#34063148

order	19197
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₇₉ ⋊ #6858

	subgroup	G/H
center	C₃²	C₃²⋊(C₇₉⋊C₃)
commutator, prime radical, cosocle	C₃³×C₇₉	C₃²
Frattini	C₃³	C₃×C₇₉⋊C₃
Fitting	C₇₉×C₃²⋊C₉	C₃
socle	C₃²×C₇₉	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₇₉⋊C₃
hypocenter	C₇₉	#6858
LCS	G ▷ C₃³×C₇₉ ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

60 conjugacy classes of subgroups.

μ_t(G) = 6399

Polycyclic presentation:

3^5,79|a^3=d,b^3=d,b^a=bc,c^a=cd,f^a=f^23,c^b=ce,f^b=f^23

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 77);