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C₁₉×C₉⋊#1044 #30685595

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

Aliases

direct product	C₁₉×C₉⋊#1044
unambiguous semidirect product	C₉⋊(C₁₉×#1044)

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₄
derived, Hall	C₅²×C₉ ⋊ C₄×C₁₉
Hall	C₅²×C₁₉ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ #1044
Sylow	C₅² ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×#1044

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#1044
commutator, hypocenter	C₅²×C₉	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#1044
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₅⋊D₅	D₃
cosocle	C₉×C₅⋊D₅	C₂×C₁₉
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 232);