#44524921

order	30861
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₁₂₇ ⋊ #6858

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₂₇⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₂₇	C₃²
Frattini	C₃³	C₃×C₁₂₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6858
LCS	G ▷ C₃³×C₁₂₇ ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

60 conjugacy classes of subgroups.

μ_t(G) = 10287

Polycyclic presentation:

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

1421 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 75);