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C₁₉×C₃⋊(C₃⋊#1039) #30685693

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₅

Aliases

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

Splittings

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

Subgroups

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

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

Conjugacy classes & character table

4332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 330);