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C₉×C₁₉⋊#1042 #30685580

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉⋊#1042

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₄
derived, Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₅²×C₉ ⋊ Dic₁₉
Hall	C₉×C₁₉ ⋊ #1042
Sylow	C₅² ⋊ C₉×Dic₁₉
Sylow	C₁₉ ⋊ C₉×#1042

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₁₉⋊#1042
commutator, hypocenter	C₅²×C₁₉	C₄×C₉
Frattini	C₃	C₃×C₁₉⋊#1042
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical, cosocle	C₃×C₅×D₅×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₉

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1737 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 217);