Finite Group Databasebeta

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C₉⋊C₉×C₁₂₇⋊C₃ #44525005

order	30861
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

C₉⋊C₉×C₁₂₇⋊C₃

Splittings

Fitting	C₉⋊C₉×C₁₂₇ ⋊ C₃
Sylow	C₁₂₇ ⋊ C₃×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator	C₃×C₁₂₇	C₃²×C₉
Fitting	C₉⋊C₉×C₁₂₇	C₃
socle, cosocle	C₃²×C₁₂₇	C₃³
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×C₉⋊C₉
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10287

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 159);