Finite Group Databasebeta

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C₉×D₅×C₁₉₁ #31769895

order	17190
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅×C₁₉₁
unambiguous semidirect product	C₅⋊(C₂×C₉×C₁₉₁)

Splittings

Fitting, Hall	C₅×C₉×C₁₉₁ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₉×C₁₉₁
Hall	C₅×C₁₉₁ ⋊ C₂×C₉
Hall	C₅×C₉ ⋊ C₂×C₁₉₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉₁	D₅
commutator, hypocenter	C₅	C₂×C₉×C₁₉₁
Frattini	C₃	C₃×D₅×C₁₉₁
Fitting	C₅×C₉×C₁₉₁	C₂
socle	C₃×C₅×C₁₉₁	C₂×C₃
prime radical	C₃×D₅×C₁₉₁	C₃
cosocle	C₃×C₅	C₂×C₃×C₁₉₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₁₉₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8595

Conjugacy classes & character table

6876 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×AGL(1,𝔽₅)×C₁₉₁, C₉×C₁₉₁⋊AGL(1,𝔽₅), C₉×D₅×D₁₉₁, …
maximal normal subgroup of	C₉×AGL(1,𝔽₅)×C₁₉₁, C₉×C₁₉₁⋊AGL(1,𝔽₅), C₉×D₅×D₁₉₁, …
maximal quotient of	C₉×Dic₅×C₁₉₁, C₂×C₉×D₅×C₁₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17190, 4);