Finite Group Databasebeta

← Prev (#46798534) Next (#46798536) →

C₉⋊C₉×C₁₃₉⋊C₃ #46798535

order	33777
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

C₉⋊C₉×C₁₃₉⋊C₃

Splittings

Fitting	C₉⋊C₉×C₁₃₉ ⋊ C₃
Sylow	C₁₃₉ ⋊ C₃×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₃₉⋊C₃
commutator	C₃×C₁₃₉	C₃²×C₉
Fitting	C₉⋊C₉×C₁₃₉	C₃
socle, cosocle	C₃²×C₁₃₉	C₃³
prime radical	C₃²×C₁₃₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₃×C₉⋊C₉
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11259

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 159);