#13133448

order	1701
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃²	C₇⋊H(3,𝔽₃)
commutator, prime radical, cosocle	C₃³×C₇	C₃²
Frattini	C₃³	C₃×ΓL(1,𝔽₈)
Fitting	C₇×C₃²⋊C₉	C₃
socle	C₃²×C₇	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	ΓL(1,𝔽₈)
hypocenter	C₇	#6861
LCS	G ▷ C₃³×C₇ ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

50 conjugacy classes of subgroups.

μ_t(G) = 567

Polycyclic presentation:

3^5,7|a^3=e,b^3=d,b^a=bc,c^a=cd,c^b=ce,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 84);