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H(3,𝔽₃)×C₇₉⋊C₉ #34063240

order	19197
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₇₉⋊C₉

Splittings

C₇₉ ⋊ C₉×H(3,𝔽₃)

Subgroups

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

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6399

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 169);