Finite Group Databasebeta

← Prev (#30685576) Next (#30685578) →

C₉×C₁₉×#1044 #30685577

order	17100
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₉×C₁₉×#1044

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₄
derived, Sylow	C₅² ⋊ C₄×C₉×C₁₉
Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₅²×C₉ ⋊ C₄×C₁₉

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 214);