Finite Group Databasebeta

← Prev (#30685382) Next (#30685384) →

C₉×C₁₉×#1035 #30685383

order	17100
isoclinism	isoclinic class of #1035
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×#1035

Splittings

Fitting, Hall	C₉×C₁₉×C₂₅ ⋊ C₄
derived, Sylow	C₂₅ ⋊ C₄×C₉×C₁₉
Hall	C₁₉×C₂₅ ⋊ C₄×C₉
Hall	C₉×C₂₅ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	#1035
commutator, hypocenter	C₂₅	C₄×C₉×C₁₉
Frattini	C₃×C₅	C₃×C₁₉×AGL(1,𝔽₅)
Fitting	C₉×C₁₉×C₂₅	C₄
socle	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)
prime radical	C₃×C₁₉×D₂₅	C₂×C₃
cosocle	C₃×D₂₅	C₂×C₃×C₁₉
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₉×C₁₉

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4275

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, 20);