#31801233

order	17739
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₇₃ ⋊ #6861

	subgroup	G/H
center	C₃²	C₃²⋊(C₇₃⋊C₃)
commutator, prime radical, cosocle	C₃³×C₇₃	C₃²
Frattini	C₃³	C₃×C₇₃⋊C₃
Fitting	C₇₃×C₃²⋊C₉	C₃
socle	C₃²×C₇₃	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₇₃⋊C₃
hypocenter	C₇₃	#6861
LCS	G ▷ C₃³×C₇₃ ▷ C₃²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

50 conjugacy classes of subgroups.

μ_t(G) = 5913

Polycyclic presentation:

3^5,73|a^3=e,b^3=d,b^a=bc,c^a=cd,f^a=f^64,c^b=ce,f^b=f^8

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17739, 86);