Finite Group Databasebeta

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C₅×C₃⋊D₃×C₃₆₁ #44570449

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₆₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₃⋊D₃×C₃₆₁
unambiguous semidirect product	C₃⋊(C₅×D₃×C₃₆₁)

Splittings

Fitting, Hall	C₃²×C₅×C₃₆₁ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₅×C₃₆₁
Hall	C₃²×C₃₆₁ ⋊ C₂×C₅
Hall	C₃²×C₅ ⋊ C₂×C₃₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₃₆₁	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₅×C₃₆₁
Frattini	C₁₉	C₅×C₃⋊D₃×C₁₉
Fitting	C₃²×C₅×C₃₆₁	C₂
socle	C₃²×C₅×C₁₉	C₂×C₁₉
prime radical	C₅×C₃⋊D₃×C₁₉	C₁₉
cosocle	C₃²×C₁₉	C₂×C₅×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₃₆₁

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16245

Conjugacy classes & character table

10830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 33);