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#34063255

order	19197
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³

Aliases

No aliases for this group.

Splittings

C₇₉ ⋊ C₉⋊H(3,𝔽₃)

Subgroups

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

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6399

Polycyclic presentation:

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

Conjugacy classes & character table

909 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 184);