Finite Group Databasebeta

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C₃×C₁₉×C₃⋊#1035 #30685488

order	17100
isoclinism	isoclinic class of C₃⋊#1035
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×C₃⋊#1035
unambiguous semidirect product	C₃⋊(C₃×C₁₉×#1035)

Splittings

Fitting, Hall	C₃²×C₁₉×C₂₅ ⋊ C₄
derived	C₃×C₂₅ ⋊ C₃×C₄×C₁₉
Hall	C₁₉×C₂₅ ⋊ C₃×Dic₃
Hall	C₃²×C₂₅ ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ #1035
Sylow	C₂₅ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×#1035

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₃⋊#1035
commutator, hypocenter	C₃×C₂₅	C₃×C₄×C₁₉
Frattini	C₅	C₃×C₁₉×ΓL(1,𝔽₁₆)
Fitting	C₃²×C₁₉×C₂₅	C₄
socle	C₃²×C₅×C₁₉	AGL(1,𝔽₅)
prime radical	C₃²×C₁₉×D₂₅	C₂
cosocle	C₃×D₂₅	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₃×C₁₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2850

Conjugacy classes & character table

1368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 125);