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C3×#10588065 #13133667

order1701
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×#10588065

Splittings

FittingC3×C7×3−1+2 ⋊ C3
SylowC7 ⋊ C3×#737

Subgroups

subgroupG/H
centerC32C32×ΓL(1,𝔽8)
commutator, cosocleC3×C7C34
FrattiniC3C33×ΓL(1,𝔽8)
FittingC3×C7×3−1+2C3
socleC32×C7C33
prime radicalC3×C7⋊H(3,𝔽3)C3
hypercenterC3×3−1+2ΓL(1,𝔽8)
hypocenterC7C3×#737
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C32 ◁ C3×3−1+2

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(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, 303);