

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C₃×C₁₉×C₃⋊#1039 #30685687

order	17100
isoclinism	isoclinic class of C₃⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₃×C₁₉×C₃⋊#1039
unambiguous semidirect product	C₃⋊(C₃×C₁₉×#1039)

Splittings

derived	C₃×C₅² ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₅²×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₅² ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ #1039
Sylow	C₅² ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×#1039

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×C₃⋊(C₅⋊D₅)
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₁₉	C₂
cosocle	C₂×C₃×C₅²	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5700

Conjugacy classes & character table

4446 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 324);