#50302490

order	38151
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₁₅₇ ⋊ #6860

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₅₇⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₅₇	C₃²
Frattini	C₃³	C₃×C₁₅₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₅₇	C₃
socle	C₃²×C₁₅₇	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₁₅₇⋊C₃
hypocenter	C₁₅₇	#6860
LCS	G ▷ C₃³×C₁₅₇ ▷ C₃²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

70 conjugacy classes of subgroups.

μ_t(G) = 12717

Polycyclic presentation:

3^5,157|a^3=d,b^3=d^2,b^a=bc,c^a=cd,c^b=ce,f^b=f^12

1751 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38151, 82);