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H(3,𝔽₃)×C₇⋊C₉ #13133533

order	1701
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₇⋊C₉

Splittings

C₇ ⋊ C₉×H(3,𝔽₃)

Subgroups

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

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 567

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 169);