Finite Group Databasebeta

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C32×#4427 #13133662

order1701
isoclinismisoclinic class of #4427
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC32×#4427

Splittings

FittingC32×C7×C9 ⋊ C3
SylowC7 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC33C3×ΓL(1,𝔽8)
commutator, cosocleC3×C7C34
FrattiniC3C33×ΓL(1,𝔽8)
FittingC32×C7×C9C3
socleC33×C7C32
prime radicalC33×ΓL(1,𝔽8)C3
hypercenterC32×C9ΓL(1,𝔽8)
hypocenterC7C32×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C33 ◁ C32×C9

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 567

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 298);