#44565439

order	32157
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₃₉₇ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₃₉₇⋊C₃)
commutator, prime radical, cosocle	C₃²×C₃₉₇	C₃²
Frattini	C₃²	C₃×C₃₉₇⋊C₃
Fitting	3₋¹⁺²×C₃₉₇	C₃
socle	C₃×C₃₉₇	H(3,𝔽₃)
hypercenter	3₋¹⁺²	C₃₉₇⋊C₃
hypocenter	C₃₉₇	#733
LCS	G ▷ C₃²×C₃₉₇ ▷ C₃×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

26 conjugacy classes of subgroups.

μ_t(G) = 10719

Polycyclic presentation:

3^4,397|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^b=e^362

1469 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32157, 36);