Finite Group Databasebeta

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#44525030

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

Aliases

No aliases for this group.

Splittings

C₁₂₇ ⋊ C₉⋊H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting, prime radical	C₃×H(3,𝔽₃)×C₁₂₇	C₃
hypercenter	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₉⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10287

Polycyclic presentation:

3^5,127|b^3=d,b^a=bd,c^a=ce,f^b=f^107

Conjugacy classes & character table

1437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 184);