Finite Group Databasebeta

C3×#10588062 #13133665

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

Aliases

direct productC3×#10588062

Splittings

SylowC7 ⋊ C3×#737

Subgroups

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

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, 301);